2019
Critical
concepts
for the
CFA EXAM
CFA® EXAM REVIEW
Wiley’s CFA
Program Level III
Smartsheets
®
Fundamentals For CFA Exam Success
WCID184
Wiley’s CFA Program Exam Review
®
ETHICAL AND
PROFESSIONAL STANDARDS
Standards of Professional Conduct
• Thoroughly read the Standards, along with related
guidance and examples.
Asset Manager Code of
Professional Conduct
• Firm-wide, voluntary standards
• No partial claim of compliance.
• Compliance statement: “[Insert name of firm] claims
compliance with the CFA Institute Asset Manager Code of
Professional Conduct. This claim has not been verified by
CFA Institute.”
• Firms must notify CFA Institute when claiming
compliance.
• CFA Institute does not verify manager’s claim of
compliance.
• Standards cover:
• Loyalty to clients
• Investment process and actions
• Trading
• Risk management, compliance, and support
• Performance and valuation
• Disclosures
BEHAVIORAL FINANCE
Behavioral Finance Perspective
• Prospect theory
• Assigns value to changes in wealth rather than levels
of wealth.
• Underweight moderate- and high-probability
outcomes.
• Overweight low-probability outcomes.
• Value function is concave above a wealth reference
point (risk aversion) and convex below a wealth
reference point (risk seeking).
• Value function is steeper for losses than for gains.
• Cognitive limitations
• Bounded rationality: deciding how much will be done
to aggregate relevant information and using rules of
thumb.
• Satisficing: finding adequate rather than optimal
solutions.
• Traditional perspective on portfolio construction
assumes that managers can identify an investor’s
optimal portfolio from mean-variance efficient portfolios.
• Consumption and savings
• Mental accounting: wealth classified into current
income, currently owned assets, PV of future income.
• Framing: source of wealth affects spending/saving
decisions (current income has high marginal
propensity to consume).
• Self-control: long-term sources unavailable for current
spending.
• Behavioral asset pricing models
• Sentiment premium included in required return.
• Bullish (bearish) sentiment risk decreases (increases)
required return.
• Behavioral portfolio theory
• Strategic asset allocation depends on the goal
assigned to the funding layer.
• Uses bonds to fund critical goals in the domain of
gains.
• Uses risky securities to fund aspirational goals in the
domain of losses.
• Adaptive markets hypothesis
• Must adapt to survive (bias towards previously
information.
• Confirmation bias: only accept supporting evidence.
• Gamblers’ fallacy: overweight probability of mean
successful behavior due to use of heuristics).
• Risk premiums and successful strategies change over
reversion.
time.
• Hot hand fallacy: overweight probability of similar
returns.
Behavioral Biases
• Overconfidence, availability, illusion of control, self-
• Cognitive errors (belief persistence biases)
• Conservatism: overweight initial information and fail to
update with new information.
attribution and hindsight biases also possible.
• Market behavioral biases
• Momentum effects due to herding, anchoring,
availability and hindsight biases.
Private W
• Bubbles due to overconfidence, self-attribution,
information, disregard contradictory information.
Private Wealth
confirmation and hindsight biases.
• Representativeness: extrapolate past information into
individual
inveStor
the future (includes base-rate neglect and sample-size
• Managing
Value stocks have
outperformed
growthPortfolioS
stocks; smallCross-Reference
to CFA Institute
Assigned
Reading #8
neglect).
cap
stocks have
outperformed
large-cap
stocks.
Managing
individual
inveStor
PortfolioS
Cross-Reference to CFA Institute Assigned Reading #8
• Illusion of control: believe that you have more control
investment Policy Statement
over events than is actually the case.
investment Policy Statement
• Hindsight bias: only remember information that
Return Calculation
reinforces existing beliefs.
Return Calculation
When you read through the exam question relating to the investment policy statement (IPS)
• Cognitive errors (information-processing biases)
for
theyou
individual
investor,
see that
there to
arethe
two
possible investment
goals(IPS)
for the
When
read through
the you
examwill
question
relating
investment
policy statement
• Anchoring and adjustment: develop initial estimate portfolio:
for theInvestment
individual investor, you will
see that there
are two possible investment goals for the
Policy
Statement
portfolio:
and subsequently adjust it up/down.
1. The investor wishes to maintain the real value of the portfolio. For calculation
Return
calculation
• Mental accounting: treat money differently depending 1. • The
investor
wishes
maintain
the real
value
of of
thethe
portfolio.
Foriscalculation
purposes,
this
meanstothat
the present
value
(PV)
asset base
equal to the future
on source/use.
purposes,
this
thatbase.
the
present
(PV)you
of the
base
is equal
to the future
value
of means
the asset
In this
situation,
willasset
not
be given
an investment
• To(FV)
maintain
real
value
ofvalue
portfolio,
the
required
real
value
(FV)
of the asset base. In this situation, you will not be given an investment
horizon
(N).
• Framing: make a decision differently depending on
after-tax
return is calculated as:
horizon
(N).
The required real after-tax rate of return is simply:
how information is presented.
The required real after-tax rate of return is simply:
• Availability bias: use heuristics based on how readily
Annual after-tax withdrawal from the portfolio / Asset base
Annual after-tax withdrawal from the portfolio / Asset base
information comes to mind.
The asset base excludes the value of the family home.
The
asset
base excludes
the value
of the family to
home.
• Emotional biases
• convert
To
convert
after-tax
withdrawal
a pre-tax withdrawal
To
the after-tax
withdrawal
to a pre-tax withdrawal:
To convert the after-tax withdrawal to a pre-tax withdrawal:
• Loss aversion: strongly prefer avoiding losses to
Pre-tax
withdrawal
=
After-tax
withdrawal
/
(1
– Tax rate on withdrawals)
making gains (includes disposition effect, housePre-tax withdrawal = After-tax withdrawal / (1 – Tax rate on withdrawals)
money effect and myopic loss aversion).
Nominal pre-tax
pre-taxreturn
return==Real
Realpre-tax
pre-taxreturn
return+ +
Inflation
rate
Nominal
Inflation
rate
• Overconfidence: overestimate analytical ability
• Nominal return
= Real return + Inflation rate
Private Wealth Mana
or usefulness of their information (prediction
Nominal
after-tax
return==
Real
after-tax
return
+ Inflation
rate
• If investor
wishes
to
grow
portfolio,
TVM
worksheet
Nominal
after-tax
return
Real
after-tax
return
+ use
Inflation
rate
overconfidence and certainty overconfidence).
to compute I/Y over investment horizon.
2.
The investor
investor wishes
wishestotogrow
growthe
theportfolio.
portfolio.For
For
calculation
purposes,
means
• Self-attribution bias: self-enhancing and self2. investor
The
calculation
purposes,
thisthis
means
thatthat
four
Personality types
• the
Risk
tolerance
the
present
value(PV)
(PV)ofofthe
theasset
assetbase
baseisisequal
equal
future
value
(FV)
of the
asset
present
value
to to
thethe
future
value
(FV)
of the
asset
protecting biases intensify overconfidence.
Based onyou
thinking
decisions horizon
Based
on
feeling
base.decisions
In this
this situation,
situation,
you
willbebegiven
givenananinvestment
investment
horizon
(N).
base.
In
will
(N).
• Above-average ability if longer time horizon or large
• Self-control bias: fail to act in their long-term interests
Methodical
Cautious
find
the required
required
rateofofreturn,
return,
youwill
willneed
need
populate
time
value
of money
To find
the
rate
you
to to
populate
thethe
time
value
of money
asset
base
compared
with
needs.
(includes hyberbolic discounting).
(TMV)
worksheet:
More (TMV)
• Relies
on hard facts
• Disciplined and conservative
worksheet:
• Willingness
based
on psychological
profile.
risk
• Follows analysts
or conducts
own
• Strong
need for security from
• Status quo bias: prefer to do nothing than make a
The
present
value
theasset
assetbase
baseentered
entered
with
aorminus
sign
present
ofofthe
with
a minus
averse Pv: The
research
onvalue
trading
strategies
current
pastsign
experiences
change.
• Overall
tolerance
is athat
combination
of ability
and
fv:
projected
future
value
would
like
to to
have,
entered
with
a a
The
projected
future
value
theinvestor
investor
would
like
have,
entered
with
•The
Not
emotionally
attached
tothatthe
• Preference
for
low-volatility
positive
sign
positive
sign
willingness.
investments
because of reliance on
investments (principal protection)
• Endowment bias: value an owned asset more than if
n: Investment
horizon
Investment
horizon
and databases
• Dislikes losing small amounts
you were to buy it.
• PMt:
TimeIfanalysis
constraint:
length
number
of
stages.is withdrawing
the
isissaving,
using
sign;
if the
investor
PMt:
Ifhorizon
the investor
investor
saving,enter
enter
usinga minus
aand
sign;
if and
the
investor
• minus
Overanalyzes
missesis withdrawing
the
use
sign
ofof
thethe
payment.
opportunities
from
the portfolio,
portfolio,
useaaplus
plusongoing
signininfront
front
payment.
• Regret aversion: avoid making decisions for fear of
• from
Liquidity
constraint:
needs,
one-time
•
Portfolio
low
turnover
being unsuccessful (includes errors of commission and
Compute
for
expenditures,
Compute
forii//YYemergencies.
The PMt
terms.
Convert
thethe
after-tax
PMT
to to
omission).
PMt isis given
giveninineither
eitherpre-tax
pre-taxororafter-tax
terms.
Convert
after-tax
PMT
• aThe
Tax
constraint:
different
ratesafter-tax
may
apply
to the
different
individualist
Spontaneous
pre-tax
PMT
using
where
investor
wishes
to to
a
pre-tax
PMT
usingthe
thesame
samecalculation
calculation(as(asearlier)
earlier)
where
the
investor
wishes
• Goals-based investing
maintain
the
real
value
of
the
portfolio.
If
fv
is
expressed
in
real
terms,
then
add
the the
sources
income
capitalIfgains.
Less riskmaintain
• Self-assured
and hardworking
• Always
adjusting
portfolio
theof
real
value
ofand
the portfolio.
fv
is expressed
in real
terms,holdings
then add
rate
to the computed
I/Y.
• inflation
Considers
information
from various
following the market or second• Base of pyramid: low-risk assets for obligations/needs. averse• given
given
inflation
rate
to the computed
I/Y.
Legal
and
regulatory
constraint:
less
of
a
concern
for
sources
guessing self
• Moderate-risk assets for priorities/desires; speculative
individuals,
restricted
trading periods
may
apply toadvice
• Takes action
by him- or herself
• Doubtful
of investment
• Believesinsiders.
that work and unique
• Highest portfolio turnover
assets for aspirational goals.
corporate
insights will be rewarded with long• Most investors have below-average
• Behaviorally modified asset allocation
• Unique
client-imposedreturns
restrictions, e.g.
term constraint:
investment success
• Quick to make decisions
• Greater wealth relative to needs allows greater
socially responsible investing, client-directed
brokerage.
• More concerned about
©
2018
Wiley
adaptation to client biases
• Psychological profiling
missing a trend than with
© 2018 Wiley
portfolio risk
• Advisor should moderate cognitive biases with high
• More risk averse: methodical (thinking),
cautious
standard of living risk (SLR).
(feeling).
c04.indd 93
93
• Advisor should adapt to emotional biases withc04.indd
a low
Less
risk averse: individualist (thinking), spontaneous
Strategic•asset
allocation
SLR.
(feeling).
You might be presented with a choice of three to five strategic portfolios, one of which will
• Strategic
allocation
best satisfy
the client’sasset
overall investment
policy statement. To determine which portfolio is
Investment Processes
best, follow the four-step process of elimination:
• Return: eliminate portfolios that do not meet return
objective.
need
pre-tax
nominal
• Behavioral biases in portfolio construction
1. return:
EliminateMay
portfolios
thatto
failconvert
to meet theaclient’s
return
objective. You might
havereturn
to convert
pre-tax
nominal return
to an after-tax real return, so be sure that you
toa an
after-tax
real return.
• Inertia and default: decide not to change an asset
know this formula:
allocation (status quo bias).
After-tax real return = Pre-tax nominal return × (1 – Tax rate) – Inflation rate
• Naïve diversification: exhibit cognitive errors resulting
from framing or using heuristics like 1/n diversification.
2. risk:
Eliminate
portfoliosportfolios
that fail to meet
the client’s
risk objective.
• Risk:
eliminate
that
do notquantifiable
meet shortfall
or
• Company stock investment: overallocate funds to
Shortfall risk is expressed as the expected return minus two standard deviations. Roy’s
othercriterion
risk objectives.
safety-first
is another risk measure, which is the expected return minus the
company stock.
lowest
acceptable return
divided by the
expected standard
deviation;
portfolios with
• Constraints:
eliminate
portfolios
that do
not meet
• Overconfidence bias: engage in excessive trading
the highest safety-first criteria are preferred.
constraints,
e.g.
cash holding
for the
liquidity.
Managing individual investor Portfolios
3. Constraints:
Eliminate
portfolios
that fail to meet
investor’s constraints. The most
(includes disposition effect).
quantifiable
is the portfolios,
cash holding. Eliminate
thatwith
do not contain
• Of theconstraint
remaining
select portfolios
portfolio
• Home bias: prefer own country’s assets.
enough cash to satisfy the liquidity constraint. Be careful not to consider portfolios
highest
risk-adjusted
performance,
usually on Sharpe
Managing
Individual
Investor Portfolios
that
contain
too
much
cash.
• Mental accounting: portfolio may not be efficient due
ratio.
to goals-based investing as each layer of pyramid is Sharpe Ratio
© 2018 Wiley
optimized separately.
(expected return – risk-free rate)
• Behavioral biases in research and forecasting
Sharpe ratio is:
expected standard deviation
• Representativeness: due to excessive structured
• Confirmation bias: only accept belief-confirming
PRIVATE WEALTH
MANAGEMENT
c04.indd
97
7 Mar
Capital gains tax payable = Price appreciation × tCG × turnover rate
Wiley © 2019
where:
tCG = capital gains tax rate
FVIFafter-tax = [1 + rpre-tax (1 − tI )]
FVIFafter-tax = [1 + rpre-tax (1 − tI )]n
rafter-tax
= rpre-tax (1 − tI )
Relative
Value
ofapproach
Gifts Taxable
to Recipient
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Carlo
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ranges
for eachexcess
variableCapital
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experiences, tax changes, etc.).
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rg (1 − tigof) the
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Combining
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risk as a funding portfolio.
where:
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Relative Value
of Gifts
Taxable
to Gift
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RVgifting
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n
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= return
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where:
RV
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=
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nt =
of periods
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FVIF
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) ] (1 − Tloss
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[1 + re (1the
to recipient
Tg = gift tax rate
e ) from inter vivos gifting.
implemented
giftthat
andapplies
donation
taxes to minimize
n = number of periods
Tg = gift tax rate that applies to recipient
Relative value describes the relative benefit of an inter vivos gift to the value of a bequest
Deferral Method with a Single, Uniform Tax Rate (Capital Gain)
where:
Tax-Free
Gifting
Relative
Gifts Taxable
to Donor
Not
to Recipient
where:
at
death. Value
In
this of
scenario,
the relative
value But
of the
tax-free
gift equals return on investments
Deferral
Method
with
a Single,
Tax Rate
(Capital Gain)
FVIF
= Future
value
interest
(i.e., Uniform
accumulation)
factor
Relative
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to Donor But Not to Recipient
taxwith
rateof
Tg = gift Value
n
taxrecipient
on
the gift’s return tig, divided by return on estate investments
purchased
athat
giftapplies
rg less to
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r = return
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the relativereturn
benefit
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antax
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Charitable
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Taxable
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n = number of periods
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purchased
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ig −divided
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)
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Taxable
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Taxable
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n not pay
•
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n
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r
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t
)]
+
−
FVGift
g [1 +ig
− Tgift
re (1 −of
tiea)pay
) tax
When
theRV
donor
pays
the gift
tax
and
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does
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thecredit
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etax,
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equivalent
partial
from
= the the
Taxable gain
= VT −n Cost basis
tax − freeGift =
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where: rFVIF
Gifts
Taxable
tointhe
• Personal line of credit secured by company shares.
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+ rthe
− This
numerator
term
parentheses
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egift.
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reducing
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byRecipient
theFVamount
of[1the
rg =
after-tax = rpre-tax (1 − t I )
valuefactor with accrual taxes
IMPORTANT:
value
reducing the estate by the amount of the gift. This formula assumes rg = re and tig = tie.
T = terminal
where:•VFuture
• Initial
public
Taxable
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When
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n
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Gratuitous
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Employee
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IMPORTANT:
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reducing the estate by the amount of the gift. Thisnformula assumes rg = re and tig = tie.
to the recipient
FVGift
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company
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Taxable
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iscan
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For
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Taxable
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still be
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FVIFafter-tax = [1 + rpre-tax (1 − tI )]
than
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Relative Value
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Gratuitous
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RVCharitable
the tax
rate on strategies
gifts
FVIFCG = (1 + rpre‐tax)n (1 − tCG) + tCGB
• Monetization
for real estate
rate
(denominator).
Gift = FV
Charitable Gift =e (1 + rie
g
oi
e
ie
e
to the recipient
r (1 t ) (1 T )
RVCharitable Gift = FVFVBequest[1 + r= (1 − t )][1n +
where:
where:
(1r−e(1Tg−−)t ie) ]n (1 −−T e)
(numerator)financing
is less
GiftBequest
g
ig [1 +
FV
vaTe WealTh ManageMenT
in
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global
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•
Mortgage
(no tax consequences and can use
where:• VFuture
e
ie
e
valuefactor when deferring taxes on capital gains
RVtaxable Gift =
=
T = terminal
than
the
estate
tax
n
value
n
•
Trusts
where:
FVFV
[1 + r (1 − t )]n (1 − T )
Bequest
FVIFCost
= Future
valuepaid
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CG =FVIF
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proportion
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n
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all rights
reserved. any unauthorized
copying or distribution will constitute an infringement of copyright.
CG = (1 + rpre‐tax) (1 − tCG) + tCGB
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nt DP− −
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will constitute
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copyright.
= tSC
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−
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= t RC + tSC − t RC tSC
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tax
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)
Risk Management for Individuals
• Financial capital: includes all tangible assets including
family home
• Human capital: PV of future expected labor income
•
•
0
t DM = t RC + tSC5− t RC tSC
©
2018 all
reserved.
anypurchased
unauthorized copying or distribution will constitute an infringement of copyright.
V0Wiley
= value
ofrights
an asset
when
n
n
FVIFafter-tax =Return
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*)
FVIF
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(1n−(1
© Wiley 2018 all Rights Reserved. any unauthorized copying or distribution will constitute an infringement of copyright.
after-tax
CG T
after-tax = 
CG − B)
1 + r *)
 + T * − tCG
© Wiley 2018 all Rights Reserved. any unauthorized copying or distribution will constitute an infringement of copyright.
Accumulation Factor with Annual Wealth Tax
Concentrated Single-Asset Positions
• Objectives: risk reduction (diversification), monetization,
n
If
the
non‐dividend
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portfolio
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= 00
0 (non‐dividend
AE )
• =Equivalent
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after-tax
return
tax
optimization,
control.
n
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all Rights
Reserved. any unauthorized
copying or distribution will constitute an infringement of copyright.
1) held
held=to
to the
end of
of the
horizon,
the formula
formula reduces
reduces to:
to:
and P
PCG =
1)
the
and
1 + rend
1 − horizon,
tW ) 
CG FVIF
W Vn  the
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• Considerations: illiquidity, triggering taxable gains
rAE = n
−1 n
Vn = V0 (V10+ rAE )
on sale, restrictions on amount and timing of sales,
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(1 − r )nn ((11 −− ttCG )) ++ ttCG
after-tax =
FVIFafter-tax
CG
V = (1 − r ) Return
Effectiver Annual
in aCG
Blended Tax Regime
emotional and cognitive biases.
= n nAfter‐Tax
−1
where: AE
V0
• Monetization strategies
If
portfolio
= value
afteris
compoundingpaying
periodsequity
V
Ifnthe
the
portfolio
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non‐dividend
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equity securities
securities with
with 100
100 percent
percent turnover
turnover and
and
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r* = r (1 formula
t )
D t D − PCG
taxed
to:
taxed annually,
annually, Tthe
the formula
reduces
to: CG
• Monetization by (1) hedging the position, and (2)
Accrual
where: Equivalent Tax Rate
• Accrual equivalent tax rate
borrowing against hedged position.
Vwhere:
n = value after n compounding periods
n
n
FVIFafter-tax
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1from
+ rr ((1
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−
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rof
− T=
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by: (1) short sale against the box (least expensive); (2)
rAE
TAE
1 − reserved.
5 equity swap; (3) short forward or futures
© Wiley 2018
all =rights
any unauthorized copying or distribution will constitute an infringement of copyright.
Accrual
Return
total return
Accrual rEquivalent
Equivalent
= r (1 −rTReturn
)
(
AE
)
AE
0
• Tax-deferred
accounts (TDAs): contributions from
Tax‐Exempt
Accounts
untaxed
ordinary
tax-free growth during the
+ r )n (1 − t )income,
tCG B
where: FVIF
TDA = (1
where:
n
= value
value
after n
n=
compounding
periodsat time of withdrawal
Vn =
holding
taxed
FVIF
1+ r)
(period,
after
compounding
periods
V
deferring capital gains tax).
• Use zero-premium collars (long put and short call with
n
TEA
offsetting premiums) to reduce costs vs buying puts.
Accrual
Accrual Equivalent
Equivalent Tax
Tax Rate
Rate
• Use prepaid variable forward (combine hedge and
FVIFTDA = (1 + r)n (1 – tn)
FVIFTDA = FVIFTEA (1 − t )
loan in same instrument), with number of
Taxes and PrivaTe WealTh ManageMenTmargin
in a global ConTexT
rrAE =
rr ((1
T
AE ))
1−
−reserved.
TAE
AEall=rights
shares delivered at maturity dependent on share price
© Wiley•2018
any unauthorized copying or distribution will constitute an infringement of copyright.
Tax-exempt
rrAE accounts (TEAs): after-tax contributions,
T
− AE
at maturity.
Value Formula
a Tax Exempt Account
AE = 1for
T
tax-free
AE = 1 − rgrowth during the holding period, no future tax
r
Tax‐Exempt Accounts
liabilities.
© Wiley 2018
all rights reserved. any unauthorized copying or distribution will constitute an infringement of copyright. • Yield enhancement strategies:
V0 (1 − t0)(1n+ r)n
Vn = Accounts
Tax‐Deferred
• Write covered calls to generate income.
Tax‐Deferred
FVIFAccounts
TEA = (1 + r )
• Does not reduce downside risk.
n
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for
a Tax‐Deferred
Account
=
rr ))n ((1
B
1+
1−
FVIF
= ((1
+after-tax
− tt )) ttCG
B
• FVIF
TDATDA
offers
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TDA
CGreturn
• Tax optimized equity strategies
FVIFTDA = FVIFTEA (1 − t )
rate
at withdrawal
is lower than tax rate at initial
n
V
n = V0(1 + r) (1 − tn)
• Index-tracking separately managed portfolio: designed
contribution.
to outperform benchmark from an investment and tax
Value Formula for a Tax Exempt Account
The Investor’s
After‐Tax
Risk of investment risk on a taxed return
• Investor’s
shared
perspective.
• Completeness portfolio: tracks index given
V
σnAT= V
= 0σ(1
(1−− tt0))(1 + r)n
concentrated portfolio characteristics and new
©
2018
any
copying
investments.
Value
forreserved.
a Tax‐Deferred
Account
© Wiley
WileyFormula
2018 all
all rights
rights
reserved.
any unauthorized
unauthorized
copying or
or distribution
distribution will
will constitute
constitute an
an infringement
infringement of
of copyright.
copyright.
where:
Estate
Planning
σ = standard
deviation
of returns
•
Exchange
fund: investors with concentrated positions
Vn = V0(1 + r)n (1 − tn)
Private Wealth ManageMent
contribute
these positions in exchange for a sharer12.indd
in a95
•
Core
capital
Ratio of Long-Term Capital Gains to Short-Term Capital Gains
diversified fund (non-taxable event).
The Investor’s After‐Tax Risk
• Assets for maintaining lifestyle, funding desired
• Monetization strategies for concentrated private shares
Survival Probability
Approach
spending
and
V0 (1 + rgoals
)n (1 − t LTG
) providing emergency reserve.
VLTG
σ
• Strategic buyers: gain market share and earnings
AT ==σ (1 − t )
n
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Joint
probability
Joint survival
probability
couple
1 + r (1for
− taSTG
V0survival
) is: for a couple
growth.
where:
• Financial buyers: acquire and manage companies using
p(survival
survival H
H ) + p(survivalW
W)
JJ ) =ofp(returns
σ = standard
deviation
private equity fund.
− p(survival H
H ) × p(survivalW
W)
• Leveraged
recapitalization: private equity firm uses
IMPORTANT:
IMPORTANT:
Ratio of Long-Term Capital Gains to Short-Term Capital Gains
PV survival
of jointprobability,
spending
needs
more conservaconservamore
Based on•joint
present
value of joint spending needs is:
debtAAtive
toapproach
purchase
majority of owner’s stock for cash.
tive approach
asassumes
both
spouses
sumes both spouses
n
• Management
live through
through the
the buyout: management borrow money to
live
)
VLTG V0 (1 + r ) (NN1 −pt(LTG
survival
J ) × (spendingJJ )
J
longest expectancy
expectancy
=
longest
PV (spending
J) =
t
n
purchase
owner’s stock.
VSTG V0 1 +J r (1∑
for either
either life.
life.
(1 + r )t
for

=1
1t STG ) 
tt−
=

• Divestiture of noncore assets: owner uses proceeds to
The emergency reserve incorporated into liabilities considers the shortfall risk of funding
assets. A two-year emergency reserve is designed to satisfy anxiety about market cycles and is
•
contract; (4) synthetic short forward (long put and
r
n
1 − +AErof )tax
n
Tax‐Deferred
Accounts
AE =
• TMeasure
drag = Difference between accrual
short call).
V
AE )
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=V
V00 ((1
1 +r rAE
Taxes and
in a global ConTexT
equivalent
after-tax return and the actual return
ofPrivaTe
theWealTh ManageMenT
Vn
•
Hedging
strategies
V
= nn n −
−1 n
AE =
rrAE
portfolio.
FVIF
Tax‐Deferred
Accounts
V=0 (1 1+ r ) (1 − t ) tCG B
TDAV
• Buy puts (protect downside and keep upside while
The survival probability approach discounts each period’s spending needs by the real risk-free
rate because they are nonsystematic (i.e., unrelated to market-based risk inherent in the assets). However, they can be hedged using life insurance.
•
IMPORTANT:
IMPORTANT:
Do not
not discount
discount
Do
expected spending
spending
expected
with the
the required
required
with
return on
on aa portfoportforeturn
lio of
of assets
assets used
used to
to
lio
fund them.
them.
fund
•
Risk Mana
(higher income volatility requires higher discount rate).
Income volatility risk can be diversified by appropriate
The international shift away from defined-benefit (DB) pension plans has caused a shift
financial capital, e.g. if human capital is equity-like,
toward annuities. At the individual level, there are five factors that would likely increase
financial
should contain more bonds.
demand
for capital
any annuity:
Economic (holistic) balance sheet
1. Longer-than-average life expectancy
• Assets:
financial
capital,
personal
2. Greater
preference
for lifetime
income property, human
3. Less concern
for value.
leaving money to heirs
capital,
pension
4. More conservative investing preferences
• Liabilities:
total debt,
lifetime
consumption
5. Lower guaranteed
income
from other
sources (such asneeds,
pensions)
bequests.
9
Lesson 7: IMpLeMentatIon
oF RIsK ManageMent FoR IndIVIduaLs
• Net wealth
9 is the difference between total assets and
total liabilities.
Los 12j: analyze and critique an insurance program. Vol 2, pp 431–440
9 has high % of economic assets in human
Young family
Los
12l:As
Recommend
and justify
strategies for asset allocation
capital.
the household
ages,appropriate
weight of human
and
risk
reduction
given an investor
profile of key inputs.
(financial) capitalwhen
will decrease
(increase).
Vol 2, pp 440–443
Risks to human and financial capital
The
decision torisk:
retainprotect
risk or buyagainst
insuranceearnings
is determined
byrelated
a household’s
• Earnings
risk
to risk tolerance.
At injury
the samewith
level disability
of wealth, a more
risk-tolerant household will prefer to retain more
insurance.
risk, either through higher insurance deductibles or by simply not buying insurance. A
• Premature
death
(mortality
protect
with life
risk-averse
household
would
have lower risk):
deductibles
and purchase
more insurance. For
all insurance.
households, insurance products that have a higher load (expenses) will encourage a
household to retain more risk. Finally, as the variability of income increases, the need for
• Longevity risk: protect with annuities.
life insurance decreases because the present value of future earnings (human capital) will
be
lower with arisk:
higherprotect
discount with
rate. homeowner’s insurance.
• Property
• Liability
risk:
withofliability
insurance.
Table
7-1 shows
the protect
appropriateness
the four risk
management techniques depending on
the
severity of
lossprotect
and the frequency
of loss. insurance.
• Health
risk:
with health
Risk management
techniques
table
7-1: Risk Management
techniques
Loss Characteristics
High Frequency
Low Frequency
High severity
Risk avoidance
Risk transfer
Low severity
Risk reduction
Risk retention
• Adequacy of life insurance
An
investmentlife
advisor
willmethod:
often be asked
how muchthe
life PV
insurance
is enough. There are
• Human
value
estimates
of earnings
Exhibit 10, Volume 2, CFA Curriculum CFA 2017
twothat
techniques
will be responsible for on the exam:
mustthat
beyou
replaced.
• Needs
analysis
method:
financial
needs
ofvalue of earnings
1. Human
life value
method:estimates
This technique
estimates the
present
that must be replaced.
dependents.
2.
needs analysis method: This technique estimates the financial needs of the
dependents.
INSTITUTIONAL INVESTORS
Defined benefit pension plan
• Risk tolerance: greater ability to assume risk if
• Plan surplus
© 2018 Wiley
• Lower sponsor debt and/or higher current profitability
• Lower correlation of plan asset returns with company
profitability
• No early retirement and lump sum distributions
options
• Greater proportion of active versus retired lives
• Higher proportion of younger workers
• Risk objective: usually related to shortfall risk of
achieving funding status.
• Return objective: to achieve a return that will fully fund
liabilities (inflation-adjusted), given funding constraints.
• Liquidity: to meet required benefit payments.
• Time horizon: usually long-term and could be multistage.
Wiley © 2019
D/P = expected D
dividend yield
E ( R) ≈ − %∆S + INFL + g + %∆PE
S = number ofP shares outstanding r(Note: % change in S is the opposite of the
repurchase yield)
INFL = inflation rate
where:
gr = real earnings growth
D/P
= price-earnings
expected dividend
PE =
ratioyield
S = number of shares outstanding (Note: % change in S is the opposite of the
repurchase
yield)
Build‐Up
Approach
Expected
Return,rate
E(R)
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growth
gr = real
E ( Rearnings
)
=
R
i
F + RP1 + RP2 + ... + RPk
PE = price-earnings
D (1 +ratio
g)
D
E ( R) = 0
+g= 1 +g
P0
P0
Build‐Up Approach
where:
Capital Market expeCtations
RF = nominal risk-free rate interest rate
RPk = •riskExpected
Epremium
( Ri ) = Model
RF k+return
RP1 + RPon
+ RPk from Grinold-Kroner model
Grinold‐Kroner
Liquidity: limited liquidity needs since cash inflows
equity
2 + ...
Wiley’s CFA Program Exam Review
®
nvestors
foundations
Capital Market e
Types
• Independent (private or family): Funded by donor, donor’s family, or independent
•trustees
Tax: investment
income and capital gain usually tax•
to further educational, religious, or other charitable goals
exempt.
exceed cash outflows, but need to consider
• Company-sponsored:
Same as independent foundation, but a legally independent
Financial
Market
Equilibrium Models
Fixed‐Income
Premiums
Capital
expeCtationswhere: E ( R) ≈ D − %∆S + INFL + g + %∆PE
sponsored by
a profit-making
corporation
disintermediation risk (when interest rates
areMarket
rising)
r
•organization
Legal/regulatory:
plan
trustees have
a fiduciary
P
• Operating: Funded same as independent foundation, but conducts specific research orand asset marketability risk.
Financial
market
modelsrate
assume a relationship for return given priced risk in the
=
nominal
risk-free
rate interest
R
F
E ( Rb ) = equilibrium
rrF + RP
responsibility to beneficiaries under ERISA (US).
INFL + RPDefault + RPLiquidity + RPMaturity + RPTax
provides a special service (e.g., operates a private park or museum)
global
investable
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all
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premiums-to-surplus ratios.
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Liquidity
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Net interest margin: Net interest income divided by average earning assets where:
on endowment to cover high fixed costs.
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7 March 2018 3:50 PM
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government
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c07.indd 158
7 March 2018
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all rights
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Spendingt = Spending rate × 1⁄3 [Ending market valuet−3
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18
© Wiley
2018
all
rights
reserved.
any unauthorized
copying
%exports
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(X
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2018
all
rightsless
reserved.
any be
unauthorized
copying capital
or distributionaccount
will constitutesurplus
an infringement
deficits
must
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to Asset AllocAtIon
k=
where: Leverage-adjusted
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where:• Unique: types of investments constrained by size or
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intermediate-term.
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board member sophistication.
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Foundations
Non-life insurance companies
Endowments
Banks
Equity Market Valuation
Life insurance companies
• Risk tolerance/objective
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• Large % of securities portfolio in government securitiesH-Model
where: • H-model for equity market valuation
where:
as pledge against reserves.
• Regulators restrict allocation to common shares and
portfolio that affects reserves.
below-investment-grade bonds.
• Risk-based capital requirements.
• Interest rate risk: reinvestment risk and valuation
© 2018 Wiley
risk (due to duration mismatch between assets and
• Unique: Lending activities may be influenced by
liabilities).
community needs and historical banking relationships.
c06.indd 149
• Credit risk of bond investments.
• Cash volatility risk: relates to timely receipt and
reinvestment of cash.
• Disintermediation risk: policy owners withdraw
Capital Market Expectations
funds to reinvest with other intermediaries in higherreturning assets.
• Expected
Expected
Return, E(R)return on equity from Gordon growth model
Return
objective:
minimum
returnwillrequirement
(based
© Wiley•2018
all rights reserved.
any unauthorized
copying or distribution
constitute an infringement
of copyright.
on rate initially specified to fund life insurance contract)
D (1 + g)
D
E ( R) = 0
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and net interest spread.
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ECONOMIC ANALYSIS
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α = output elasticity of capital.
where:
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value
models
(1
output
elasticity
of labor.
N –= α)
period
of years
from higher
to lower linear growth rate.
where: • Fed model: equity market undervalued if S&P earnings
gVS = short-term
high growth rate.
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steady
growth
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7 March 2018rate.
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rate.
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reserved.
copying
or distribution
will constitute an infringement of copyright.
p any unauthorized
p
0
gL = long-term steady growth rate.
• Cyclically adjusted P/E (CAPE) ratio
where:
where:
Earnings-Based
Models
= Moody’s
A-rated
corporate
bond yield
yB E
• 010-year
moving
average
CAPE ratio controls for
= Earnings
yield
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d
=
earnings
projection
weighting
factor
pbusiness
= dividend
payout
ratio
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cycle
effects
and is mean reverting.
LTEG = Consensus
S&P
500
5-year
annual
earning
growth
y = 10-year T-note yield
T
© Wiley 2018 all rights reserved. any unauthorized copying or distribution will constitute an infringement of copyright.
Grinold‐Kroner Model
© Wiley 2018 all rights reserved. any unauthorized copying or distribution will constitute an infringement of copyright.
yieldreal
on economic
treasury inflation
YTMTIPS
Y ==total
output.protected securities
ROE(1 – P) = sustainable growth rate
Wiley © 2019
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r − ROEassumes
y − y (1 − p)
(1 − P ) that
Fed Model
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P/E Ratio
=
= T r =TROE = y=T,yTwhich ignores the equity risk premium.
P0
p
p
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© Wiley 2018 all rights reserved. any
unauthorized
distribution will constitute an infringement of copyright.
Real
S&P500copying
Price orIndex
1
b. Dynamic hedge: The investor increases the allocation to the hedging portfolio as
the funding ratio increases.
Forward Premium/Discount
The two-portfolio approach has its limitations.
where:
a. It cannot be used when the funding ratio is less than 1.
Actualof foreign currency;
(i − i in) ×
terms
FFC/DC = forward rate for domesticcurrency
b. It cannot be use when a true hedging portfolio is unavailable; for example, the
360 
FFC/DC − SFC/DC = SFC/DC  FC DC Actual

liabilities are related to payments for damages due to hurricanes or earthquakes.
currency
in terms of pricecurrency”
1 + (i DC ×
360 ) 
3. The integrated asset-liability approach is used by some institutional investors to
= spot rate for domestic currency in termsActual
of foreign currency
S
jointly optimize asset and liability decisions. Banks, long/short hedge funds, insurance FC/DC
 (i PC − icountry
360 
BC ) ×
=
interest
rates
in
foreign
currency
i
F
S
S
−
=
FC
companies, and reinsurance companies often must render decisions regarding the
PC/BC
PC/BC
PC/BC 
1 + (i BCcountry
× Actual 360) 
iDC = interest rates in domestic currency
composition of liabilities in conjunction with their asset allocation. The process is
called asset-liability management (ALM) for banks and dynamic financial analysis
(DFA) for insurance companies. The approach is often implemented in the context
of multiperiod models via a set of projected scenarios. The integrated asset-liability Forward
DomesticPremium/Discount
Return on Global Assets
approach provides a mechanism to discover the optimal mix of assets and liabilities. It
is the most comprehensive approach among the three liability-relative asset allocation
 (i − i ) × Actual 360 
approaches.
FRDC = −(1S+ RFC )(1
= S+ RFX ) − 1FC DC
Wiley’s CFA Program Exam Review
®
same as “base
FC/DC
FC/DC 

Actual
360 ) 
= RFC + RFX + RFC RFX1 + (i DC ×
 (i − i ) × Actual 360 
≈R +R
FPC/BC − SFCPC/BC FX
= SPC/BC  PC BC Actual

 1 + (i BC ×
360 ) 
FC/DC
Characteristics of liability-relative asset allocation approaches are summarized in the
• CAPE value is current-year real S&P 500 index value
• following
Liability-relative
asset allocation approaches
table.
divided by average real earnings over previous 10
years.
• Asset-based models
• Tobin’s q: market value of debt and equity capital
divided by replacement cost of assets (undervalued if q
ratio < 1 assuming mean reversion).
• Equity q: market value of equity divided by
replacement cost of net assets (undervalued if q ratio <
1 assuming mean reversion).
Integrated Asset-liability
Simplicity
Linear correlation
All levels of risk
Any funding ratio
Simplicity
Linear or nonlinear correlation
Conservative level of risk
Positive funding ratio for
basic approach
Single period
Increased complexity
RDC = return
in domestic
) terms
expressed
ascurrency
SDC/FC
Return
on Global
Assets
Linear or nonlinear correlation Domestic
RFC = return in foreign currency terms
All levels of risk
in+SRDC/FC
(i.e., foreign
RFX = percentage
Any funding ratio
RDC = (1change
+ RFC )(1
)
FX − 1
Multiple periods
It’s important to examine the robustness of asset allocation strategies. Four commonly used
where:•
Domestic return on global asset (where exchange rate is
currency in terms of domestic currency)
= Rin
+ RFX + RCurrency
FCDomestic
FC RFX
Portfolio
Return
Terms currency terms
• Portfolio
return in domestic
≈ RFC + RFX
cuRRency MAnAgeMent: An in
RDC = [ w1 × (1 + RFC1 )(1 + RFX 1 ) + w2 × (1 + RFC 2 )(1 + RFX 2 )] − 1
tests are: asset allocations
• robustness
Goal-based
where:
Simulation based
on historical return and
risk data. modules based on Risk on Global Assets in Domestic Currency Terms
• 1.Creation
of differentiated
portfolio
RDC = return
in domestic
currency
terms return
• Variance
of the
domestic
2. Sensitivity analysis where the level of one underlying risk factor is changed and the
capital
expectations.
resultingmarket
asset allocation
outcomes are investigated.
where:
RFC = return in foreign currency terms
wn = weight2 of asset in2 the portfolio
2
domestic
Scenario analysis where the levels of multiple risk factors are changed in a correlated RFX = percentage
σ ( RDC change
) ≈ σ ( RinFCS)DC/FC
+ σ ((i.e.,
RFX )foreign
+ [2 × σcurrency
( RFC ) × σin( Rterms
ρ( R
FX ) × of
FC , RFX )]currency)
• 3.Identifying
clients’ goals and matching the goals to
manner and the resulting asset allocation outcomes are investigated. Stress testing is
one such case. sub-portfolios and modules.
appropriate
Asset
Allocation with Real-World
© 2018 Wiley
Constraints
Asset Allocation Approaches
Principles of Asset Allocation
AA
• Mean variance optimization (MVO)
• Produces an efficient frontier based on returns,
standard deviation of returns and pairwise
correlations.
Principles of Asset Allocation
• Finds optimal asset allocation mix that maximizes
Risk Objectives
client’s utility.
U p = E ( R p ) − 0.005 × A × σ 2p
Portfolio
Return in Domestic
Terms
• Factors
favoringCurrency
more currency
hedging
Roll Yield
•RDCSignificant
objectives, e.g. income/liquidity
= [ w1 × (1 + Rshort-term
FC1 )(1 + RFX 1 ) + w 2 × (1 + RFC 2 )(1 + RFX 2 )] − 1
185
Y
requirements.
( FP / B − SP / B )
=
SP / B
• RollGlobal fixed-income
investments.
where:
• All
Markets
high
currency
assetwillvolatility.
= weight
ofRights
assetReserved.
in with
the Any
portfolio
w©n wiley
• Constraints on asset allocation due to: 28
2018
unauthorized
copying or or
distribution
constitute an infringement of copyright.
where || indicates
value. Positive roll yield occurs when a trader buys base
• Highabsolute
risk aversion.
AllocAtion with ReAl-woRld
constRAints
• Asset size: more acute issue for individual rather Asset
than
currency at a forward discount or sells it at a forward premium.
• Doubt about value of currency return potential.
institutional investors.
Asset Allocation
with Real-World
Constraints
Lower possibility
of regret if the hedge is not profitable.
Hedge
• Liquidity:
liquidity needs
of asset owner
and liquidity Minimum• Variance
• Low costs of hedging.
characteristics
of different asset classes.
After-tax Portfolio
Optimization
yt = α + βxt strategies
+ εt
• Hedging
• Time horizon: asset allocation decisions evolve
Optimizing a portfolio subject to taxes requires using the after-tax returns and risks on an
• AllPassive
hedging:
manager
with fullof copyright.
28
with changes in time horizon, human capital,
utility © wiley 2018
Rights Reserved.
Any unauthorized
copying orprotects
distribution willportfolio
constitute an infringement
ex-ante basis.
c08.indd
asset allocation that can pay off liabilities when they
come due.
• Goals-based investing: specifies sub-portfolios
aligned with a specific goal (sum of all sub-portfolio
asset allocations results in an overall strategic asset
allocation).
Asset AllocAtion
Asset AllocAtion
two-Portfolio
Single period
ASSET ALLOCATION
• Asset-only: does not explicitly model liabilities
• Liability-relative (liability-driven investing): aims at an
Currency Management
Surplus optimization
185
7 March 2018 3:34 PM
function, financial market conditions, characteristics ofwhere:
hedging.
yt = percentage change in asset to be hedged
• Discretionary
hedging:
manager reduces risk with
change in hedging
instrument
xt = percentage
hedging
but has
discretion
to make currency bets for
β
= hedge ratio
for minimum
variance
hedge
• Regulatory:
regulatory
entities
• Taxes
and portfolio financial
rebalancing:markets
As marketand
conditions
change over
time, asset class
ε = error term
to be minimized
return
enhancement.
where: weights
often
constraints.
in aimpose
portfolio additional
change and tend
to move away from previously set target
rat = expected
levels. after-tax
Portfolioreturn
rebalancing is needed to return actual allocation to the strategic
• Active currency management: manager seeks alpha by
Minimum Hedge Ratio
• asset
Taxes
pre-tax return
rpt = expected
allocation
(SAA). However, discretionary portfolio rebalancing can trigger
making currency bets.
t = expected
tax
rate
realized
capital
and losses and
the associated
tax liabilities that could have been
• Place
lessgains
tax-efficient
assets
in tax-advantaged
• Currency overlay:
management outsourced
 σ ( currency
RDC ) 
otherwise deferred or even avoided.
Extending this
to a portfolio
with both income
and portfolio
capital gains:optimization.
h = β = ρ ( RDC ; RFX ) × 
accounts
to achieve
after-tax
to specialists.  σ( RFX ) 
Taxable asset owners should consider the trade-off between the benefits of tax
• Active currency management
rat = pd rpt (1 −
td )the
+ pmerits
tcgmaintaining
)
a rpt (1 −of
minimization
and
the targeted asset allocation by rebalancing.
where:
• Economic fundamentals: real exchange rate will
h = hedge ratio
eventually
to fairterms
market
values,
with shortwhere: Because after-tax volatility is smaller than pre-tax volatility, it takes a largerρ = correlation
of return inconverge
domestic currency
and return
on conversion
to domestic
movement
in
a
taxable
portfolio
to
change
the
risk
profile
of
the
portfolio.
•
Rebalancing
range
for
a
taxable
portfolio
(R
)
can
pd = proportion of return from dividend income
term increases in the domestic currency due to (1)
currency.
taxable
can be wider than
Consequently,
rebalancing
for aotherwise
taxable
portfolio
(R taxable)taxbe wider
than
of an
identical
of return
from those
priceranges
appreciation
(i.e., capital
gain)
pa = proportion
increase in domestic currency’s real purchasing power,
of dividend
an otherwise
identical tax-exempt portfolio (R tax exempt ).
rate on
income
t = taxthose
Asset
decisions
shouldowner’s
be made on
an after-tax basis.
the asset
priorities.
ratliability
=allocation
rpt (1 − t )and
where:
• investor’s
MVO limitations
U is the
utility.
exempt portfolio (Rtax exempt).
E(Rp) is the
portfolio
expected return.
• Asset
allocations
are highly sensitive to small changes d
(2) higher domestic interest rates, (3) higher expected
tcg = tax rate on capital gain
A is the investor’s
risk aversion.
in input
variables.
foreign inflation, and (4) higher foreign risk premiums.
R taxable
= R taxthe
/ (1 − t) benefit from compounding capital gains rather than
σ 2p is the•variance
of
the
portfolio.
This
formula
ignores
multi-period
exempt
Asset allocations can be highly concentrated.
• Technical analysis: based on belief that historical
recognizing the annual capital gain.
Roy’s Safety
Firstfocuses
Ratio (SFon
Ratio)
currency patterns will repeat over time and those
• Only
mean and variance of returns.
Taxaffect
loss harvesting
is another
commonly used strategy related to portfolio rebalancing repetitions are predictable.
Taxes •also
expected
standard
Revision
to asset
an deviation.
allocation
• SourcesE (of
risk
may
not
be
well
diversified.
and
taxes.
R p ) − RL
• Carry trade: borrow in lower interest rate (or forward
Ratio =
•σ atChanges
= σ pt (1 − t )in goals
•SFAsset-only
σstrategy.
p
premium) currencies and invest in higher interest rate
Strategic
asset location refers to placing less tax-efficient assets into tax-deferred or
• Changes
in constraints
tax-exempt
accounts
such as pension and retirement accounts. For example, equities (or forward discount) currencies, based on assumption
• Single-period framework and ignores trading/
CurrenCy ManageMent: an IntroduCtIon
should
heldhigher
in taxable
taxablethe
bonds
high-turnover
Taxes result
in generally
lower highs
and
lows,accounts,
effectivelyand
reducing
meanand
return
and
where:
rebalancing costs and taxes.
that uncovered interest rate parity does not hold.
• Changes
inbeinvestment
beliefs
assets should be placed in tax-exempt or tax-deferred accounts to maximize
muting trading
dispersion.
RL is the lowest acceptable return over a period of time.
• Does not address evolving asset allocation strategies,
•
Roll
yield: positive when trading the forward rate bias
the
tax benefits
of those
accounts.(TAA) approaches
•
Tactical
asset
allocation
options
expire within that range. The “short” position comes from the fact that the out-ofE(Rp) is the portfolio’s expected return.
the-money put and call in the seagull spread have been shorted.
path-dependent decisions, non-normal distributions. Equivalent After-Tax Rebalancing Range
cuRRency MAnAgeMent: An intRoduction (buying base currency at forward discount or selling
σp is the portfolio’s standard deviation.
• Discretionary
uses market
skills
to avoid
or
Asset allocation
decisions are aTAA:
dynamically
changingtiming
and adjusting
process.
Market
base currency at forward premium); negative when
• Approaches to improve quality of MVO asset allocation
hedge
negative
returnsoften
in down
enhance
conditionsRand
asset owner
circumstances
requiremarkets
revising anand
original
asset allocation Exotic Options
at = R pt (1 − t )
trading against the forward rate bias (selling base
decision. There
are basically
threeinelements
that may trigger a review of an existing ©
asset
Currency
Management:
Ancannot
Introduction
Exotic
options
are those
that
are creative
in nature
and
categorized
as being of copyright.
positive
returns
up markets.
wiley 2018
Allcurrency
Rights
Reserved.
unauthorized
copying
or distribution
willbeconstitute
an infringement
atAnyforward
discount
or buying
base
currency
allocation policy:
“plain.”
Exotic strategies
provide the lowest
cost investment
to achieve
a specific
outcome.
where: • Systematic TAA: uses signals to capture asset-classThese
are
quitepremium).
helpful for clients with significant unique circumstance constraints
atoptions
forward
Forward Exchange
Rates
in the investment policy statement or who have specific income needs that cannot be
= After-tax
rebalancing
range
Rat 1.
Changes
in
goals:
level return anomalies that have been empirically
produced by traditional financial securities.
rebalancing
range in business conditions and changes in expected future cash
a. As
a result of changes
• Adding constraints to incorporate short-selling and Rpt = Pre-tax
1 + (i FC × Actual 360)
demonstrated
as producing abnormal returns.
FFC/DC
= SFC/DC
×
flows over time, a mismatch may arise between the original intended goal and the
One
commonly
used exotic
option isActual
option in which the option does not
other
real-world
restrictions
into
optimization.
1 + (i
× a knock‐in
360 )
DC rate
Portfolio
Value
After
Distributions
SR[ New] > SR[ p] × Corr ( R[ New], R[ p])
actually exist until a barrier spot
is realized.
Keep in mind that the barrier rate is not
current
goalTaxable
of
the fund
best serve
the fund’s needs.
• Behavioral
biases
intoasset
allocation
1 + (iFor
)
× Actual 360
strike price.
consider
a call option with an exercise rate of
PCexample,
b. Changes in an asset owner’s personal circumstances may alter risk appetite or theFsame as=the
• Resampled MVO technique combining MVO and Monte
S
×
PC/BC
PC/BC
and a barrier
rate ×
ofActual
CAD1.12/USD.
If the spot rate is currently CAD1.10/
•
Loss
aversion:
mitigate
bymarriage,
framing
riskchildren,
in terms
ofbecoming ill CAD1.15/USD
Vatrisk
= Vcapacity.
− ti ) Life events
+
1
(i
)
pt (1
such
as
having
and
Carlo
approaches to seek the most efficient and
Portfolio Risk
Budgeting
USD, the option does not evenBC
exist until 360
the spot rate rises to CAD1.12/USD. It works
Asset AllocAtion
shortfall
or needs
funding
high-priority
goals
with from an
may
all haveprobability
an impact on the
and goals
of an individual
benefiting
like a regular option, but if the barrier rate is never realized, it’s as if the option never
consistent optimization.
investment
existed. A knock-out option ceases to exist when the exchange rate touches the barrier.
low-risk portfolio.
assets.
Marginal contribution to total risk identifies the rate at which risk changes as asset i iswhere:
where: Think
of a put optiontrade:
of the base
currency
with a barrier
slightly or
below
the strike price.
portfolio
value Any material change in constrains, including asset size,
vat =2.after-tax
Changes
in constraints:
Carlotrading
simulation
and
scenarioa analysis
•theVolatility
long
(short)
straddle
strangle
if
3. •toItMonte
canportfolio:
incorporate
costs and costs
of rebalancing
portfolio. It may also
added
the
AA
base currency
the barrier,
then of
theforeign
option nocurrency;
longer exists.
These
• Illusion
control:
mitigate
byexternal
using constraints,
the globalshould
market
rate forappreciates
domesticabove
currency
in terms
same
as “base
FFC/DC
portfolio
value
vpt = pre-tax
liquidity,
time of
horizon,
regulatory,
or other
trigger
a =Ifforward
incorporate taxes.
volatility
expected
to
increase
(decrease).
exotics
are cheaper
than
regularly
traded
options and offer
less protection.
•
Used
in
a
multiple-period
framework
to
improve
currency
in
terms
of
price
currency”
rateportfolio
on distributions
income
ti = taxreexamination
ofas
existing
asset allocation
decisions.
4. It can model non-normal multivariate return distributions, serial and cross-sectional
aasstarting
point and
using a formal asset
=Exhibit
spot
rate
for
domestic
currency
in
terms
of
foreign
currency
SFC/DC
MCTR
βi ,P σ P requirements,
single-period
MVO.
correlations,
an evolving asset allocation strategy, path•
Currency
management
tools
3. Changes
in
beliefs:
Investment
beliefs
change
with
market
conditions,
among
many
i =distribution
5‐1: Select Currency Management Strategies
allocation process based on long-term return and risk
dependent decisions, nontraditional investments, non-tradable assets, and human
foreign currency country
iFC = interest rates in27
other
factors.
TheyAny
areunauthorized
a set of guiding
that
govern
asset owner’s
Allforecasts,
Rights
Reserved.
copying
orprinciples
distribution will
constitute
anthe
infringement
of copyright.
• Provides a realistic picture of distribution of potential © wiley 2018
optimization
constraints
anchored
around
capital.
Over‐/under‐hedging
interestContracts
rates in domestic
currency country Profit from market view
iDC =Forward
investment decisions. Investment beliefs include expected returns, volatilities, and
where:
future outcomes.
asset class
weights
in the
global
market
portfolio, and
Option Contracts
OTM options
Cheaper than ATM
correlations
among
asset
classes
in
the
opportunity
set.
budget
a particular
allocation
of portfolio
risk. Anreturns
optimal risk budget is one to
= beta
of isasset
i returns
with respect
to portfolio
βAi,Prisk
strict policy ranges.
Forward Premium/DiscountRisk reversals
Write options to earn premiums
satisfy
portfolio
Our goal
is to seek
an optimal
risk budget.
Portfolio
risk
can be
• Canoptimization.
incorporate
trading/rebalancing
costs
and
taxes.
return
volatility
measure
as standard
deviation
of asset
i returns
σ = portfolio
Including International Assets
• Use
reverse
optimization
compute
implied returns
• The
Sharpe
ratio of the
proposed new to
asset
class: SR[New]
improve
quality
inputs,
e.g. Black-Litterman
• Theand
Sharpe
ratio of the
existing of
portfolio:
SR[p]
• Themodel.
correlation between asset class return and portfolio return:
Corr (R[New], R[p])
P
Exotic Options
Put/call spreads
Write options to earn premiums
• Mental accounting: goal-based investing incorporates
Actual
 (ispreads
 options to earn premiums
360
FC − i DC ) ×
Seagull
Write
this bias directly into the asset allocation solution by
FFC/DC − SFC/DC = SFC/DC
sectional correlations, evolving asset allocations,
path 1 + (i × Actual ) 

194
360Reduced downside/upside exposure
© 2018 Wiley
DC
1. The risk budget identifies the total amount of risk and allocates the risk to different
Knock‐in/out features
aligning each goal with a discrete sub-portfolio.
dependent
decisions, non-traditional investments,
asset
classes
in
a
portfolio.
Actual
ACTR
=
w
×
MCTR
i
i
i
−i )×
 (ioptions

360
Digital
Extreme
payoff strategies
2. An optimal
risk capital.
budget allocates risk efficiently, which is to maximize return per unit
FPC/BC − SPC/BC = SPC/BC  PC BC Actual
human
• Recency or representativeness bias: mitigate by using

ACTRi
 1 + (i BC ×
360 ) 
of%
risk
taken.
ACTR
i to total risk =
a formal asset allocation policy with prespecified
c09.indd 194
7 March 2018 3:17 PM
Risk
budget
σ P risk budget is risk budgeting.
3. • The
process
of finding the optimal
digital option, which
might also
be calledratio
an “all‐or‐nothing”
or binary option, earns a
•Apredetermined,
Minimum
variance
hedge
for a cross-hedge
fixed payout if the underlying reaches the strike price at any time during
allowable ranges.
• Identifies
total amount
risk
allocates
risk
to
The concept
of marginal contribution
to portfolioof
risk
is anand
important
one because
it allows
Domestic
Global
Assets
the• Return
life
of theon
option.
It does
not
have to cross the strike
price, nor does
it have toof
remain
Obtained
from
a regression
of change
in value
us to (1) track
the change in
portfolio
risk due to a change in portfolio holding, (2) determine
in‐the‐money until expiration to earn the payoff amount. This feature makes the option
• Framing bias: mitigate by presenting the possible asset
different
asset
classes.
assetspeculation
in domestic
currency terms against
© Wileypositions
2018 All rights
reserved.and
Any unauthorized
or distribution will constitute an infringement of copyright.
moreunderlying
appropriate for currency
than hedging.
which
are optimal,
(3) create a copying
risk budget.
allocation choices with multiple perspectives on the
RDC = (1 + RFC )(1 + RFX ) − 1
• Asset allocation is optimal when ratio of excess return
change in value of the hedging security.
risk-reward tradeoff.
= RFC + RFX + RFC RFX
In a risk budget
following
to setting,
MCTRweishave
thethesame
forrelations:
all assets.
• Beta
(slope coefficient) of the regression equation is
≈ RFC + RFX
• Familiarity or availability bias: mitigate by using the
the
optimal hedge ratio.
Marginal contribution to total risk (MCTR) = Asset beta × Portfolio standard deviation
global market portfolio as the starting point in asset
Absolute contribution to total risk ( ACTR ) = Asset weight × MCTR
where: • Basis risk occurs due to imperfect correlation between
allocation and carefully evaluating any potential
Ratio of excess return to MCTR = (Expected return − Risk-free rate)/ MCTR
movement
and hedging instrument.
RDC = returncurrency
in domesticprice
currency
terms
deviations.
total risk, market risk, active risk, or residual risk. Here are three statements that are directly
Can
model
non-normal
and
crossrelated to •the
risk budget
process:
Absolute
contribution
to
total
risk identifies distributions,
the contribution toserial
total risk
for asset
i
RFC = return in foreign currency terms
RFX = percentage change in SDC/FC (i.e., foreign currency in terms of domestic currency)
An asset allocation is optimal when the ratio of excess return (over the risk-free rate) to
MCTR is the same for all assets.
Factor-based asset allocation utilizes investment risk factors instead of asset classes to
make asset allocation decisions. These factors are fundamental factors that historically have
produced return premiums or anomalies to investors. These factors include, but not limited to:
Portfolio Return in Domestic Currency Terms
Wiley © 2019
108
RDC = [ w1 × (1 + RFC1 )(1 + RFX 1 ) + w2 × (1 + RFC 2 )(1 + RFX 2 )] − 1
© 2018 Wiley
Wiley’s CFA Program Exam Review
®
IntroductIon to FIxed-Income PortFolIo management
Market Indexes
Liability-Driven Strategies Yield Curve StrategieS
Total Return Analysis
• Buy and hold: choose parts of curve where yield
changes will not affect return or purchase longerduration/higher-yield securities.
Portfolio duration generally can be increased by reallocating cash (which has duration at
Semiannualarising
total return
=  interest rate volatility
− 1 over the
is security’s capitalization value as a % of total index
funding
from
•
Rolldown:
riding
curve
when yield
curvewith
is longer Full price of the bond 
or close to zero)
to duration
assets,the
or byyield
replacing
shorter-duration
securities
market cap.
planning horizon.
upward-sloping.
duration securities.
Decreasing duration involves selling securities for cash. If the manager
prefers to•continue
certain securities,
however, the same
types of duration altering
• Advantages: broad acceptance; requires less
Immunizing a single liability
Sellingholding
convexity:
sell lower-yielding
higher-convexity
Dollar•Duration
may be accomplished via derivatives.
rebalancing as index remains properly weighted after
bonds if expecting low interest rate volatility.
• Market value of assets is greater
than
or
equal
to
PV
of
Dollar
duration = Duration × Bond value1 × 0.01
a price change.
altering •portfolio
withlonger-maturity,
derivatives
liability
Carry duration
trade: buy
higher-yielding
• Disadvantages: overly influenced by overpriced
securities and finance them with shorter-maturity,
•
Macaulay
duration of assets matches liability’s due
1
value is market value not par value
LoS 23d:lower-yielding
explain how derivatives
may be used to implement yield curve
securities; price movements overly concentrated in a Note: Bonddate
securities.
strategies. vol 4, pp 137–141
few large companies.
• Changing yield curve strategies
Spread Duration
• Convexity of asset portfolio is minimized.
• Price weighted index: weight of each security is
• Durationportfolio
management:
shorten
(lengthen)
if
A derivatives-overlay
makes duration
management
a separateduration
decision from
• Portfolio needs rebalancing as time passes.
proportional to its price (represents portfolio holding Three major types of spreads:
security selection andyield
can avoid
the costly(decreases).
capital gain component present for a securities
increases
• Risk: non-parallel shifts in yield curve (risk is reduced sale. For thisexpect
one share of each security).
discussion,
the
overlay
consists
of
puts
and
calls
on
bonds
and
interest
rate
• Nominal spread is the difference between the portfolio yield and the treasury yield
• Buying
with falling
yields,
portfolios
withstructured
by minimizing convexity).
futures (which
are alsoconvexity:
a form of derivative).
Other types
of derivatives
include
for the same maturities.
• Advantages: simple; long track record.
greater
convexity
will
increase
more
in
value
than
notes, interest-only strips (IOs) and principal-only strips (POs) used for portfolios of MBS
Cash flow spread
matching
for multiple
liabilities
• • Zero-volatility
(Z-spread)
is the constant
spread over all the Treasury spot
assets, and collateralized
obligations
(i.e., securities
basedyields,
on underlying MBS
• Disadvantages: not relevant to most strategies;
portfolios mortgage
with less
convexity;
with rising
rates at all maturities that forces equality between the bond’s price and the present
•
Portfolio
has
cash
flows
matching
the
amount
and
assets).
influenced by highest priced securities; must be
portfolios with greater convexity will decrease less.
value of the bond’s cash flows.
timing of liabilities.
• Option-adjusted
spread (OAS) is the spread over the treasury or the benchmark
rebalanced after stock splits.
Fixed-income
futuresand
contracts
may structures
be used to adjust duration without any cash outlay
• Bullet
barbell
incorporating
the effects
any embedded
options in the bond.
• after
Duration
matching
forofmultiple
liabilities
other than initial margin and the mark-to-market cash flows required to maintain margin.
• Equal weighted index: all securities are held in equal
Managers
can
find
the
correct
number
of futures
contracts
to buy or sell as a function of
Relative
Outperformance
Given
Scenario
Market value of assets is greater than or equal to the
weights at rebalancing (represents portfolio holding an Economic• Surplus
the money duration or, more specifically, the price value of a basis point (PVBP). Recall
Yield Curve Scenarios
Structure
market value of liabilities.
equal $ amount of each security).
that
money
duration
is
the
currency
change
in
portfolio
market
value for a 1% change in
Economic Surplus = MVAssets − PVLiabilities
Parallel shift
Barbell
• Asset basis point value (BPV) equals the liability BPV. rates: Level change
• Advantages: more diversified away from highest-priced
companies.
Slope change
Flattening
Barbell
where: • Dispersion of cash flows and convexity of assets are
D
Bullet
market value
of those
assets of the liabilities.
MVAssets =greater
DMoney = VP × Modified Steepening
than
• Disadvantages: must be rebalanced frequently to
100
PVLiabilities = present value of liabilities
Curvature change
Less curvature
Bullet
maintain weighting; price movements of smaller
• Derivatives overlay
More curvature
Barbell
PVBP, then, is money duration divided by 100 yet again:
companies may be overrepresented.
Derivatives Overlay
• Uses bond futures contracts to immunize liabilities.
Bullet
Decreased volatility
Volatility change
• Fundamental weighted index: uses accounting data or
increased
volatility
Barbell
DMoney
DModified
Liability portfolio BPV – Asset portfolio BPV
PVBP
=
V
×
=
V
×
otherwith:
valuation metrics to weight the securities.
P
P
Lower liquidity
Nf =
100
10,000
IntroductIon to FIxed-Income PortFolIo management
Futures BPV
•
Duration
management
methods
Lower
liquidity
with:
Lower liquidity
with:
• Advantages:
better representation of economic
Formulating a Portfolio Positioning Strategy for a Market View
• Time since issuance (because dealers have supply right after issuance, but buyers of
BPVCTD
• Buy (sell)
futures
to desired
increase
(decrease)
duration.
That information
can thenbond
be used
along with
additional
PVBP and
PVBP of the
Futures BPV ≈
importance.
those
bondsissuance
may hold
them todealers
maturity).
Time
since
issuance
(because
dealers
have supply
supply right
right after
after issuance,
issuance, but
but buyers
buyers of
of
CFCTD
•• Time
since
(because
have
futures
contract
determine
Parallel to
Upward
Shiftthe number of contracts to be purchased or sold:
Investors
liquid
fixed-income
opportunities
may also
choose a fixed• those
Lower
credit
quality.
those
bonds
may
hold them
them
toinvestment
maturity).
•seeking
Disadvantages:
relyto
on
creator’s
subjective
judgment;
bonds
may
hold
maturity).
income
exchange-traded
fund
(etF),
which
may
allow
authorized
participants
to
Lower credit
acceptance
as collateral in repo market (sovereigns are more liquid than lowercredit quality.
quality.
•• Lower
restrictive
may
result
in less In high-where:• Contingent immunization
Additional
PVBP
Bonds
with forward
implied
yield change greater than forecast yield change will enjoy higher
transact
using
in-kind
(i.e.,valuation
portfolios
ofscreens
securities)
deposits
and redemptions.
quality
corporates).
Lower
acceptance
as
collateral
in
repo market
market
(sovereigns
are more
more liquid
liquid than
than lowerlower# Contracts
=
•• Lower
acceptance
as
collateral
in
repo
(sovereigns
diversification;
investability
ofare
smaller
return in a magnitude
based
on duration as they roll down the yield curve.
yield• andSmaller
other
illiquid
sectors,
portfolio
managers
may
ETF
shares,
which are Nf = number of futures contract to immunize portfolio
Futures
PVBP
issue size
(because
smaller
issuesconstraints
will purchase
not be included
in index/benchmark).
quality
corporates).
• Active management if surplus (assets less liabilities) is
quality
corporates).
converted
tocompanies;
positions
in
individual
securities
via an
authorized
participant
of
the ETF.BPV = Basis point value
not
transparent
because
of
proprietary
•
Smaller
issue
size
(because
smaller
issues
will
not
be
included
in
index/benchmark).
Yield Curv
• Smaller issue size (because smaller issues will not be included in index/benchmark). above a designated threshold.
CTD = Cheapest to deliver
The leverage (i.e., value of bonds to be purchased to reach the desired additional PVBP)
Using exchange-traded
(e.g., futures and options on futures) may provide a more
valuationoptions
weightings.
rTotal
= Y0 − D1 (Y1 − Y0 )
Lesson
4: coMPonents
oF
FIxed-IncoMe
RetuRns
CF
factor
by the
formula:
liquid
Usingoptions
over-the-counter
(OTC)-traded
instruments
interest aarate
and= Conversion
Using alternative.
exchange-traded
options
(e.g.,
futures
and options
options
on futures)
futures) (e.g.,
may provide
provide
more
• If the surplus
falls below threshold, revert to a pure can be found
Using
exchange-traded
(e.g.,
futures
and
on
may
more
•
Use
leverage
to
increase
duration
credit
swaps)
mayover-the-counter
also help reduce(OTC)-traded
risk.
liquid default
alternative.
Using
over-the-counter
(OTC)-traded
instruments (e.g.,
(e.g., interest
interest rate
rate and
and
immunization strategy.
liquid
alternative.
Using
instruments
where
subscripts
indicate
beginning
or end
The portfolio duration
is then
in effect
multiplied
by the ratio
of of
thethe
newperiod.
notional value
Additional PVBP
credit default
default swaps)
swaps) may
may also
also help
help reduce
reduce risk.
risk.
credit
after adding
the overlay
to the original portfolio
VLeveraged
=
× 10,000 value so that the PVBP of the combined
Los
21d:
describe
and
interpret
a
model
for
fixed-income
returns.
Exchange-traded funds (ETFs) may provide a liquid option. Portfolio managers may purchase• Use gains on actively managed funds to reduce cost of
DModified of bonds
portfolio
is
as
desired:
Vol
4,shares
pp 23–27
ETF
and then
redeem
them
the underlying
bonds using
authorized
participants
Exchange-traded
funds
(ETFs)
mayfor
provide
liquid option.
option.
Portfolio
managers
may purchase
purchase meeting liabilities.
A portfolio facing no constraints can position to maximize rTotal.
Exchange-traded
funds
(ETFs)
may
provide
aa liquid
Portfolio
managers
may
(e.g.,
qualified
and other
institutions)
as intermediaries
withauthorized
ETF sponsors.
ETF shares
shares
andbanks
then redeem
redeem
them
for the
the underlying
underlying
bonds using
using
authorized
participants
ETF
and
then
them
for
bonds
participants
VEquity + VLeveraged
• Horizon matching: cash flow matching for short-term
(e.g.,
qualified
banks
and
other
institutions)
as
intermediaries
with
ETF
sponsors.
DNew = D
Parallel
Yield
Old × Changes of Uncertain Direction
(e.g.,
qualified
andonly
other
institutions)inasrestructuring
intermediaries
with ETF sponsors.
expected
yield banks
is not the
consideration
a fixed-income
portfolio, and
liabilities
(< 5anyyears),
duration
matching
for long-term
Equity
Fixed-Income Returns Model
33 byVusing
© Wiley 2018
all rights reserved.
unauthorized
copying or distribution
will constitute
an infringement of copyright. Increase convexity
a barbell strategy when a yield change is certain, but the direction
lookingIntroduction
only at the yield curve would provide an incomplete pictureIntroductIon
in deciding
to prospective
FIxed-Income PortFolIo management
liabilities.
Fixed-Income Returns
Returns Model
Model
of the change is not. Current portfolio duration is maintained by weighting the best bonds at
Fixed-Income
restructuring trades.
Instead, portfolio managers can deconstruct approximate expected returns:
Portfolio managers use expected returns to position assets for risk and return properties
The leveraged
value
is
assumed
to
be
funded by overnight loans, which would have
either end by:
• Interest rate swap overlay to reduce duration gap
• Use interest rate swaps: receive-fixed, pay-floating
desired
the portfolio:
•forFixed-income
returns
model
Portfolio
managers
use expected
returns
to position assets for risk and return properties
• Market cap weighted index: weight of each security
1
• Immunization: reduces
or eliminates the
risks to liability
 Total future dollars  n
FIXED INCOME PORTFOLIO
MANAGEMENT
Portfolio
to FIxed-Income
PortFolIo managers
management use expected returns to position assets for risk and return properties
158
desired for
for
the
portfolio:
r ) =portfolio:
Yield income
desired
Liability portfolio BPV – Asset portfolio BPV
•E (the
Expected
return decomposition
NP =
× 100
Roll-down
return
E(R) +≈ Yield
income
Swap BPV
Introduction
to Fixed-Income Portfolio Management
E(R) +
Yield
income
ERoll
due toreturn
yield change and spread )
( ∆Pdown
E(R)
≈≈+Yield
income
r23.indd 158
Roll
down
return
∆ Price
due
to yields
Roll
down
return
Expected Return
+++EE(
Credit
gains/losses
(Decomposition
) and spreads)
where:
+ E(
∆ Price
Pricelosses)
due to
to yields
yields and
and spreads)
E(Credit
• Risksprincipal
when of
managing
∆
due
NP = Notional
the swap portfolio against a liability
++−EE(
gains/losses
( Currency
) spreads)
−Yield
E(Credit
losses)
E(Currency
gains and losses)
income
E ( R) ≈−+
structure: model risk, spread risk, counterparty credit
E(Credit
losses)
Index
Matching
to
a
Fixed-Income
Portfolio
+ E(Currency
E(Currency
gains and
and losses)
losses)
risk.
+Rolldown
return
+
gains
Fixed income
This model for fixed-income returns can help investors better understand the assumptions
Assuming
no
reinvestment
income,
yield
income
(aka
current
yield)
is
computed
as:
+E(
based
on
investor’s
yield
and
spread
view)
∆
P
embedded in their return expectations across virtually any fixed-income security.
Yield
incomeincome,
equals
current
yield
assuming
Active return = Portfolio return – Benchmark index return
Assuming• no
no
reinvestment
yield
income (aka
(aka
current
yield) is
isno
computed as:
as:
–E(Credit losses)
Assuming
reinvestment
income, yield
income
current
yield)
computed
Index-Based Strategies
reinvestment
income
Expectedcredit
return
due torepresent
yield
income
represents
coupon
plusdefault
any reinvestment
Expected
losses
the
probability
(i.e.,income
expected
rate) multiplied by
Annual
coupon
payment
+E(Currency
gains
orloss
losses)
Current
yield
= (i.e.,
interest
relative
a bond’s
price.
Ingiven
the absence
of reinvestment income, yield income is • Total return mandates
the
expected
losstoseverity
losscoupon
default):
Annual
payment
price
Annual
coupon
Current
yield
= currentBond
simply theCurrent
bond’syield
annual
yield. payment
=
Bond price
price
where:
Bond
• Pure indexing (full replication): match benchmark
Yield income
= Annual
payment/Current
price =asCurrent
yield
E(Credit
losses)
=the
E(Default
rate)
× E(Losss
everity)
Roll-down
return
equalscoupon
bond’s
change
the bond
approaches
Rolldown
return
recognizes
the
valuepercentage
change
asprice
abond
bond
approaches
maturity
(“pull to par”)
weights and risk factors by owning all bonds in the
−
B
)
/
B
=
%
change
in
bond
price due
changing
to price
maturity
Rolldown
return
=
(B
1unchanged
0 the
1value
maturity,
assuming
anof
yield
curve.
In
the
absence
of to
default,
the time
bond’s
under
an
assumption
zero
rate
volatility
(i.e.,
unchanged
yield
curve).
Rolldown
return
recognizes
change
as
a
bond
approaches
maturity
(“pull
to
par”)
•
Rolldown
return:
value
change
as
bond
approaches
index with the same weighting.
Rolldown
return
recognizes
theand
value
change
as a= bond
approaches
(“pull to par”)
ΔY%)
+ maturity
(0.5 pull
×C×
E(ΔP based
on value
investor’s
yield
spread
view)
(− D(i.e.,
M × the
approaches
par
as
the
time
tovolatility
maturity
decreases
so-called
toΔY%)
maturity).
under an
an currency
assumption
of zero
zero
rate
(i.e.,
unchanged
yield
curve).
under
assumption
of
rate
(i.e.,
unchanged
yield
curve).
maturity
(pull
tovolatility
par)
Expected
gains
or losses
in
reporting
currency
terms
must
also be considered.
duration equal to 0 and therefore have no effect on the equation.
© 2018 Wiley
swaps increase duration; pay-fixed, receive-floating
DPunable
= ws Dto
wL D
If the manager
were
bonds
with the same duration, bonds of different
s +find
L
swaps
reduce
duration.
duration could be added.
it would
take twice as many bonds if the manager
= wFor
+ (1 − ws )D
s Ds example,
L
• Convexity
management
17 August 2017
used those
with duration
equal to half thatmethods
of the current portfolio, or half as many bonds if
we used those
with
duration
twice
that
of
the
current
portfolio.
Clearly,
theseP,alternatives
where
the
subscripts
indicate
duration
forlarge
the
portfolio
the short-maturity
• Shift bonds in portfolio (difficult
with
portfolios).
have different outcomes
forS,transaction
costs and curve
risk. L.
security
and the long-maturity
security
• Buying callable bonds and MBS (equivalent to selling
Using leverage
in portfolios with credit risk amplifies both credit and liquidity risk. The
convexity).
Using Butterflies
higher duration
of the leveraged portfolio amplifies interest rate risk.
• The
Portfolio
positioning
appropriate
long positionstrategy
depends on whether the manager expects flattening (i.e., long
Although
as liquid
as futures,
swaps
also
beasused
adjustimplied
duration.
Swaps
barbell)
or steepening
(i.e.,
longcould
bullet),
just
itforward
istooutside
the
butterfly
structure:
•notParallel
upward
shift:
bonds
with
yield
have the advantage of being created for any maturity rather than being limited to standard
change
greater
than
forecast
yield change
will enjoy repo
maturities as•areLong
futures.
futures
contract
can be compared
theAwings
(barbell
structure)
and shortto
thea long
bodybond/short
(bullet structure):
as they
roll
down
the yield
curve
(upward
position, andhigher
leverage
can
be compared
long
bond/short
financing
position.
Receive○ return
Flattening
curveto
ora volatile
interest
rates
sloping).
fixed, pay-floating
swaps
are comparable
long bond/short
short-term
○ Buying
convexitytoinaexchange
for lower
yield debt security
position.
○ yield
Parallel
yield curve
increase
• Parallel
change
of uncertain
direction: increase
convexity
by using
strategy.
Because a new
futures position
or newbarbell
swap position
is initiated at a value of 0, there
is an undefined duration for the position itself. Portfolio duration, however, will still be
relatively easy to calculate using money duration or PVBP effects on the portfolio’s equity
primary risk factors; slight mismatch with benchmark value.
weights to achieve a higher return compared to full
© 2018 Wiley
Sizing the swap position resembles sizing a futures position, but will be scaled to
replication.
USD1,000,000 in the absence of any standard contract size (such as with the standard
Active management:
aggressive mismatches with
FI
contract size of bond futures). After determining the desired PVBP of the equity portfolio,
c11.indd 237
• Usingthebutterflies:
longrequired
the wings
(barbell)
and short
benchmark weights and primary risk factors to achieve
we can determine
size of the overlay
to provide
that additional
PVBP.the
There
body
(bullet)
if flattening
volatile
rates,pricing
may be a slight
difference
between
swap sizingcurve,
and futures
sizing,interest
because futures
outperformance.
reflects cheapest-to-deliver
bonds, whereas
swapsyield
do not.curve increase; short
buying convexity
or parallel
• Enhanced indexing: sampling approach to match
Currency
losses
occur
when
the asset
currency
against
the reporting currency.
Rolling
return
=currency
Yield
income
+ Rolldown
Note: Credit
losses
and
gains
or
lossesdepreciates
are return
discussed
elsewhere.
B −
B0 + Rolldown return
Rolling return
return
Yield
income
return
= 1 income
Roll-down
Rolling
== Yield
+ Rolldown return
Limitations
of the model
include:
B0
Effect of Leverage
on the
Portfolio
Expected price change due to change in the yield or spread depends on the bond’s modified
duration
and
convexity,
or
effective
duration
and
convexity
in
the case
with
options:
Expected
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where: involves using borrowed capital to enhance return. Leverage
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2018
Wiley
Structured
notes
allow
cost-efficient
packaging
risks
or
bets:
VE = Equity
balancing the position between cash flow reinvestment
duration
is used
in this variation
and falling rate scenarios.
 Portfolio
return  ofrIthe
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+ VB ) − rB VB
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2018 Wiley
Wiley
VB = Borrowed
©
rP =  amount
=
and
market
price
volatility.

• Inverse floaters have coupon rates that rise as the reference rate falls, and may be
 Portfolio equity 
VE
leveraged to several times the reference rate change.
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•7 March
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135
= rI + Bcontribution
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• Deleveraged floaters have coupon rates that rise as the reference rate rises, but at a
in a positive
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leverage.
environments.
7 March 2018 3:10 PM
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7 March 2018 3:10 PM
fraction of the reference rate change.
Risk considerations
• Higher convexity and liquidity.
• • Ratcheting
floaters increase directly with the reference rate, but specify increasing
Leverage
Using Futures
• where
Leverage
with futures
rI = investment asset return, rB is the cost of funds, and VE and VB are
floor
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the values of equity and borrowing, respectively. Therefore, the numerator
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borrowing costs.
Credit Strategies
Yield Curve Strategies
• Stable yield curve strategies
© 2018 Wiley
Securities
Lending
Methods
of Leverage
Futures contracts
allow
large positions
to be
controlled
with
little rate
margin (i.e., equity).
Rebate rate
= Collateral
earnings
rate
− Security
lending
Leverage is the exposure (i.e., position size greater than margin) normalized for the margin
amount:
migration risk, spread risk.
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Wiley’s CFA Program Exam Review
®
• Spread duration (measure of spread risk): percentage
• Returns-based: regressing portfolio returns on
companies at a discount to intrinsic value; capturing
increase in bond price for a 1% decrease in spread.
returns of a set of securities indices (betas are the
gains from debt structuring.
portfolio’s proportional exposure to the particular style
• Credit spread measures
• Compensation to fund manager of private equity fund
represented by index).
consists of management fee plus incentive fee (carried
• G-spread: bond’s yield to maturity less interpolated
•
Price
inefficiency on the short side
interest).
yield of correct maturity benchmark bond.
Fixed-inCome aCtive management: Credit StrategieS
• Restrictions to short selling.
• Benchmarks: IRR, benchmarks for VC funds and buyout
• I-spread: uses swap rates rather government bond
funds provided by Cambridge Associates and Thomson
• Management’s tendency to deliberately overstate
yields.
Fixed-Income
Active Management: Credit Strategies
Venture Economics.
profits.
• Z-spread: spread added to each yield-curve point so
Excess Return on Credit Securities
• Commodities
• Sell-side analysts issue fewer sell recommendations.
that PV of bond’s cash flows equals price.
• Direct investment: purchase of physical commodities
• Option-adjusted spread (OAS) for bonds with
• Sell-side analysts are reluctant to issue negative
XR ≈ (s × t ) − ( ∆s × SD)
Fixed-inCome aCtive management:
Credit StrategieS
and commodity derivatives.
embedded options: spread added to one-period
opinions.
• Indirect investment: companies specializing in
forward rates that sets arbitrage-free value equal to
• Sell disciplines
where: Fixed-Income Active Management: Credit Strategies
commodity production.
price
• Substitution: opportunity cost sell and deteriorating
s = spread at the beginning of the measurement period
• Return
Excess
and expected
• Energy and precious metals provide significant
t = holding
period
(i.e., fractional
portion ofexcess
the year)return on credit
fundamentals sell.
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onreturn
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duration of the bond
securities
inflation hedge.
• Rule-driven: valuation-level sell, down-from-cost sell,
• Benchmarks: RJ/CRB, S&P GSCI, DJ-AIGCI and S&P CI
≈ (s ×Return
t ) − ( ∆s on
× SD
)
up-from-cost sell, target price sell.
AlternAtive investments
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Excess
Credit
Securities
are indices based on futures prices.
Equity Portfolio
Portfolio ManagEMEnt
ManagEMEnt
• Semiactive equity strategies
Equity
• Hedge funds
where: EXR ≈ (s × t ) – ( ∆s × SD) − (t × p × L )
• Derivative-based semiactive equity strategies:
• The Sharpe ratio can be gamed. The reported Sharpe ratio can be increased without
s = spread at the beginning of the measurement period
• investment
Broad range
strategies
exposure to equity market through derivatives and
the
reallyof
delivering
higher risk-adjusted returns by five methods:
t = holding period (i.e., fractional portion of the year)
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Core–Satellite
• Bottom-up
to credit strategy (security
where:
1.• Lengthening
the measurement
interval.
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structure
consists of management fee
enhanced return through non-equity investments, e.g.
SD
= spread
duration of approach
the bond
p = annual
probability
of
default
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the
monthly
returns
calculating
the standardmark
deviation from the
selection): for two issuers with similar credit risks,
include
high-water
fixed
income.
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core–satellite
portfolio
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constructed when
when applying
applying the
the optimization
optimization to
to aa group
group of
of equity
equity plus incentive fee and maybut
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portfolio
is
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loss
monthly
returns
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compounded).
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on
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purchase bond with greater spread to benchmark rate. managers
managers• that
that
includes indexers,
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and
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managers,
judged by
by their
their
and
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rate.
includes
enhanced
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active
judged
Stock-based
enhanced
strategies:
portfolio
information ratios.
ratios. Index and
and semiactive
semiactive managers
managers constitute
constitute the
the core
core holding,
holding, and
and active
active 3. Writing out-of-the-money puts and calls on a portfolio.
• Top-down approach to credit strategy: macro approach information
returns.
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infrequent marking to
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in hedge
fundderivative
indices structures,
due to: selection
looks Index
like
benchmark
in those
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managers represent
represent
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opportunistic
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satellites
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core,
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to achieve
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of illiquid
and pricing weighting
models that understate
monthly gains or
to
determine
Enhanced-index
portfolio
managers
are
essentially
active
managers
who
build
portfolios
criteria,
style assets,
classification,
scheme,
the
manager
explicitly
wishes
to
bet
on
(within
risk
acceptable level
level of
of active
active return
return while
while mitigating
mitigating some
some of
of the
the active
active risk.
risk. The
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core should
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acceptable
can reduce reported volatility.
aresemble
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control.
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information
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value.
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investor’s
benchmark
the asset
asset ratio
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while
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bias,
generate
alpha.
resemble the
investor’s
benchmark
for
the
class,
while
the
portfolios may
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5.
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extreme
returns
that
increase
the
standard
deviation.
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Law ofasset
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that:
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benchmarked
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benchmarked
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backfill bias.
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ratio fund
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standard deviation
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performance
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evaluate
such
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useful to
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divide their
their total
total active
active return
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two components:
components:
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IR such
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ratio
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active return
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= Manager’s
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return −
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return vs cash).
and when returns are asymetrical/skewed or serially
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portfolio:
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−
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return
=
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normal
benchmark
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correlated).
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constitute
core holding while active managers represent
benchmark
benchmark
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information
coefficient [IC]) multiplied by the square root of the investment discipline’s
than credit markets).
satellites.
risk-free rate)/Downside deviation
breadth, which
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manager’s
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portfolio) represents
represents
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securities
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of
year.
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about
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which
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select
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portfolio.
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investor’s benchmark
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manager normally
might
select
for
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awhich
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uses
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of
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or
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specified period of time. The higher the gain-to-loss ratio (in absolute value), the better:
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normal
benchmark
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approach
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ratio
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manager’s
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risk
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the
standard
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of
true
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active return
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normal
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risk that
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manager’s
manager’s
risk
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the
deviation
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technique
generates
positive
alpha may
become
obsolete
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investors Gain-to-loss ratio = (Number months with positive returns / Number months
patterns and using scenario analysis (historical and total
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benchmark
total active
active
risk,
reflecting
both
true and
and misfit
misfit
risk, is:
is:
reflecting
true
risk,
with negative returns) × (Average up-month return /
try benchmark
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it. –both
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hypothetical).
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modelsrisk
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• Total active
EQ
EQ
future.
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secular
changes,
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effectiveness
of
the
past
as
a
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total
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+ (Manager’s
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active risk)
risk)22 +
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“misfit” active
active risk)
risk)22
• Hedge fund structure or private equity fund structure.
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a Portfolio of Managers
Managed futures are private pooled
investment
vehicles that can invest in cash, spot, and
Management
• Risks: event risk,Risk
market
liquidity
risk, market risk,
as ABSs, MBS, CDOs and covered bonds
derivative markets and have the ability to use leverage in a wide variety of trading strategies
J-factor
judicial
precedents
ondistinguishing
bankrupt difference
When
developing
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asset allocation
policy, the
investor seeks
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a group
of toas:hedge
similar
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with (past
which EQ
they
are often
grouped. The
The
most
accurate
measure
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the
computed
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measure
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computed
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ratio
as measure
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equity
managers
within
the equity
allocation
who
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given
level ofas:
proceedings).
between
hedge
funds and managed futures is that managed futures trade exclusively in
adjustedbyperformance
active risk determined
the investor’s level of aversion to active risk:
• Improved portfolio diversification.
derivatives markets whereas hedge funds tend to be more active in spot markets while using
rP = wfor
w2r2
1r1 +
futures markets
hedging.
RISK MANAGEMENT
Manager’s “true”
“true” active
active return
return
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of managers:
bonds.
IR = Manager’s “true” active risk
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Managed Futures Market
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liquidity, asset price,
σ 2P = w12 σ12 +risks:
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2 w1w2ρσ1credit,
σ2
U A = rA − λ A σ 2A
rate,areinterest
rate.
Managedexchange
futures programs
an industry
consisting of specialist professional money
Completeness fund
fund 37
Completeness
managers.
In the United States, such programs are run by general partners known as
© Wiley 2018 all rights reserved. any unauthorized copying or distribution will constitute an infringement of copyright.
where:• Non-financial risks: operational, model, settlement
where:
commodity pool operators (CPOs), who are, or have hired, professional commodity trading
• Approaches to managing equity portfolios
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completeness fund
fund establishes an
an overall
overall portfolio
portfolio with
with the
the same
same risk
risk exposures
exposures as
asrPthe
the
= portfolio
return regulatory, legal/contract, tax, accounting,
(Herstaat),
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utility of the active
return of the
manager
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advisors
(CTAs)
to manage money in the pool. In the United States, both CPOs and CTAs
investor’s overall
overall equity
equity benchmark
benchmark when
when added
added to
to active
active managers’
managers’ positions.
positions. For
For example,
example,
investor’s
• Passive management: try to match benchmark
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of
alternative
investments
active return
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rCommon
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the completeness
completeness fund
fund may
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be constructed
constructed with
with the
the objective
objective of
of making
making the
the overall
overall portfolio
portfolio
the
w = portfolio
weights for assets
1 and 2
performance.
trade-off
between active
risk and active
λA = the investor’s
Association
(a
self-regulatory
body).
• VaR
• Relative
illiquidity
style neutral
neutral
with respect
respect
to the
the benchmark
benchmark while attempting
attempting to
to retain
retain the
the value
value added
added rfrom
from
style
with
to
= returns for assets 1 and 2
return; measures
risk aversionwhile
in active risk terms
• Active management: seek to outperform benchmark the
the active
active•2managers’
managers’
stock selection
selection
ability.
•
Minimum
amount
stock
ability.
σ
=
standard
deviation
for
assets
1 we
and 2expect to lose in a given
Diversifying
potential
σ A = variance of the active return
Types of Managed Futures Investments
by buying outperforming stocks and selling
ρ = correlation
betweenperiod
assets 1 with
and 2 a given level of probability.
reporting
•
High
due 37
diligence
costsis
© Wiley 2018 all rights reserved. any unauthorized copying or distribution will constitute an infringement of copyright.
One
drawback
of
completeness
portfolios
is
that
they
seek
to
eliminate
misfit
risk.
In
seeking
One
drawback
of
completeness
portfolios
that
they
seek
to
eliminate
misfit
risk.
In
seeking
underperforming stocks.
Managed•futures
are skill-based investment strategies like hedge funds and can been
to eliminate
eliminate
misfit
riskspecified
throughby
completeness
fund,
fund
sponsor
is giving
giving
upand
some
of the
the Analytical (variance-covariance) method: assumes
to
misfit
risk
through
aa completeness
fund,
aa fund
sponsor
some
of
• Difficult
performance
appraisal
efficient
frontier
this objective
function
is drawn
in is
active
riskup
active
described
absolute-return
strategies. Managed futures funds share the compensation
Value at as
Risk
(VAR)
• Semiactive management (enhanced indexing): seek The
value added
added
from
the
stock
selection
of the
the
active managers.
managers.
normality
in asset return distributions.
value
from
stock
selection
of
active
return
space.
Oncethe
active
and
semiactive
managers
are in the mix, the investor’s trade-off
•
Informationally
less
efficient
markets
to outperform benchmark with limited tracking risk becomes one of active return versus active risk. The amount of active risk an investor wishes
Miniumum $ VaR = VP × [ E ( RP ) − Zα σ P ]
• Real
estatethe mix of specific managers. For example, an investor wishing to
(highest information ratio).
to assume
determines
EQUITY PORTFOLIO MANAGEMENT
• Approaches to constructing an indexed portfolio
• Full replication: minimal tracking risk but high costs.
268
268
• Stratified sampling: retains basic characteristics
of
•
•
•
•
•
Ai
ALTERNATIVE INVESTMENTS
assume no
riskinvestment:
at all would hold
an index fund.
contrast, investors desiring a high
• active
Direct
ownership
in In
residences,
level of active risk and active return may find their mix skewed toward some combination of
commercial real estate, agricultural land.
where:
294
© 2018 Wiley
higher-active-risk managers with little or no exposure to index funds.
Historical
value method: VaR estimates based on historical
VP = •portfolio
• Indirect investment: real estate companies, REITs,
© 2018
2018
Wiley realizations of past returns.
©
Wiley
E(R
P) = expected portfolio return
ETFs, mutual funds, CREFs, infrastructure funds.
number Carlo
of standard
deviations
at the
confidence
level
zα = •theMonte
method:
uses
a selected
probability
distribution
for
c13.indd 294
7 March 2018
σP = standard deviation of portfolio returns (e.g., 1.65 for 5% and 2.33 for 1%)
• Benchmarks: NCREIF (sample of commercial
index without costs associated with buying all the
stocks.
each variable to randomly generate portfolio returns
c12.indd 268
7 March 2018 3:51 PM
c12.indd 268
7 March 2018 3:51 PM
properties), NAREIT.
• Optimization: seeks to match portfolio’s
risk exposures
and to
compute
VaR based
on the return
simulated
returns.
Note: To convert
to daily
values, divide
annual expected
by 250 trading
days and
• Private equity
(including covariances) to those of the index but can © 2018 Wiley
root of considers
250.
annual expected
standard deviation
(250)0.5, the
• Limitations:
can
tosquare
estimate;
only
267 bebydifficult
be misspecified if historical risk relationships change
• Direct private equity investment is structured as
downside risk; may be based on invalid distributional
(Hint: we expect that the number of standard deviations for a given probability well be
over time.
convertible preferred stock: provides priority for
provided onassumptions.
the exam.)
dividends and liquidation claims over common shares;
c12.indd 267
7 March 2018 3:51 PM
Value style investing: low P/E, contrarian, high yield.
• Stress testing
as a complement to VaR
buyout or acquisition of the common equity will trigger
Growth style investing: consistent growth, earnings
•
Used to identify unusual conditions that would lead to
conversion of convertible prefs into common shares.
momentum.
losses in excess of a threshold.
• Indirect investment primarily through private equity
Market-oriented (blend or core style) investors: market• Can be based on stylized scenarios (historical or
funds
(venture
capital
and
buyout
funds).
oriented with a value bias, market-oriented with a
hypothetical), stressing models, maximum loss
• Formative-stage investment: seed, start-up, first stage
growth bias, growth at a reasonable price, style rotators.
optimization and worst-case scenario analysis.
capital.
Market cap approach: small-cap, mid-cap, large-cap
• Credit risk
• Expansion-stage investment: second stage, third stage,
investors.
• Current credit risk (jump-to-default): risk of ongoing or
pre-IPO (mezzanine) capital.
Investment style analysis
pending default in the immediate future.
•
Buyout
funds
seek
to
add
value
by:
restructuring
• Holdings-based: analyses characteristics of individual
• Potential credit risk: risk of possible default in the
operations
and
improving
management;
purchasing
security holdings.
future.
Wiley © 2019
44
© Wiley 2018 all Rights Reserved. any unauthorized copying or distribution will constitute an infringement of copyright.
Wiley’s CFA Program Exam Review
®
Risk ManageMent applications of DeRivatives
Risk ManageMent applications of DeRivatives
• Credit VaR: minimum expected loss due to a negative creditinterest• Rate
Interest rate options
• Execution costs
option Strategies
DE
event with a given probability during a period of time.
•
Buy
interest
rate
call
option
to
protect
a
future
• Explicit:
commissions, exchange fees, duties and taxes.
interest Rate option Strategies
DE
an interest rate call option is:
• Forwards: counterparty with positive value has credit risk.The payoff ofborrowing
RiskManageMent
ManageMentapplications
applicationsofofDeRivatives
DeRivatives
against interest rate increases. Risk
•
Implicit: bid-ask spread, market impact, missed trade
The payoff of an interest rate call option is:
• Interest rate and equity swaps: potential
risk
is of DeRivatives
Interest rate call option payoff = Notional principal × max (Underlying rate at
Risk credit
ManageMent
applications
opportunity cost, delay (or slippage) costs.
Days
inatunderlying rate
Interest rate call option payoff = Notional principal × max (Underlying
rate
highest during the middle of swap’s life.
DEDE
RiSk MAnAgeMent
MAnAgeMent ApplicAtionS
ApplicAtionS
ofSwAp
SwAp
expiration − Exercise
rate,0) StRAtegieS
×StRAtegieS
•
Volume-weighted
average price (VWAP)
of
Days in#30
underlying
360 rate
Cross-Reference to
to CFA
CFA
Institute
Assigned
Reading
#30
Cross-Reference
Institute
Assigned
Reading
• Currency swap: potential credit risk is highest between
expiration
rate,0)
− Exercise
×
360
•
Advantages:
easy to compute/understand; useful for
option greeks and Risk Management Strategies
DE
Risk
ManageMent
applications
of
DeRivatives
the middle and end of swap’s life.
ExEcution
of Portfolio
DEcisions
• financial
Buy
interest
rate
putcounterparties
option toagree
protect
aExEcution
future
lending
The
payoff
an interest
ratein
put
option
comparing smaller trades in nontrending markets.
of
contract
which
two
totoexchange
aasequence
ofof DEcisions
A swap
is a of
contract
in
which
twois:
counterpartiesagree
exchange
sequence
ExEcution
of Portfolio
Portfolio
DEcisions
The payoff
an reading
interest
rate putapplications
option
is: of
Options
areof
risky
positions.
An
option
trader
does
hold
an option
positon
without hedging
• Options: option buyers hold credit risk.
(or
investing)
transaction
against
interest
rate
declines.
covers
rate
swaps,
currency
swaps,
equity
cash
flows.
This
covers
applications
of interest
interest
ratenot
swaps,
currency
swaps,
equity
ExEcution
of
Portfolio DEcisions
•
Disadvantages: Does not include costs of delayed/
swaps,
and
swaptions.
Interest
rate putwe
option
payoff
principal
= Notional
× max (Exercise
it. To hedge
an option,
need
the hedge
ratio,
also known
as optionrate
delta.
• Managing risk: apply effective risk governance model; use
Execution of Portfolio Decisions
cancelled
trades; misleading
for large
trades; can be
Execution
of
Decisions
Execution
of Portfolio
Portfolio
Decisions
Execution
Portfolio
Decisions
gamed by
delayingof
trades;
not sensitive
to trade size or
(Bid price + Ask price) 
market
conditions.
++ Ask
price
price)
Effective
spread
= 2 ×  Execution price − (Bid
(Bid
price
Ask
price) 
receive
interest
rate
using
interest
Ratefloating
calls with
Borrowing
A pay fixed,
interest
rate swap
swap can
canbe
beviewed
viewedas
asaaportfolio
portfolioofofaalong
longfloatingfloatingEffective
spread
=
2
×
Execution
price
−
2
Effective spread = 2 × shortfall
Execution price
• Sharpe ratio
• Cap:
interest
rate
call options.
using interest
Rate series
calls withof
Borrowing
• Implementation
(IS) − (Bid price +22 Ask price) 
rate bond and a short fixed-rate
fixed-rate bond.
bond. Similarly,
Similarly, aa pay
payfloating,
floating,receive
receivefixed
fixedinterest
interestrate
rateswap
swap
Effective spread = 2 ×  Execution price −
as
ascheduled
portfolio
of
aa long
fixed-rate
bond
and
aafuture,
short
floating-rate
bond.
Based
on
The goal •of Risk-adjusted
this reading is to understand
how
to use forward
and futures contracts toTo
achieve
a
can
be
viewed
of
long
fixed-rate
bond
and
short
floating-rate
bond.
Based
on
When
we
have
a
borrowing
transaction
in
the
we
are
at
the
risk
of
interest
return on
capital
(RAROC)
2
hedge
N
number
of
options,
we
need
N
number
of
stocks.

 a
•
Floor:
series
of
interest
rate
put
options.
When
we have
c a scheduled borrowing transaction in Sthe future, we are at the risk of interest
• IS is the return difference between the return on
Risk ManageMent applicationsthis
of DeRivatives
this
insight,
have
following:
wewhich
have the
the
following:
rate
increases,
which
turnincreases
increases
cost
of debt.
To reduce
this while
risk while
keeping
particular
of risk exposure of an underlying risk factor. Risk factors include market
risk, we
rate insight,
increases,
ininturn
ourour
cost
of debt.
To reduce
this risk
keeping
the the
nt applications
of DeRivatives
•level
Returnrate
over
Interest
rate collar
to protect
a future
borrowing:
buy
notional
portfolio
the actual portfolio’s return,
benefit
of•potential
potential
ratedecreases
decreases
future,
purchase
an interest
rateoption.
call option.
AImplementation
Shortfall
Costs forand
purchases
sector risk,
interest
risk,maximum
currency risk,drawdown
and others. We(RoMAD)
may either reduce our existing
benefitrisk
of
rate
inin
thethe
future,
wewe
maymay
purchase
an interest
rate call
A
Implementation
Shortfall
Costs
for purchases
∆V = 0 =ofofN
S==+Fixed-rate
N cis
∆cisasas
Implementation
Shortfallas
Costs
five-step
sequence
transactions
follows:
S ∆rate
Floating-rate
bond
bond
++sell
[Pay
receive
interest
five-step Floating-rate
sequence
transactions
follows:
bond
Fixed-rate
bond
[Payfixed,
fixed,
receivefloating
floatingfloor.
interestrate
rateswap]
swap]
exposure •(hedging)
or ratio
increase our existing risk exposure (speculation).
interest
cap
and
interest
rate
expressed
a %for
ofpurchases
the investment in the notional
Sortino
Implementation
Explicit
Costs Shortfall Costs for purchases
option greeks and Risk Management Strategies
DE
portfolio.
Explicit
Costs
Today
we
purchase
an
interest
rate
call
option.
The
call
option’s
expiration
should
1.
Today
we
purchase
an
interest
rate
call
option.
The
call
option’s
expiration
should
•
Option
Greeks
Explicit Costs
The
numberequity
of stock
index futures
Fixed-rate
bond
=
Floating-rate
bond
+
[Pay
floating,
receive
fixed
interest
rate
swap]
Managing
Market
Risk contracts needed to achieve the goals is given by the
Fixed-rate
bond
=
Floating-rate
bond
+
[Pay
floating,
receive
fixed
interest
rate
swap]
match
borrowing
event.
TheThe
duration
of the
interest
match the
thetiming
timing
future
borrowing
event.
duration
ofunderlying
the underlying
interest Explicit Costs
∆c ofofa afuture
following expression:
(for purchases)
Options rate
are
risky
positions.
Anpositive
option
trader
does
not
hold
an option
positon
hedging• Explicit costs
Commissions,
taxes, and fees
N
− Ncall
• SofOption
delta:
for
long
call;
negative
for
long
should
match
the
term
of
the
loan.
For example,
in January,
wewithout
c option
rate
of=the
the
call
should
match
the
term
of the
loan.
For example,
in January,
we
taxes, and
Expicit costs = Commissions,
∆Soption
Commissions,
and fees
fees
To hedge
antotooption,
we
need
the
hedge
ratio,
also
as
delta.
decide
borrow
funds
inin
March
for
sixsix
months.
To implement
theoption
strategy,
we should
Expicit
Market risk is measured by beta, so our risk management of an equity portfolio is allit.These
around
S ×taxes,
P
decide
borrow
funds
March
for
implement
theorstrategy,
we ashould
These
two
equations
are
recipe
for
converting
aamonths.
floater
aknown
Expicit costs
costs == Commissions,
put
two
equations
are the
the
recipe
for
converting
floatertotoTo
afixed-rate
fixed-ratebond
bond
orconverting
converting
a
S HH ×taxes,
PHH and fees
buy an interest rate call option on the six-month LIBOR rate in January that matures
Interest rate put option payoff DE
= Notional principal × max (Exercise rate
Days in underlying rate
RiSk MAnAgeMent ApplicAtionS of foRwARD AnD
aafixed-Rate
rate
atto
expiration,0)
− Underlyingloan
× loan
convert aa floating-Rate
floating-Rate
loan
to
fixed-Rate
loan
ERM system; use risk budgeting; reduce or transfer risk. using interest Rate Swaps toto convert
Days
in
underlying rate
360
Underlying
rate at expiration,0)
Change−in
option price
∆c ×
futuReS StRAtegieS
(and Vice Versa)
360
=
=
Option
delta
• Performance
evaluation
Cross-Reference
to CFA Institute Assigned Reading #28
Change in underlying stock price ∆S
RISK MANAGEMENT
APPLICATION OF DERIVATIVES
S H × PH
fixed-rate
bond
aa floater.
an to
interest
rate call option on the six-month LIBOR rate in January that matures
a beta buy
beta measures. The current stock
portfolio has a beta β S , the stock index futures havefixed-rate
Expicit costs =
bond
to
floater.
 V (1 + r )T 
in
March.
S H × PH
indelta
March.
is ainitiation,
functionweofChange
the
underlying
value, as the
value
changes, delta changes
β f , and the
beta of the stock
in borrow
optionasset
c bond
N *ftarget
= Round
 portfolio is βT . We have the following relation: Because
2. Swaps
At
theto
loan
ahead
atprice
the portfolio
spot rate=in∆the
market. If the
using
Adjust
the
Duration
of
aato
fixed-income
=
Option
delta
fq 
2.
At
theto
loan
initiation,
wegogo
ahead
to borrow
at the
spot rateportfolio
in the bond
market.
If the
using
Adjust
the
Duration
of
fixed-income
portfolio

with
it.Swaps
Consequently,
a
previously
constructed
delta-hedged
is
no
longer
hedged
Realized
Profit/Loss
borrowing rate is lower
than the
interest rate call
option’s
exercise
the call option
∆S rate, rate,
Change
inthe
underlying
stock
price
ExEcution
of Portfolio
DEcisions
Realized
Profit/Loss
borrowing
rate
is
lower
than
interest
rate
call
option’s
exercise
the
call
option
Realized Profit/Loss
after
theexpires
underlying
asset
value
changes.
isdebt.
a long
problem
because
requires
portfolio
andviewed
we enjoy
low costItofof
If the
borrowing
rateitisbond
higher
than
An interest
interest
rate worthless
swap
can
be
as
floating/fixed-rate
and
aa
Realized profit/loss (for purchases)
expires
worthless
we enjoy
lowrate,
costthe
ofaacall
debt.
If
thegenerates
borrowing
rate
isthat
higher
An
swap
can
beand
viewed
as aa portfolio
of
long
floating/fixed-rate
bond
and
a than Realized •Profit/Loss
where
of money to be invested, r is the risk-free rate, T ismanager
the
βT S = βVS is
S +the
N famount
βf f
the
interest
rate
call
option’s
exercise
option
ato
payoff
will
torate
monitor
and
rebalance
aofportfolio
hedged
portfolio
frequently.
Option
gamma
measures the
short fixed/floating-rate
fixed/floating-rate
bond.
The
value
an
rate
swap
isissensitive
rate
S × ( PE − PR )
thedelivered
interest rate
call
option’s
exercise
rate, date.
the
call
option
generates
a an
payoff
that will
short
bond.
The
value
ofrepayment
an interest
interest
rate
swap
sensitive
tointerest
interest
rate
investment horizon, q is the futures contract price multiplier, f is the stocksensitivity
index
be
at delta
the
end
of the
loan
Note
that
the
payoff
of
interest
PR )
RPL
= SS ×× ((P
•
Option
gamma:
greatest
for
options
that
are
at-theTo
hedge
N
number
of
options,
we
need
N
number
of
stocks.
changes.
Consequently,
an
interest
rate
swap
has
duration,
just
like
a
bond
does.
of
option
with
respect
to
changes
in
the
underlying
stock
price.
PEE× −−
c
S
trader
Motivations
changes.rate
Consequently,
interest
rate
swap
hasexpiration;
duration,
just
likeit athat
be
delivered
at an
the
end of at
the
repayment
date.
Note
thedoes.
payoff
an interest
RPL
PHPR )
option is not
delivered
theloan
option
rather,
isbond
delivered
one of
time
an integer
representing
the number
of long
stock index
futures
price, and
N *f is
RPL == S ×SS(HP×
•
Managing
equity
market
risk
and
changing
equity
asset
−
money
and
close
to
expiration.
rate
option
is
not
delivered
at
the
option
expiration;
rather,
it
is
delivered
one
time
SHH E× P
PHHPR )
period
after
option
expiration.
Using
the
previous
example,
in
March,
if
the
interest
We solvefutures
for the contracts
number oftofutures
needed to
the target
beta:
RPL
= motivation
Now we
we need
need to
make
two
assumptions:
convertcontracts
a cash position
to reach
an equity
position
or the number
A
trader’s
suggests
trader classifications:
Now
to
make
two
assumptions:
period
after
option
expiration.
Using
the
previous
example,
in
March,
if
the
interest
rate
the call option payoff is paid in September (and
allocation by beta adjustment
S H × PH
∆Vcall
= 0option
= N Sfinishes
∆S + Nin-the-money,
c ∆cChange in option delta
of short stock index futures contracts to convert an existing equity position into not
rate
call
option
in-the-money,
call
optioninpayoff
paida 10-year
in September
induration
March
at
Option
gamma
= expiration).
Costs) motivated—New information can move prices, and traders depend on
1. The
of option
afinishes
fixed-rate
bond is 75% the
of its
maturity
years is
(e.g.,
fixed- (and Slippage (Delay
• Information
a cash position.
1.
The
duration
of
aoption
fixed-rate
bond
isunderlying
75%premium
of its maturity
inasyears
(e.g.,
a 10-year fixedChange
in
stock
price
3. We
need
to
consider
both
the
call
option
as
well
the
time
value
Slippage
(Delay
Costs)
not
in
March
at
expiration).
•
Delay
or
slippage
costs (for purchases)
Slippage (Delay
Costs)
rate bond has a duration of 7.5).
β − βS  S 
quick
execution to capture profits from under- or over‐valued securities before the
rate
bond to
hascost/financing
a duration
of cost)
7.5).call
of the
call option
premium.
should
3.
We need
both
the
option
premium
as
wellWe
asperiod
the time
valuefrom
Nf =  T
Ment applications of DeRivatives
2. (opportunity
The
durationconsider
of
bond
is 50%
of coupon
resetting
inreduce
years
(e.g., a
 
Slippage (Delay
caa floating-rate
∆receive
restCosts)
of the market assimilates the information. These are usually a single security,
2. the
The
duration
of
floating-rate
bond
isthe
50%
of option
coupon
resetting
period
incall
years
(e.g.,from
a
amount
we
on
the
day
of
borrowing
by
the
future
value
of
the
option
 βf  f 
(opportunity
cost/financing
cost)
of
call
premium.
We
should
reduce
N
=
−
N
S
×
(
P
−
P
)
7-year
bond with semiannual coupon payment has a duration of 0.25).
S floating-rate
c
Hblocks. These traders avoid publicity and notoriety so that other
inR large
7-year
floating-rate
bond
with
coupon
payment
has and
avalue
duration
of
= S × ((P
Delaytransacted
premium.
The
value
reflects
the
call
option
premium
anyofand
all0.25).
Sreceive
∆future
As an option
moves
toward
its
expiration,
the
delta
ofthe
anfuture
in-the-money
call
R−P
H)
the amount
we
on
thesemiannual
dayboth
of borrowing
by
the
calloption
option moves
== S ×won’t
Delaytraders
avoid
S PR× −
PHPH )taking the other side of the trade.
interest
on
the
between
option
purchase
and
loan
initiation
Asset Allocation
withsynthetic
futures stock index fund or converting equity toward
premium.
future
value
reflects
bothoption
thethe
call
option
premium
and
any
and
1;
theofdelta
ofcall
anpremium
in-the-money
put
moves
toward
–1;
the
delta
of an out-of-the-Delay
Smotivated—Research
×SS(HHP×
The duration
an The
interest
rate
swapaccrued
is the difference
between
the
long
bond’s
duration
andall
× −P
PHHPH )
• Value
and valuation suggest theoretical price targets. These
• Creating
The number
of stock index
futures contracts needed to achieve the goals is given by the
The
duration
of expiration).
an interest rate
swap
is the difference
the after
long considering
bond’s duration
and
H R
(option
The
net amount
is the
fundsbetween
we
receive
hedging
=
Delay
Clearly, if the target beta βT is zero, N f will be negative, which means we need to sell
stock
interest
on
the
call
premium
accrued
between
the
option
purchase
and
loan
initiation
the short
bond’smovies
duration.toward zero.
money
option
traders purchase
S H × PHsecurities when actual prices fall below the theoretical prices
followinginto
expression:
the short
bond’s
duration.
Because
delta
isexpiration).
a function
ofexample,
the underlying
asset
value,
as the
value
changes, delta changes
costs.
Using
the previous
in March,
we should
reduce
the call
option
cash
Duration
of interest
rate
(option
The net amount
is swaps
the funds we receive after considering hedging
index futures
contracts
neutralize
ourasset
existing
long equity
If the The
targetidea
betais βT •ispremium
Futures
contracts
can betoused
to adjust
allocation
amongposition.
asset classes.
(value). These traders
may make or
infrequent
tradestrade
over a longer
time horizon incost
• Profit/Loss
Unrealized
profit/loss
missed
opportunity
and financing
cost (interest
accrued) between
January and
March from
with it. Consequently,
aprevious
previously
constructed
delta-hedged
portfolio
isoption
nothelonger hedged
Unrealized
(Missed
Trade
Opportunity
Cost)
costs.
Using
the
example,
in
March,
we
should
reduce
the
call
Duration
[Payzero
fixed
andan
receive
floating
interest
rate swap]
= Duration(Floating-rate
bond)
will be
negative
(or positive),
which
meansfunds
smaller For
(or greater)
than the portfolio,
current beta
order to avoid
price movements
away from their
intention.
(Missed
Trade
Cost)
simple.
a given existing
useβstock
futures
contracts
to adjust
theGamma
beta
we receive
in March.
S , N f index
approaches
as
option
moves
expiration,
because
delta
movesUnrealized
toward a Profit/Loss
(Missed
Trade Opportunity
Opportunity
Cost)
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[Payasset
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swap]
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underlying
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is toward
a problem
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a bond)
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and
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T index futures contracts to reduce (or increase) our existing4. At
−
Duration
(Fixed-rate
Liquidity
motivated—Traders
may
need
liquidity
to
fund
other
positions
with more
the
loan
expiration,
we
need
to
pay
off
the
loan,
but
if
the
call
option
was
we
need
to
sell
(or
buy)
stock


of the portfolio
to its target
level and use bond futures contracts
to adjust the modified
V (1 + rbeta
)
constant.
However,
gamma
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manager
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of DeRivatives
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previously
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the loangamma measures the
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whether
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)) ×× ((P
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H
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H
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the
net with
cash
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thethe
loan
cash
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P
P
H
H
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allow us to synthetically lever up/down equity beta as well as bond modified duration. The previously
UPL relinquish
= ( S − SSStheir
H ×positions
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swap] =isDuration
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option
harvested
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) ××(P
PHL − PHin) such securities too quickly.
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isout
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iscash
a combination
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in the previous
− Duration
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the net cash flow,
the future
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• Passive—Index
Option value
is also
sensitive
to the
volatility
of
the
underlying
asset
returns.
− Duration
S Htherefore
× PH are less sensitive to the timing of trades. Indexes themselves
are ready
to usedelta
interest rate
swaps(Floating-rate
to lever upbond)
or lever
horizon,
q is the
price and
multiplier,
f is the stock
index With these properties in mind, we
DE
Change
in option
lower costs,
where weinvestment
independently
handle
thefutures
equitycontract
component
fixed-income
component.
Option vega
captures
the
sensitivity
of
option
price
changes
with
respect
to
changes
in
the
*
Option
gamma
= bond
the number of long stock index down duration
futures
price,on
andtheN following
of
an floating
existing
portfolio
to afixed
target interest
duration. To
achieve
a target
portfolio
Implementation
Shortfall
f is an integer
do
not
consider
transactions
costs, costs,
so to be effective
index, the
traderUPL
•
Use
pay
and
receive
rate
swap
to
•
IS
is
the
sum
of
explicit
RPL, against
delayancosts
and
This section
focuses
tworepresenting
pieces of logic:
stock
313
Changebyinannualized
underlyingstock
stock return
price standard deviation.
© 2018return
Wiley volatility, measured
Implementation
Shortfall
futures contracts to convert a cash position to an equity position or the number duration,
Implementation
Shortfall
must
find other cost advantages.
we
may useduration
an interest rate
swap based
on the following relation:
increase
of bond
portfolio.
(for
sales,
reverse the prices used in the numerator).
of short stock
futures
contracts to convert an existing equity position into
Implementation
Shortfall



βT − βindex
S
+ S (P
+ example,
S ( PL −require
PH )
Commissions
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E − PL )for
types313
of tradersshortfall
may span =more
than one strategy.
Dealers,
aN
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++ SScosts
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
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Long
bond
• Usemoves
pay toward
fixed and
receive
floating
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rate swap
to moves7 MarchOther
LL )) +
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Advantages:
relates
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Pto
+value
PHH ))
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Change
in option
price
As an option
its
expiration,
the
delta of an
in-the-money
call option
H PL
L of
shortfall
c15.indd 313
2018
3:52executions
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quick
to earn
money =
the spread, and willS H
tend
toHtrade
more
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 β f   fS 
=offCommissions
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V
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vega
P ( MDUR
P )=+ NP ( MDUR
S ) = VP portfolio.
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of
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toward
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moves toward –1; the delta of an out-of-theH
Lwilling
L −
PHP
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idea;
tradeoff
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information‐motivated
traders
in=recognizes
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thePH
other
in stock
return
volatility
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H
H
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shortfall
• Changing bond asset allocation
317
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2018
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party
determine
the
timing
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the
trade
in
exchange
for
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their
price,
much
like
money
option
movies
toward
zero.
S
×
P
H of Hexecution costs;
c15.indd 313
7 March
2018 3:52 PM
immediacy
and price; attribution
• or:
Duration management using an interest rate swap
Long stock
+ Short futures = Long risk-free bond
where: passive
traders.
Asset Allocation
withindex
futures
where:
where:
can
be used to optimize turnover and improve
 MDURT − MDURS  B
S = shares
executed
Gamma approaches zero as an option moves toward expiration, because delta moves toward
c15.indd 317
7shares
Marcha2018 3:52
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SS =
executed
N Bf =  can be used
βy
Arbitrageurs,
on the other hand, exploit small price discrepancies in the same asset across
=
executed
Futures contracts
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is
 MDUR − MDUR  options that are at-the-money and close to where:
= shares
hypothetical
SH
performance;
cannot be gamed.
c15.indd 317
7 March 2018
3:52 PM shares executed
MDUR
constant.
However,
 demonstrates
The
first equation
create a stock index fund:
holding
cash (a
f how to fsynthetically
B
NP
= VP  gammaT is greatestP for
different
markets.
Thus,
they are dependent on quick executions at favorable prices.
=
hypothetical
shares
executed
SSexpiration
H
S
=
shares
executed
simple. For a given existing portfolio, use stock index futures contracts to adjust the beta
hypothetical
shares
executed

H
=
hypothetical
price; benchmark
price
P
MDUR

 option will be exercised or not.
H
because
of
the
uncertainty
of
whether
the
S
long
risk-free
bond)
and
buying
stock
index
futures.
The
second
equation
demonstrates
how
to
=
hypothetical
price;
price extensive data collection;
P
•
Disadvantages:
requires
of the portfolio to its target beta level and use bond futures contracts to adjust the modified
= execution
hypothetical
shares
executed
SHH =
price; benchmark
benchmark
P
price
P
Day
traders
typically
seek
to
hold price
positions in momentum securities for a very short
E
create
cash
outportfolio
of equity:
holding
a stock index
andStock
selling
stock
index
execution
price
PHE =
duration
of the
to its
target modified
duration.
index
futures
andfutures.
bond futures
hypothetical
price;
benchmark
price
P
=
execution
price
unfamiliar
framework.
The first expression is the number of stock index futures contracts used to lever up (if
N Sf •value
period, price
but often
accommodate
other
traders
much like
dealers.
when
shares are
not
purchased
at the
hypothetical price
PRE = relevant
is also
particularlyswap
sensitive to the volatility of the underlying asset returns.
Uses
of currency
allow us to synthetically lever up/down equity beta as well as bond modified duration. The Option
=
relevant
price
when
shares
are
not
purchased
P
R
execution
price
=
relevant
price
when
shares
are
not
purchased at
at the
the hypothetical
hypothetical price
price
P
where
MDUR
is
the
modified
duration
of
an
interest
rate
swap,
and
E
R
N
is
negative)
the
portfolio’s
existing
equity
market
risk
to
istechnique
positive)isor
lever
down
(if
=
last
available
valuation
price
P
S
Sf
inL thelast
•Exhibit
Types
traders
not new. It is a combination
of what we covered in the previous two sections, Option vega captures the sensitivity of option price changes with respect to changes P
available
valuation
price
3-1:of
trader
type
byare
Motivation
and Preferences
relevant
price
when
shares
not purchased
at the hypothetical price
PLRL =
= last
available
valuation
price
• Convert
loannotional
in by
one
currency
into
a loan
in another
NP
is the required
principal
tostock
change
the
duration
of
the
achieve
a synthetic
target
equity
The second
expressioncomponent.
is the number of stock
Treasury
where we
independently
handle
theallocation.
equity component
and fixed-income
return
volatility,
measured
annualized
return
standard
deviation.
=
last
available
valuation
price
P
MDUR
to
the
target
duration
of
.
existing
portfolio
duration
trader
type
Motivation
Preference
Holding Period
MDUR
L
bond futures
contracts
used to lever up (if N Bf is positive) or lever down (if N Bf is negative) currency.
P
T
• Option
strategies
Information
Unassimilated information
Time
Minutes/hours
the portfolio’s existing interest rate risk to achieve a synthetic target bond allocation.
 βT − β S   S 
•
Convert foreign
cash
receipts
into
domestic
currency.
316
© 2018 Wiley
Change in option price
Value
Valuation errors
Price
Days/weeks
using
Motivation
NStrategy
Sf = 
Construction
Option vega =
 
β f futures
Liquidity
Divest
securities,
invest
Time
Minutes/hours
 use
  fS contracts to adjust allocations between one bond class and another
Similarly, we can
Change
in stock return volatility
• Usesto of
equity
European options
using Swaps
create
and swap
Manage the Risk of Structured notes
cash, buy things
(e.g., long-term bonds and short-term bonds), or to adjust allocations between one equity class
Covered
Own
share the
andS&P 500
Earn
premium
• Diversify a concentrated portfolio.
Passive
Rebalance (to index)
Price
Days/weeks
and another
(e.g., large-cap
andunderlying
small-cap stocks,
Index,
and the to
Nasdaq-100 Index).
c15.indd 316
ExEcution
Portfolio DEcisions7 March 2018 3:52 PM
309
Interest rate swaps can be used to create and manage leveraged floating-rate
notesof(leveraged
© 2018 Wileycall  MDUR sell
56
Dealers/Day
traders AnyAccommodate
other or
traders
call
on
share.
cushion
losses.
©
Wiley
2018
All
Rights
Reserved.
unauthorized copying
distributionIndifferent
will constitute anMinutes/hours
infringement of copyright.

−
MDUR
B
T
S
• Achieve
international diversification. 56
©
Wiley
2018
All
Rights
Reserved.
Any
unauthorized
copying
or
distribution
will
constitute
an
infringement
56
N Bf = 
βy
floaters) and
inverse floaters.
©
Wiley
2018
All
Rights
Reserved.
Any
unauthorized
copying
or
distribution
will
constitute
an
infringement of
of copyright.
copyright.

Using futures
contracts,
we fcan
also
exposure
to an asset
class in advance
of actually
MDUR

 fgain
B
Protective
Own
underlying
share and
Downside
protection
Traders
in alternative
assets
tend to follow
similar
patterns (with
the exception
of not of copyright.
56and bonds. © Wiley •2018
All
Rights
Reserved.
Any
unauthorized
copying
or
distribution
will
constitute
an
infringement
Trading
tactics
•
Change
asset
allocation
between
stocks
committing
asset
class.
Essentially we buy futures
on that asset class
Exhibit 4-1: trading objectives
putfunds to thatbuy
put
on share.
with contracts
upside potential.
Leveraged floaters: A firm intends to issue a leveraged floater with a notional principal of FPhaving a counterpart to day traders). However, alternative assets tend to be less liquid and
indd 309
7 March 2018 3:52 PM
may require greater holding periods.
• Swaptions
Purpose
costs
Advantages
Disadvantages
rate of kL, where k is the leverage factor (e.g., 2.5) and L is the LIBOR rate. Focus
The first expression
is theBuy
number
index
futures
contracts
used to leveron
up (if
N Sf and a floating
Speculation
stock
Bull
callofatstock
lower
strike
and
Liquidity at
Immediately
Upsetting
Guaranteed
Information
negative)
portfolio’s
market
is positive)spread
or lever down sell
(if Ncall
stepsswaption:
to the process.
Sf is at
higherthe
strike
(can existing
priceequity
increase
inrisk
a to There are •three
Payer
holder has right to enter interest rate
Forward and Futures
Swaps
Options
achieve a synthetic target equity allocation. The second expression is the number of Treasury
useto puts
range
positive) or lever
down (if N Bf is negative)
bond futures contracts used
lever instead
up (if N Bfofiscalls)
the portfolio’s
to achieve
a synthetic
bond allocation.
Bearexisting interest
Buy rate
callrisk
at higher
strike
and target
Speculation
on stock
swap as fixed-rate payer (in-the-money when interest
any cost
execute large
blocks
1. To achieve the goal, the firm enters into an interest rate swap with a notional principal
ratesThe
gofirm
up).chooses to be the fixed rate (FS) payer and floating rate receiver.
of k(FP).
Need
Low level
spread
sell call at lower strike (can
price
316decrease in a
The
firm pays (FS)k(FP)
and receives
where
FS is the
fixed rate in©the
2018 Wiley
trustworthy
advertising on
• Receiver
swaption:
holder(L)k(FP),
has right
to enter
interest
Similarly, we can use futures contracts to adjust allocations between one bond class and another© 2018 Wiley
16 swap initiation.agent
use puts instead of calls)
range
interest rate swap to make the interest rate swap have a zero value at
large trades;
(e.g., long-term bonds and short-term bonds), or to adjust allocations between one equity class
rate as fixed-rate receiver (in-the-money when interest
possible
FS is the price of the swap.
and another
(e.g., large-capBuy
and small-cap
stocks,strike,
the S&P 500 Index,
Nasdaq-100
Betand
onthe
low
volatilityIndex).
Butterfly
call at lower
hazardous
rates
gopasses
down).
2.
The
firm
now
through
the
cash
inflow
from
the
interest
rate
swap
(L)k(FP)
spread
buy call at higher strike, sell
c15.indd 316
7 March 2018 3:52 PM
situation
r31.indd 16
as 7interest
payments
of the leveraged floater with a notional principal of FP and a
Using futures contracts, we can also gain exposure to an asset class in advance of actually
March 2018 3:52
PM
two calls at strike halfway
Costs are not
Certain
committing funds to that asset class. Essentially we buy futures contracts on that asset class
floating rate of kL.
important
execution
between strikes of long calls
3. Now the issuer may sell a leveraged floater with a notional principal of FP and a
(can use puts instead of calls)
floating rate of kL and use the funds to buy a fixed-rate bond to (partly) offset the Advertise to
Large trades
fixed-rate payments in the interest rate swap (FS)k(FP). The leveraged floater is
Collar
Buy stock, buy put and sell
Downside protection
draw liquidity without
information
successfully engineered.
call. (zero-cost collar if
and with limited
Straddle
Strap
call and put premiums are
the same)
Buy call and put with same
strike
Buy two calls and one put
with same strike
Strip
Buy one call and two puts
with same strike
Strangle
Buy call and put, put has
different exercise price
Bull call spread and bear
put spread
Box
spread
TRADING, MONITORING
AND REBALANCING
upside
Execution of Portfolio Decisions
Inverse floaters: A firm intends to issue an inverse floater with a notional principal of FP andLow
a cost
whatever the
floating rate of (b – L), where b is a constant rate (e.g., 8%) and L is the LIBOR rate. There are
liquidity
Bet on high volatility three steps to the process.
© 2018 Wiley
• Average Effective Spread
Bet on high volatility
(stock price rise more
likely)
Bet on high volatility
(stock price fall more
likely)
Bet on high volatility
318
Replicate risk-free
return or make
arbitrage profit
c15.indd
318
advantage
Indifferent to
timing; non‐
informational
trades
supply/demand
execution
leakage and
market impact
possible
Lose trade control
Higher
commissions;
information
leakage
Price
improvement
due to ability
to wait
Spread; potential
price impact
Market‐
determined
price
Market‐
determined
price
Lose trade control
Favorable
price possible
Execution
uncertainty;
possible
movement away
from price
point results in
“chasing” the
market with limit
orders
© 2018 Wiley
13 August 2017 12:00 AM
High
(organizational
and operational)
cost
High search and
monitoring costs;
low commission
Possible front
running
1. To achieve the goal, the firm enters into an interest rate swap with a notional principal
AESThe
2 × (Execution
MQ) rate (FS) receiver and floating rate payer. The
of FP.
chooses to price
be the− fixed
Buy =firm
issuer pays L(FP) and receives (FS)(FP), where FS is the fixed rate in the interest
= 2make
× (MQ
Execution
Sell to
rateAES
swap
the−interest
rateprice)
swap have a zero value at swap initiation. FS is the
price ofMQ
the=swap.
(Bid + Ask) / 2
• Algorithmic trading
2. The firm now issues an inverse floater with a notional principal of FP and a floating Automated trading
rate of (b – L). Interest payment is (b – L)FP. Cash inflow from the interest rate swap• Simple logical participation strategies: VWAP strategy
7 March 2018 3:52 PM
• Market quality
• Liquidity: resilience, quote depth, narrow bid-ask
LoS 31l: Explain the motivation for algorithmic trading and discuss the
toofmatch
expected
volumeVol
for6, the
stock; TWAP
pp 40–44
basicaims
classes
algorithmic
trading strategies.
strategy breaks order up for exposure at various time
© 2018 Wiley
spreads.
Where
very large during
transactionsthe
makeday;
more sense
to execute in order‐driven
markets
with
periods
percentage
of volume
strategy
the help of a broker, smaller trades with generally adequate liquidity may find less costly
• Transparency: pre-trade and post-trade
makes
as somemarkets.
% of The
overall
market
execution
using trades
dealers in quote‐driven
evolution
of marketsvolume
has also leduntil
to
automated
trading (i.e., non‐manual trading) such as:
completed.
• Assured completion: trade completion is guaranteed.
7 March 2018 3:52 PM
•
•
Algorithmic trading—Based on quantitative rules and subject to user defined
constraints and benchmarks (e.g., portfolio trades for an entire basket of
Wiley ©
securities); and
Smart routing—Automatically routing trades to the venue with lowest cost
execution.
2019
Wiley’s CFA Program Exam Review
®
Performance evaluation
Performance evaluation
evaluation
Performance
• Implementation shortfall (arrival price) strategies:
PERFORMANCE EVALUATION
minimize execution costs by front-loading executions
into the early part of the trading day.
• Opportunistic strategies: involve passive holdings and
opportunistically seizing liquidity.
• Specialized strategies: smart routing, “hunter”
strategies and benchmark-based algorithms.
• Characteristics of a valid benchmark: unambiguous,
investable, measurable, appropriate, reflective of
current investment opinions, specified in advance,
Performance evaluation
acknowledged.
• Types of benchmarks: absolute return, manager
universe, broad market index, investment style index,
factor-model-based, return-based, custom securitybased.
• High quality benchmark: low systematic bias; minimal
tracking error; similar risk exposure to portfolio;
significant overlap of holdings with portfolio; low
turnover; positive active positions.
• Macro attribution (fund sponsor level)
• Net contributions
• Risk-free rate
• Asset categories
• Benchmarks
PERF
PERF
PERF
• Investment managers
• Allocation effects
• Micro attribution (investment manager level)
micro attribution
• Explains three components of value-added return
Micro
attribution is often
performed atthe
the investment
level.portfolio
It focuses on value(difference
between
returnsmanager
on the
and
added return:
the benchmark).
PERF
Monitoring and Rebalancing
• Rebalancing disciplines
• Calendar rebalancing: simple but unrelated to market
behavior.
• Percentage-of-portfolio (or interval) rebalancing:
•
•
•
•
provides tighter control and triggers rebalancing
related to market performance.
Calendar and percentage-of-portfolio: rebalancing
occurs at calendar intervals only if corridors have been
exceeded (lower monitoring and rebalancing costs).
Equal probability rebalancing: corridors are based on
a common multiple of asset class standard deviation;
does not address transaction costs or correlations.
Tactical rebalancing: less frequent rebalancing during
trending markets; more frequent rebalancing during
reversals.
Optimal corridor width of asset class
Factor
Effect
Higher transaction costs
Wider corridor
Higher risk tolerance
Wider corridor
Higher correlation with rest of
portfolio
Wider corridor
Higher volatility of asset class
Narrower corridor
Monitoring and rebalancing Higher
volatility of remaining
portfolio
Narrower corridor
buy‐and‐hold
cPPI
Underperform
Outperform
Underperform
Outperform
Neutral
Outperform
Outperform
Underperform
Outperform
Concave
Selling insurance
0<m<1
Linear
None
m=1
Convex
Buying insurance
m>1
above
and beyond rates;
the exposure
of normal
benchmark
exposures. in
Theforward
incremental exposure
forward
return
due
to changes
rates.
in each risk factor is a strategic decision of the investment manager as a result of active
management.
342 return
Contribution of the investment manager:
•
from interest
rate management;
fixed-income
micro attribution
1. Effect of the external interest environment:
• Return on the default-free benchmark, assuming no change in forward rates
• Return due to changes in forward rates
2. Contribution of the investment manager:
• Return from interest rate management
342
• Return from sector/quality management
• Return from selection of specific securities
® trading activities
• Return from
1.
2.
3.
4.
2
reporting requirements and recommendations of GIPS.
•
•
results.
•Minimize
Be ablemanager
to identify
and correct errors in a performance
turnover.
© 2018
2018 Wiley
Wiley
©
Include
relevant nonperformance
in the
manager review process.©
presentation
that claimsinformation
to be GIPS
compliant.
2018 Wiley
Reduce the following two errors:
•
•
Type I error: keeping (or hiring) managers who do not have investment skills.
Type II error: firing (or not hiring) managers who do have investment skills.
Lower transactions costs;
More rapid implementation of systemic exposure versus individual security
positions; and
Minimal impact on the underlying strategy because it does not require trading
individual positions.
As the result of liquidity limits and the lack of replicable positions, managers tend to use
some combination of cash market and derivatives strategies.
7 March 2018
The secret is out.
341
c17.indd 341
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38
7 March 2018
77 March
March 2018
2018
© 2018 Wiley
Interest rate management effect
Sector/quality effect
Security selection effect
Trading activity
© 2018 Wiley
Futures and total return swaps are often used for rebalancing due to many potential
advantages:
2.indd
5. Information
Information ratio
ratio RA − rf
5.
Information
5.
Sharpe
ratioratio
=
• Ex post
Aalpha
Aand Treynor measure provide the same
σ
RA − RB on
conclusion
manager performance as they are based
RAA −
RBB
−R
IRA = R
IR
=
A = σ
2 evaluation
A
AA−− BB
Performance
on systematic
risk.
4. MIR
σ
σ
A− B
c17.indd 342
Fixed-income attribution analysis focuses on the manager’s performance
in addressing four
factors within the manager’s control:
derivatives
38

M
 σ
M
σ
 σ M

Wiley’s CFA Program Exam Review
Cash market transactions involve buying or selling individual security positions or ETFs.
Cash market trades will often require more time to execute and may require higher capital
commitments than derivatives. Tax considerations may favor cash market trades over
derivatives trades if there is no equivalent derivatives trade on an after‐tax basis, or if the
jurisdiction has unfavorable tax consequences for the derivatives trade (as in the U.S.).
Even for non‐taxable portfolios, individual derivative exposures may be limited by policy
or a particular asset class may not be replicated by any derivatives.
•
342
342
return from sector/
The total return of a fixed-income portfolio is made up of the following two groups of
c17.indd 342
components:
c17.indd
c17.indd 342
342
Portfolio managers often have two choices in portfolio rebalancing decisions; executing
cash market trades (buy/sell decisions) or using a derivatives overlay. Choices between
these two methods depend on the assets owned, the tax consequences, and available
derivatives.
•
•
4. M
M 22
4.
M•2 M2RA − rf
4.
TA =
β A
 RA − rf
RAA −
− rrf
M 222 = rf +  R
M
=
r
f
M = ratio
rff +
+  σ
3. Sharpe
AAA
 σ
σ
GLOBAL INVESTMENT PERFORMANCE
STANDARDS
constant Mix
Executing the Rebalancing Strategy
cash Markets
2. Treynor
Treynor
measure
• Treynor
measure
2.
measure
2.
Treynor
measure
risk-adjusted Performance measures
RA − rf
RA −
− rrf
T =R
TAAA =
= areAβ fivef risk-adjusted performance measures:
The following
T
β AA
β
A
1. Ex post alpha
3. Sharpe
Sharpe ratio
ratio
3.
• Sharpe
3.
Sharpe
ratio ratio
Rt − r ft = α + β( RMt − r ft ) + εt
RA − rf
− rrf
RAA −
Sharpe ratio A = R
Sharpe ratio
ratio AA =
f
Sharpe
= σ
AAA
σ
2. Treynor measure
σ
ratioand
and
M provide
the same
conclusion
Note that
that •the
theSharpe
Ex post
post alpha
alpha
Treynor
measure provide
provide
the same
same
conclusionon
about manager
manager
Note
Ex
and
Treynor
measure
the
conclusion
about
 Ralpha
 Treynor
thatbecause
the Ex
post
measure
provide
the
same
conclusion
about
manager
A − rfand
Note
on systematic
rankings
they
areperformance
based
risk.
The
Sharpe
ratio
and
M 222 risk.
also
provide
the
as they
areSharpe
based
on
total
M 2manager
= rf +
 are
 σ Mon
rankings
because
they
are
based
on systematic
systematic
risk.
The
ratio
and
M
also
provide
the
A based
rankings
because
they
risk.
The
Sharpe
ratio
and
M
also
provide
the
σ


same conclusion about
about manager rankings
rankings because they
they are based
based on total
total risk.
same
• Information
ratio
same conclusion
conclusion
about manager
manager
rankings because
because they are
are based on
on total risk.
risk.
5. Information
ratio
Performance
Evaluation
Performance
Evaluation
Performance
Evaluation
S
S
S
rv = rP − rB = ∑ [( wPi − wBi ) × (rBi − rB )] + ∑ [( wPi − wBi ) × (rPi − rBi )] + ∑ [ wBi × (rPi − rBi )] Quality control R
A − RB
charts
are one
one effective
effective and
and visual
visual means
means of
of presenting
presenting the
the performance
performance
IR
=
A
Quality control
control
charts
are
i =1
i =1
i =1
Quality
are
one
and visual
means
of presenting
the performance
manager
σ
A− B
of an
an investmentcharts
overeffective
time. It uses
uses
statistical
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to systematically
evaluate
of
manager
over
time.
methods
to
of
an investment
investment
manager
over
time. It
It retention
uses statistical
statistical
methods
to systematically
systematically evaluate
evaluate
performance
data
and
assist
in
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or
removal
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performance data
data and
and assist
assist in
in making
making retention
retention or
or removal
removal decisions.
decisions.
performance
S
Note
that
the
Ex
post
alpha
and
Treynor
measure
provide
the
same
conclusion
about
manager
• First
term
is
pure
sector
allocation
effect.
•
Manager
continuation
policies
Pure selection allocation = ∑ [( wPi − wBi ) × (rBi − rB )]
Managerbecause
continuation
policies
(MCPs):
rankings
they are
based(MCPs):
on systematic risk. The Sharpe ratio and M 2 also provide the
i =1
Manager
policies
Manager
continuation
policies
(MCPs):
• Second term is allocation/selection
interaction effect. same
•continuation
Typeabout
I error:
keeping
hiring)
do not
conclusion
manager
rankings(or
because
theymanagers
are based onwho
total risk.
• Retain
Retain
managers
with investment
investment
skills.
have
investment
skills.skills.
• Third term is stock selectionS effect.
managers
with
••• Retain
managers
investment
skills.skills, and do so before they produce negative
Remove
managerswith
without
investment
Performance
Evaluation
Allocation / selection interaction effect = ∑ [( wPi − wBi ) × (rPi − rBi )]
Remove
managers
without
investment
skills, and
andmanagers
do so
so before
beforewho
they produce
produce
negative
• Type
II error:without
firinginvestment
(or not hiring)
do negative
•• Remove
managers
skills,
do
they
i =1
• Fixed income micro attribution
results.
results.
results.
have
investment
skills.
Minimize
manager
turnover.
charts
are one
effective
and visual means of presenting the performance
• Decomposes total return of a fixed-income portfolio Quality
••• control
Minimize
manager
turnover.
Minimize
manager
turnover.
S
Include relevant
relevant
nonperformance
information
in the
the manager
manager
review process.
process.
of an•• investment
manager
over
time. It uses
statistical methods
to systematically
evaluate
Include
nonperformance
information
in
review
intoSelection
two effect
groups
components: effect of external
• Include
nonperformance
information
in
thedecisions.
manager review
process.
= ∑ [ wof
Bi × (rPi − rBi )]
performance
datarelevant
and assist
in making retention
or removal
i =1
interest environment
(out of manager’s control) and Reduce the following two errors:
Reduce
following
errors:
Reduce the
the
following two
two
errors:
Manager
continuation
policies
(MCPs):
contribution of the investment manager.
fundamental factor models
•
Type
I
error:
keeping
(or hiring)
hiring) managers
managers who
who do
do not
not have
have investment
investment skills.
skills.
PERF
Type II error:
error: keeping
keeping (or
(or
•
Effect of external interest environment: return on
••• Retain
Type
hiring)
managers
who
dodo
nothave
haveinvestment
investmentskills.
skills.
Type
II
error:
firing
(or
not
hiring)
managers
who
•
managers
with
investment
skills.
Fundamental factor model micro attribution is performed to analyze active returns in the
Focus
on required
disclosures,
and
presentation
andskills.
• • Type
Type
II error:
error:
firing (or
(or not
not
hiring)
managers
who
do have
have investment
investment
skills.
II
firing
hiring)
managers
who
do
the
benchmark,
notochange
in
context
of adefault-free
factor model. The analysis
identifies theassuming
portfolio exposure
these risk factors
•• Remove
managers
without
investment
skills, and
do
so before
they produce
negative
• exhibit
Rebalancing
strategies
3-2: summary
of Rebalancing approaches
Market conditions
UP—Momentums
FLAT—Reversals
DOWN — Momentums
Implications
Payoff curve
Portfolio insurance
Multiplier
quality management; return from selection of specific
risk-adjusted Performance
Performance measures
measures
risk-adjusted
Performance
measures
risk-adjusted
securities;
return
from trading activities.
The
following
are
five
risk-adjusted
performance measures:
measures:
The following
following
are five
five risk-adjusted
risk-adjusted
performance
• Risk-adjusted
performance
measures
The
are
performance
measures:
1.
Ex
post
alpha
•
Ex
post
alpha
1. Ex
Ex post
post alpha
alpha
1.
R − r ft = α + β( RMt − r ft ) + εt
Rttt −
− rr ftft =
=α
α+
+β
β(( R
RMt
− r ft )) +
+ εεtt
R
Mt − r ft
13 August 2017 12:00 AM
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