# salt-cfa-level-3-formulasheet-2023

```CFA&reg; Level III
Formula Sheet – 2023 Syllabus
ECONOMICS
ECONOMICS
CAPITAL MARKET EXPECTATIONS:
CAPITAL MARKET
FRAMEWORK
ANDEXPECTATIONS:
MACRO
FRAMEWORK AND MACRO CONSIDERATIONS
CONSIDERATIONS
A Decomposition of GDP Analysis to CME
- One commonly used framework decomposes a
country’s aggregate trend growth rate into two
parts: labor inputs and labor productivity.
- The components of the labor input are:
o Growth in potential labor force size.
o Growth in actual labor force participation.
- The components of labor productivity are:
o Growth from increasing capital inputs.
o Growth in total factor productivity (TFP).
Anchoring Asset Returns to Trend Growth
The trend GDP growth rate is linked to equity
prices, as captured by the following formula:
ππ = πΊπΊπΊπΊπΊπΊ &times; ππ &times; ππππ
where
- V: aggregate value of equity
- GDP: level of nominal GDP
- S: share of earnings relative to
the overall economy
- PE: market price-to-earnings ratio
Monetary Policy
Taylor Rule
To determine where the policy rate should be set,
central banks can use the Taylor rule:
ππ ∗ = ππ&quot; + πΌπΌ# + .0.52πΊπΊπΊπΊππ# − πΊπΊπΊπΊππ\$ 4 + 0.52πΌπΌ# − πΌπΌ\$ 45
where
- ππ ∗ : optimal nominal policy rate
- ππ&quot; : neutral real policy rate
- πΊπΊπΊπΊππ# : expected GDP growth rate
- πΊπΊπΊπΊππ\$ : long-term trend GDP growth rate
- πΌπΌ# : expected inflation
- πΌπΌ\$ : inflation target
The link between current and capital accounts is
expressed as follows:
(ππ − ππ) = (ππ − πΌπΌ) + (ππ − πΊπΊ)
where
- X: exports
- M: imports
- S: domestic savings
- I: domestic investment
- T: taxation
- G: government spending
CAPITAL
EXPECTATIONS:
CAPITAL MARKET
MARKET EXPECTATIONS:
FORECASTING ASSET CLASS RETURNS
FORECASTING ASSET CLASS RETURNS
The Building Block Approach to
Fixed-Income Returns
The building block model breaks a bond’s YTM
into the components that compensate investors
for various risks.
www.saltsolutions.com
Component
Compensation for
One-period default
risk-free rate
Interest rate risk
Credit/Default risk
Duration risk
Illiquidity
DCF Approach to Equity Returns
Gordon Growth Model
π·π·&amp;
πΈπΈ(ππ% ) =
+ ππ
ππ'
Grinold-Kroner Model
π·π·&amp;
πΈπΈ(ππ% ) ≈
− % π₯π₯π₯π₯ + %π₯π₯π₯π₯π₯π₯ + %π₯π₯π₯π₯
ππ'
where
- %π₯π₯π₯π₯: nominal rate of earnings growth
- %π₯π₯π₯π₯π₯π₯: change in the P/E ratio
- % π₯π₯π₯π₯: change in the number of
shares outstanding
The Singer-Terhaar Model
- The model estimates risk premiums for assets
(or asset classes) based on their degree of
integration with the global market portfolio.
- Risk premium assuming full integration:
ππππ( = ππ(,* ππ( &times; ππππππππππππ ππβππππππππ ππππππππππ
- Risk premium assuming complete segmentation:
ππππ( = ππ( &times; ππππππππππππ ππβππππππππ ππππππππππ
- The Singer-Terhaar asset risk premium
is simply the weighted average of the
fully-integrated and completely segmented
Forecasting Real Estate Returns
ππππππ
πΆπΆπΆπΆπΆπΆ ππππππππ =
ππππππππππ
πΈπΈ(ππ+% ) = πΆπΆπΆπΆπΆπΆ ππππππππ + %π₯π₯π₯π₯π₯π₯π₯π₯
For finite time periods:
πΈπΈ(ππ+% ) = πΆπΆπΆπΆπΆπΆ ππππππππ + %π₯π₯π₯π₯π₯π₯π₯π₯ − %π₯π₯π₯π₯π₯π₯π₯π₯ ππππππππ
Estimating Volatility from Smoothed Returns
ππ\$ = (1 − ππ)ππ\$ + ππππ\$,&amp;
1 + ππ
ππππππ(ππ) = O
P ππππππ(ππ) &gt; ππππππ(ππ)
1 − ππ
Time-Varying Volatility: ARCH Models
- )
+ π½π½(ππ\$- − ππ\$,&amp;
ππ\$- = πΎπΎ + (πΌπΌ + π½π½)ππ\$,&amp;
where
- ππ\$- : variance of a single asset
- πΎπΎ: a constant
- )
- π½π½: the effect of a “shock” (ππ\$- − ππ\$,&amp;
- πΌπΌ + π½π½: mean reversion
DERIVATIVES
DERIVATIVES
OPTION STRATEGIES
OPTION STRATEGIES
Put-Call Parity
ππ' + ππ' = ππ' +
ππ
(1 + ππ).
ππ' − ππ' = ππ' −
ππ
(1 + ππ).
Synthetic Positions
Forward
Call
ππ' = ππ' −
Put
ππ' =
ππ
+ ππ'
(1 + ππ).
ππ
− ππ' + ππ'
(1 + ππ).
where
- ππ' : time-0 stock price
- ππ' : time-0 put price
- ππ' : time-0 call price
-
/
(&amp;2+)!
: strike price ππ, discounted at risk-free rate
ππ for a period of ππ years
Useful Greeks
Delta
πΆπΆβππππππππ ππππ π£π£π£π£π£π£π£π£π£π£ ππππ ππππππππππππ
β≈
πΆπΆβππππππππ ππππ π£π£π£π£π£π£π£π£π£π£ ππππ π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’
Gamma
πΆπΆβππππππππ ππππ π£π£π£π£π£π£π£π£π£π£ ππππ ππππππππππ
π€π€ ≈
πΆπΆβππππππππ ππππ π£π£π£π£π£π£π£π£π£π£ ππππ π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’π’
Vega
πΆπΆβππππππππ ππππ π£π£π£π£π£π£π£π£π£π£ ππππ ππππππππππππ
π£π£ ≈
πΆπΆβππππππππ ππππ π£π£π£π£π£π£π£π£π£π£ ππππ π£π£π£π£π£π£π£π£π£π£π£π£π£π£π£π£π£π£π£π£
Theta (Θ)
Indicator of an option price’s sensitivity to the
passage of time (usually negative).
Covered Call
Covered call = Written call + Long stock
πΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈ π£π£π£π£π£π£π£π£π£π£ = ππ. − ππππππ[(ππ. − ππ), 0]
ππππππππππππ ππππ ππππππππππππ = ππ. − ππππππ[(ππ. − ππ), 0] + ππ'
− ππ'
Investment objectives:
- Yield enhancement
- Reducing a position at a favourable price
- Target price realization
Protective Put
Protective Put = Long put + Long stock
πΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈ π£π£π£π£π£π£π£π£π£π£ = ππ. + ππππππ[(ππ − ππ. ), 0]
ππππππππππππ ππππ ππππππππππππ = ππ. + ππππππ[(ππ − ππ. ), 0] − ππ'
− ππ'
Investment objectives:
- Protects against losses in the underlying asset
1
Sell
Low-strike call
Low-strike put
High-strike call
High-strike put
Expiration Value for Call Bull Spread
= ππππππ[(ππ. − ππ4 ), 0] − ππππππ[(ππ. − ππ5 ), 0]
= ππππππ[(ππ. − ππ4 ), 0] − ππππππ[(ππ. − ππ5 ), 0]
− (ππ4 − ππ5 )
where
- ππ. : time-T stock price
- ππ4 : lower strike price
- ππ5 : higher strike price
- ππ4 : call premium with lower strike price
- ππ5 : call premium with higher strike price
Sell
High-strike call
High-strike put
Low-strike call
Low-strike put
Expiration Value for Put Bear Spread
= ππππππ[(ππ5 − ππ. ), 0] − ππππππ[(ππ4 − ππ. ), 0]
= ππππππ[(ππ5 − ππ. ), 0] − ππππππ[(ππ4 − ππ. ), 0]
−(ππ5 − ππ4 )
where
- ππ. : time-T stock price
- ππ4 : lower strike price
- ππ5 : higher strike price
- ππ4 : put premium with lower strike price
- ππ5 : put premium with higher strike price
Straddle = Long call + Long put (same strike)
= ππππππ[(ππ. − ππ), 0] + ππππππ[(ππ − ππ. ), 0]
= ππππππ[(ππ. − ππ), 0] + ππππππ[(ππ − ππ. ), 0] − ππ' − ππ'
Collar (on Existing Holding)
Collar = Long put + Short call + Underlying asset
Expiration Value for Collar (ππ&amp; &gt; ππ- )
= ππ. + ππππππ[(ππ&amp; − ππ. ), 0] − ππππππ[(ππ. − ππ-), 0]
Profit of Collar (ππ&amp; &gt; ππ-)
= ππ. + ππππππ[(ππ&amp; − ππ. ), 0] − ππππππ[(ππ. − ππ- ), 0] − ππ'
− ππ' + ππ'
Combination of options with same strike prices but
different expiration times.
- Buy longer-term call, sell shorter-term call
- Buy longer-term put, sell shorter-term put
www.saltsolutions.com
Volatility Conversion
ππ:&quot;&quot;;(8 ππ*&lt;&quot;\$=89
=
ππ6(789 =
√252
√21
Futures Hedge
Other Key Terms:
- Implied volatility: derived from option
pricing model
- Realized volatility: historical observed volatility
- Volatility smile: u-shaped volatility curve
- Volatility skew: implied volatility increases for
OTM puts but decreases for OTM calls
- Risk-reversal: long call and short put on same
underlying with same time to expiration
- Term structure of volatility: implied volatility
according to different maturities of option
- Implied volatility surface: 3D plot of
days to expiration, option strike prices,
and implied volatilities
Identifying Appropriate Strategies
For implied volatility and underlying asset:
Volatility
Bearish
Decrease
Write
calls
+
Write
calls
Same
Increase
Neutral
Write
Calendar
SWAPS, FORWARDS,
SWAPS,
FORWARDS,AND
ANDFUTURES
STRATEGIES
FUTURES
STRATEGIES
Bullish
Write
puts
+
Write
puts
Interest Rate Swaps
Notional value of Swap
ππππππππ. − ππππππππ?
ππ&gt; = O
P ππππ?
ππππππππ&gt;
where
- ππππππππ? : portfolio’s modified duration
- ππππππππ&gt; : modified duration of the swap
- ππππππππ. : portfolio’s targeted modified duration
- ππππ? : portfolio’s market value
Fixed-Income Futures
Principal Invoice Amount for CTD Bond
@;\$;+%A &gt;%\$\$8%B%&quot;\$ ?+7C%
=f
g &times; πΆπΆπΆπΆ &times; πΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆ ππππππππ
&amp;''
where
- CF: Conversion factor of CTD bond
βππ
P &times; πΆπΆπΆπΆ
βπΆπΆπΆπΆπΆπΆ
π΅π΅π΅π΅π΅π΅. − π΅π΅π΅π΅π΅π΅?
ππ# = O
P &times; πΆπΆπΆπΆ
π΅π΅π΅π΅π΅π΅D.6
π»π»π»π»π»π»π»π»π»π» ππππππππππ = O
where
- π΅π΅π΅π΅π΅π΅. is targeted basis point value
for the bond portfolio
- π΅π΅π΅π΅π΅π΅? is the bon portfolio’s current
basis point value
- π΅π΅π΅π΅π΅π΅D.6 is the basis point value of the CTD bonds
in the futures contract
ππππππππ. − ππππππππE ππ
ππ# = O
P O P &times; πΆπΆπΆπΆ
πΉπΉ
ππππππππD.6
where
- ππππππππ. : portfolio’s targeted modified duration
- ππππππππE : bond portfolio’s current
modified duration
- ππππππππD.6 : modified duration of the CTD bond
- P: market value of the bond portfolio
- F: market value of the futures contract as
product of future contract’s size and the price of
the CTD bond per 100 par
Equity Forwards and Futures
π½π½. − π½π½&gt; ππ
ππ# = l
mO P
πΉπΉ
π½π½#
where
- π½π½. is the target beta
- π½π½&gt; is the equity portfolio’s current beta
- π½π½# is the beta of the futures contract
- ππ is the value of the equity portfolio
- πΉπΉ is the value of the futures contract as a
product of the contract price and multiplier
Derivatives on Volatility
Variance swaps
ππππππππππππππππ ππππππππππππππππ = O
ππππππππ πππππ‘π‘π‘π‘π‘π‘π‘π‘π‘π‘π‘π‘
P
2 &times; ππππππππππππ
ππππππππππππππππππππ π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄.
= (ππππππππππππππππ ππππππππππππππππ)(ππππππππππππππππ π£π£π£π£π£π£π£π£π£π£π£π£π£π£π£π£
− ππππππππππππππππ π π π π π π π π π π π π )
ππππππππππππππ\$ = ππππππππππππππππ ππππππππππππππππ &times; ππππ\$ (ππ)
π‘π‘
&times; O &times; [ππππππππππππππππ ππππππ(0, π‘π‘)]ππ
ππ − π‘π‘
+
ππ
&times; [πΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌ ππππππ(π‘π‘, ππ)]− ππππππππππππ - P
where
- ππππ\$ (T) is the value of \$1 at time π‘π‘ which will
mature at time ππ
- ππππππππππππππππ ππππππ(0, π‘π‘) is the realized volatility from
time 0 to time π‘π‘
- πΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌππ ππππππ(π‘π‘, ππ) is the implied volatility
remaining in the period (ππ − π‘π‘)
2
CURRENCY MANAGEMENT:
CURRENCY MANAGEMENT:
AN INTRODUCTION
AN INTRODUCTION
Domestic Currency Return
ππ6D = (1 + ππ@D )(1 + ππ@/ ) − 1
where
- ππ6D is the domestic-currency return (in percent)
- ππ@D is the foreign-currency return (in percent)
- ππ@/ is the percentage change in the foreign
currency against the domestic currency
Approximations:
ππ6D ≈ ππ@D + ππ@/
-
-
-
ππ (ππ6D ) ≈ ππ (ππ@D ) + ππ (ππ@/ ) + 2ππ(ππ@D ) β ππ(ππ@/ )
β ππ(ππ@D , ππ@/ )
Uncovered Interest Rate Parity
%βππ5/4 ≈ ππ5 − ππ4
- %βππ5/4 is percentage change in the ππ5/4 spot
exchange rate (low-yield currency is base
currency)
- ππ5 is interest rate on high-yield currency
- ππ4 is the interest rate on low-yield currency
Minimum-Variance Hedge Ratio
ππ9
πΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆ (π¦π¦, π₯π₯)
= ππ9,G O P
ππππππππππππππππ(π₯π₯)
ππG
FIXED INCOME FIXED INCOME
OVERVIEW
OF FIXED-INCOME
OVERVIEW OF
FIXED-INCOMEPORTFOLIO
MANAGEMENT
PORTFOLIO MANAGEMENT
Roles of Fixed-Income Securities in Portfolios
- Diversification Benefits
- Benefits of Regular Cash Flows
- Inflation Hedging Potential
Fixed-Income Mandates
Liability-Based Mandates
- Cash flow matching
- Duration matching
- Contingent immunization
- Horizon matching
Total Return Mandates
- Pure indexing
- Enhanced indexing
- Active management
Effective Duration and Effective Convexity
ππππ, − ππππ2
πΈπΈπΈπΈπΈπΈ6;+ =
2 ⋅ π₯π₯π₯π₯π₯π₯π₯π₯π₯π₯π₯π₯ ⋅ ππππ'
ππππ, + ππππ2 − 2 ⋅ ππππ'
πΈπΈπΈπΈπΈπΈD&lt;&quot; =
(π₯π₯π₯π₯π₯π₯π₯π₯π₯π₯π₯π₯)- ⋅ ππππ'
www.saltsolutions.com
Decomposition of Expected Returns
πΈπΈ[ππ]
≈ πΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆ ππππππππππππ &plusmn; ππππππππππππππππ ππππππππππππ
&plusmn; πΈπΈ[ππππππππππ β ππππππππ ππππππππβππππππππ π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦ ]
&plusmn; πΈπΈ[ππππππππππ β ππππππππ π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦ π π π π π π π π π π π π π π  ]
&plusmn; πΈπΈ[ππππππππππ β ππππππππ ππππππππππππππππ π£π£π£π£π£π£π£π£π£π£ ππβππππππππππ]
π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄ ππππππππππππ ππππππππππππππ
πΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆ ππππππππππππ =
πΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆ ππππππππ ππππππππππ
ππππππππππππππππ ππππππππππππ
π΅π΅π΅π΅π΅π΅π΅π΅ ππππππππππH&quot;I − π΅π΅π΅π΅π΅π΅π΅π΅ ππππππππππE%J7&quot;&quot;7&quot;J
=
π΅π΅π΅π΅π΅π΅π΅π΅ ππππππππππE%J7&quot;&quot;7&quot;J
πΈπΈ[ππππππππππ β ππππππππ ππππππππβππππππππ π¦π¦ππππππππππ ]
= −ππππ(βππππππππππ)
1
+ (πΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆ)(βππππππππππ)2
where
- MD: modified duration
Leveraged Portfolio Return
ππππππππππππππππππ ππππππππππππ ππK (ππH + ππE ) − ππE ππE
ππ? =
=
ππππππππππππππππππ ππππππππππππ
ππH
ππE
= ππK + (ππK − ππE )
ππH
where
- ππK : return on invested funds
- ππE : borrowing rate
Futures Leverage
πΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏ@;\$;+%A =
ππππππππππππππππ π£π£π£π£π£π£π£π£π£π£ − ππππππππππππ
ππππππππππππ
Dollar Interest in Repurchase Agreement
π·π·π·π·π·π·π·π·π·π·π·π· ππππππππππππππππ = ππππππππππππππππππ ππππππππππππ
&times; ππππππππ ππππππππ
&times; (ππππππππ ππππ ππππππππ ππππ ππππππππ
/360)
Rebate Rate in Securities Lending
ππππππππππππ ππππππππ = πΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆ ππππππππππππππππ ππππππππ
− ππππππππππππππππ ππππππππππππ ππππππππ
LIABILITY-DRIVEN AND
&amp; INDEX-BASED
LIABILITY-DRIVEN
STRATEGIES
INDEX-BASED STRATEGIES
Convexity
πΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆ
(ππππππππππππππππ ππππππ. )- + ππππππππππππππππ ππππππ. +π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·
=
(1 + πΆπΆππππβ ππππππππ π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦ )Duration
ππππππππππ ππππππππππππππππ = ππππππππππππππππ ππππππππππππππππ
&times; ππππππππππππ ππππππππππ
ππππππππππππππππ ππππππππππππππππ =
ππππππππππππππππ ππππππππππππππππ
ππ
1+
ππ
# Futures Contracts (for Immunization)
πΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏ ππππππππππππππππππ π΅π΅π΅π΅π΅π΅
= π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄ ππππππππππππππππππ π΅π΅π΅π΅π΅π΅
+ 2ππ# &times; πΉπΉπΉπΉπΉπΉπΉπΉπΉπΉπΉπΉπΉπΉ π΅π΅π΅π΅π΅π΅4
where:
E?L&quot;!#
- πΉπΉπΉπΉπΉπΉπΉπΉπΉπΉπΉπΉπΉπΉ π΅π΅π΅π΅π΅π΅ ≈
D@&quot;!#
- πΆπΆπΆπΆD.6 : conversion factor for the CTD security
- A positive ππ# implies buying futures contracts
- A negative ππ# implies selling futures contracts
Accumulated &amp; Projected Benefit Obligation
1
ππ &times; πΊπΊ &times; ππ'
1
~
&times;} −
π΄π΄π΄π΄π΄π΄ =
(1 + ππ).
ππ ππ &times; (1 + ππ)M
ππππππ =
ππ &times; πΊπΊ &times; ππ' &times; (1 + π€π€).
(1 + ππ).
1
1
~
&times;} −
ππ ππ &times; (1 + ππ)M
where:
- ππ: percentage of final salary
- πΊπΊ: number of years worked
- ππ' : current salary
- π€π€: wage growth
- ππ: discount rate on high-quality corporate bonds
- ππ: years until retirement
- ππ: years after retirement
Swap Notional Principal to Close Duration Gap
ππππππππ π΅π΅π΅π΅π΅π΅
~
πΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏ π΅π΅π΅π΅π΅π΅ = π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄ π΅π΅π΅π΅π΅π΅ + }ππππ &times;
100
Full Interest Rate Hedging
(π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄ π΅π΅π΅π΅π΅π΅) &times; (βπ΄π΄π΄π΄π΄π΄π΄π΄π΄π΄ π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦)
+ (π»π»π»π»π»π»π»π»π»π» π΅π΅π΅π΅π΅π΅)
&times; (βπ»π»π»π»π»π»π»π»π»π» π¦π¦π¦π¦π¦π¦π¦π¦ππππ)
≈ (πΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏ π΅π΅π΅π΅π΅π΅)
&times; (βπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏ π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦π¦)
YIELD CURVE
CURVE STRATEGIES
STRATEGIES
YIELD
Butterfly spread = −Short-term yield +2 Mediumterm yield −Long-term yield
Duration Approximation
1
&times; πΆπΆ &times; (βππ)2
Sensitivity of a Bond Futures to Changes in
Yield
π΅π΅π΅π΅π΅π΅D.6
πΉπΉπΉπΉπΉπΉπΉπΉπΉπΉπΉπΉπΉπΉ π΅π΅π΅π΅π΅π΅ ≈
πΆπΆπΆπΆD.6
Sensitivity of a Swap to Changes in Yield
ππππππππ ππππππππππππππππ
ππππππππ π΅π΅π΅π΅π΅π΅ ≈ ππππππππππππ&gt;N(O &times;
10,000
%π₯π₯ππππ @;88 ≈ −π·π· &times; βππ +
where
- ππ is the annualized cash flow yield
- ππ is the compounding periods per year
3
FIXED
FIXED INCOME
INCOME ACTIVE
ACTIVE MANAGEMENT:
MANAGEMENT: CREDIT
STRATEGIES
CREDIT STRATEGIES
Credit Risk
A borrower's credit risk is determined by default
risk and loss severity.
- Default risk: Measured by the probability of
default (POD)
- Loss severity: Measured by the loss given
default (LGD). It can be calculated as LGD = 1
– RR, where RR is the recovery rate
Over a single period, a bond's credit spread can be
approximated as ππππππππππππ ≈ ππππππ &times; πΏπΏπΏπΏπΏπΏ.
between the yields on a risky bond and an onthe-run government bond with a similar
maturity.
between a bond's yield and an interpolated
government bond yield.
between a bond's yield and a swap rate, or
market reference rate (MRR), rather than the
government yield. This measure relies on a
single point on the curve and it can only be used
for option-free bonds.
- Asset swap spread (ASW): The difference
between a bond's coupon rate and the MRR on a
swap of the same maturity.
government spot curve to force the present
value of a bond's future cash flows to equal its
current market value. This can only be used for
bonds without embedded options.
- CDS basis: The difference between a bond's Zspread and the spread on credit default swaps
(CDS) of the same (or interpolated) maturity for
the issuer
similar to the Z-spread but it also works for
bonds with embedded options. This measure is
highly dependent on assumptions about interest
rate volatility and prepayment speed.
Floating-rate notes (FRNs) make payments based
on a variable MRR.
- Coupon rate: Determined by taking the sum of
the MRR and a quoted margin (QM)
- Discount rate: Determined by taking the sum of
the MRR and discount margin (DM)
ππππ =
(ππππππ + ππππ)(πΉπΉπΉπΉ)
ππ
(ππππππ + π·π·π·π·) &amp;
O1 +
P
ππ
(ππππππ + ππππ)(πΉπΉπΉπΉ)
ππ
+
+β―
(ππππππ + π·π·π·π·) O1 +
P
ππ
(ππππππ + ππππ)(πΉπΉπΉπΉ)
+ πΉπΉπΉπΉ
ππ
+
(ππππππ + π·π·π·π·) P
P
O1 +
ππ
www.saltsolutions.com
π·π·π·π·π·π· ≈ πΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈ &times; ππππππππππππ
πΈπΈ[πΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈ] ≈ ππππππππππππ'
− πΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈ &times; π₯π₯π₯π₯π₯π₯π₯π₯π₯π₯π₯π₯π₯π₯
− ππππππ &times; πΏπΏπΏπΏπΏπΏ
Credit Default Swap (CDS)
The amount of the upfront payment can be
approximated as:
ππππππππππππππ πΆπΆπΆπΆπΆπΆ ππππππππππππππ
≈ (πΆπΆπΆπΆπΆπΆ ππππππππππππ − πΉπΉπΉπΉπΉπΉπΉπΉπΉπΉ πΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆ)
&times; πΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπππΆπΆπΆπΆπΆπΆ
The CDS price per unit of par value can be
calculated as:
πΆπΆπΆπΆπΆπΆ ππππππππππ
≈ 1 − (πΆπΆπΆπΆπΆπΆ ππππππππππππ − πΉπΉπΉπΉπΉπΉπΉπΉπΉπΉ πΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆ)
&times; πΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈππD6&gt;
The change in a CDS' price can be approximated as:
%π₯π₯ πΆπΆπΆπΆπΆπΆ ππππππππππ ≈ −π₯π₯π₯π₯π₯π₯π₯π₯ ππππππππππππ
&times; πΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈππD6&gt;
EQUITY INVESTMENTS
EQUITY INVESTMENTS
PASSIVE EQUITY INVESTING
PASSIVE
EQUITY INVESTING
Index Concentration
- The Herfindahl-Hirshaman Index (HHI) can be
used to measure stock concentration risk in a
portfolio. The HHI is the sum of the constituent
weightings squared:
&quot;
π»π»π»π»π»π» = &Eacute; π€π€77T&amp;
- The effective number of stocks represents
the number of stocks required in an
equally-weighted portfolio that would
have the same HHI:
1
πΈπΈπΈπΈπΈπΈππππππππππππ ππππππππππππ ππππ π π π π π π π π π π π π  =
π»π»π»π»π»π»
Approaches to Passive Equity Investing
- Pooled Investments: Mutual funds and
exchange-traded funds, are easy to purchase,
hold, and sell.
- Derivatives-Based Approaches: Options,
swaps, and futures contracts can be used
to gain index performance.
- Separately Managed Equity Index-Based
Portfolios: An indexed portfolio can be
built by purchasing the constituent securities
of the index.
Portfolio Construction
- Full Replication: Hold all the securities in an
index in proportion with the index weightings.
- Stratified Sampling: Index constituents are first
divided into strata or subgroups. Securities are
chosen for the portfolio so the portfolio weights
by strata will match the index weights by strata.
- Optimization: Minimize the tracking error
subject to specified constraints.
- Blended Approach: A blend of the three
approaches can be used to track a
particular index.
Tracking Error Management
- The excess return is the difference between the
portfolio returns and the benchmark returns.
πΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈ ππππππππππππO = ππO − ππU
- Tracking error measures how closely the
portfolio return matches the benchmark return.
ππππππππππππππππ ππππππππππO = &Ntilde;ππππππππππππππππV\$,V%
ACTIVE EQUITY INVESTING
ACTIVE
EQUITY INVESTING
Active Return
Active return is the sum of the security returns
times the weight differences between the portfolio
and benchmark:
P
ππ: = &Eacute; π₯π₯ππ7 ππ7 π₯π₯ππ7 = π₯π₯ππ?7 − π₯π₯ππE7
7T&amp;
Expected Active Return
The expected active portfolio return can be
determined as follows:
πΈπΈ[ππ: ] = πΌπΌπΌπΌ &times; √π΅π΅π΅π΅ &times; ππV&amp; &times; ππππ
where
- IC: Expected information coefficient of the
manager, which is how much the manager’s
forecasted active returns correspond to the
manager’s realized active returns
- BR: Breadth, which is the number of
- TC: Transfer coefficient, which is the ability to
convert portfolio insights into investment
decisions; an unconstrained portfolio has a
transfer coefficient of 1
Active Share and Active Risk
- Active share measures how the size
positions in a manager’s portfolio differs
from the benchmark:
π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄ ππβππππππ =
&quot;
1
&Eacute;&Ouml;ππO&lt;+\$,7 − ππU%&quot;C=B(+W,7 &Ouml;
2
7T&amp;
- Active risk can be measured using realized
historical numbers or using predicted estimates
of correlations and variances:
&quot;
π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄ ππππππππ = &Uuml;ππ - &aacute;&Eacute;.π½π½OW − π½π½UW 5πΉπΉW &agrave; + ππ%WT&amp;
Causes and Sources of Absolute Risk
The total portfolio variance (ππO ) and contribution
of each asset to portfolio variance (πΆπΆπΆπΆππ ) can be
calculated with the following formulas:
&quot;
&quot;
ππO = &Eacute; &Eacute; π₯π₯7 π₯π₯Y πΆπΆ7Y
7T&amp; YT&amp;
&quot;
πΆπΆπΆπΆ7 = &Eacute; π₯π₯7 π₯π₯Y πΆπΆ7Y = π₯π₯7 πΆπΆ7O
YT&amp;
where
- π₯π₯Y : the asset’s weight in the portfolio
- πΆπΆ7Y : the covariance of returns between asset i
and asset j
- πΆπΆ7O : the covariance of returns between asset i
and the portfolio
4
Causes and Sources of Relative/Active Risk
The variance of the portfolio’s active return %π΄π΄π΄π΄ππ &amp;
can be used to measure relative risk.
&quot;
&quot;
π΄π΄π΄π΄O = &Eacute; &Eacute;(π₯π₯7 − ππ7 )2π₯π₯Y − ππY 4πππΆπΆ7Y
7T&amp; YT&amp;
where
- π₯π₯7 : asset’s weight in the portfolio
- ππ7 : benchmark weight in asset i
- πππΆπΆ7Y : covariance of relative returns between
asset i and asset j
ALTERNATIVE
INVESTMENTS
ALTERNATIVE
INVESTMENTS
HEDGE
STRATEGIES
HEDGE FUND
FUN STRATEGIES
Classification of Hedge Funds and Strategies
Hedge Fund Characteristics
- Legal/ Regulatory Overview
- Flexible Mandates
- Large Investment Universe
- Aggressive Investment Styles
- High Leverage
- Liquidity Constraints
- High Fees
Equity Strategies
- Long/Short Equity: Buy undervalued stocks and
sell overvalued stocks short.
- Dedicated Short-Selling and Short-Biased: Take
short-only positions in equities but may vary the
short positions by holding cash.
- Equity Market-Neutral: Use offsetting long
and short positions to establish an overall
portfolio with near zero net exposure to equity
market risk (beta).
Event-Driven Strategies
- Merger Arbitrage: Take positions based on
- Distressed Securities: Focus on firms that are
either already in the bankruptcy process or
that are currently experiencing financial
distress and are expected to file for bankruptcy
in the near future.
Relative Value Strategies
- Fixed-Income Arbitrage: Seek to profit from
relative mispricing.
o Yield curve trades involve taking long and
short positions based on expected changes
in the shape of the yield curve in response
to macroeconomic conditions.
o Carry trades are executed by shorting
higher-yielding bonds.
- Convertible Bond Arbitrage: Seek to take
advantage of discrepancies between the prices
of an issuer’s convertible bonds and their
straight bonds.
Opportunistic Strategies
- Global Macro Strategies: Generally hold views
on macro-level economic activity based on
top-down analysis and express views by
taking positions in a variety of asset
classes and instruments.
- Managed Futures: A highly technical and
systematic strategy that is executed using
primarily futures and options on futures.
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Specialist Strategies
- Volatility Trading: Relative value volatility
arbitrageurs can take advantage of differences
in implied volatility for the same product across
time zones (time-zone arbitrage) or markets
- Reinsurance/Life Settlements: The sale of a life
insurance policy to a party other than its
originator is called a life settlement. Third-party
brokers will then package the individual policies
that they have acquired into pools to be resold
to hedge funds.
Multi-Manager Strategies
- Fund-of-Funds: The FoF manager will make
allocations to a diverse group of funds.
- Multi-Strategy Hedge Funds: Multiple
teams pursuing distinct strategies within
the same organization.
Conditional Factor Risk Model
- A conditional risk-factor model goes a step
further to account for the possibility that
factor exposures can change under different
market conditions.
- Using the example of a managed futures with
exposure to equity and commodity risks, the
conditional factor model is:
ππ=# = πΌπΌ + π½π½H ππH + π½π½D ππD + π·π·π½π½H ππH + π·π·π½π½D ππD
where
o π·π·: Dummy variable with a value of 0 under
normal market conditions and 1 during crises
o π·π·π½π½H ππH : Incremental exposure to equity risk
during periods of market stress
ASSET ALLOCATION
ASSET
ALLOCATIONTO
TOALTERNATIVE
ALTERNATIVE
INVESTMENTS
INVESTMENTS
Achieving and Maintaining the
Strategic Asset Allocation
- In private partnerships, GPs have broad
discretion over decisions related to capital
calls and distributions.
- The net asset value of a private fund with a
drawdown structure at time t is:
ππππππ\$ = ππππππ\$,&amp;(1 + ππ) + πΆπΆ\$ − π·π·\$
where:
o ππππππ\$,&amp; : fund’s net asset value at the end of
the previous period
o g: growth rate
o πΆπΆ\$ : amount of new contributions
(capital calls) during period t
o π·π·\$ : the amount of distributions made
during period t
- One particular model for forecasting
contributions uses the following formula:
πΆπΆ\$ = πππΆπΆ\$ &times; (πΆπΆπΆπΆ − πππππΆπΆ\$ )
where:
o πππΆπΆ\$ : rate of contributions during period t
o πΆπΆπΆπΆ: capital commitment
o πππππΆπΆ\$ : amount paid-in-capital prior to period t
- The formula for forecasting distributions uses a
variable for the rate of distributions:
π·π·\$ = πππ·π·\$ &times; ππππππ\$,&amp; (1 + ππ)
PORTFOLIO MANAGEMENT (PART I)
PORTFOLIO MANAGEMENT (PART I)
THE BEHAVIORAL BIASES OF INDIVIDUALS
THE BEHAVIORAL BIASES OF INDIVIDUALS
Cognitive vs. Emotional
- Cognitive errors are statistical,
information-processing, or memory errors.
Can be moderated through better
information and education.
- Emotional biases stem from attitudes or
feelings. Must often be adapted to because
it is very difficult to reduce or eliminate them.
Cognitive Errors
Belief Perseverance Biases
- Conservatism Bias: Maintain prior views by
Tend to overweight initial beliefs and
underreact to new information.
- Confirmation Bias: Tend to only notice what
confirms their beliefs.
- Representativeness Bias: Tend to use past
classifications for new information, even if it
does not fit into the category.
- Illusion of Control Bias: Believe they can control
outcomes that they cannot.
- Hindsight Bias: Look at past events and think
they would have been predictable.
Information-Processing Biases
- Anchoring and Adjustment Bias: When people
estimate an unknown value or probability, they
often start by adjusting from an “anchor” value.
- Mental Accounting Bias: Put money in separate
mental buckets and treat them differently.
- Framing Bias: Answer the same question
differently just based on how the question
is framed.
- Availability Bias: Use heuristics (mental
shortcuts) when making decisions.
Emotional Biases
- Loss-Aversion Bias: Prefer avoiding losses more
than achieving gains.
- Overconfidence Bias:
o Overestimate their own abilities.
o Can come from the illusion of superior
knowledge or consistently attributing success
to skill and failure to external factor.
o Self-enhancing and self-protecting biases are
the two sides of the self-attribution bias.
- Self-Control Bias: Fail to make decisions that
are best for their long-term goals because of a
lack of self discipline.
- Status Quo Bias: Inclined to do nothing
rather than change.
- Endowment Bias: Value an asset more
when they hold the rights to it.
- Regret-Aversion Bias: Avoid decisions
5
BEHAVIORAL
BEHAVIORAL FINANCE
FINANCEAND INVESTMENT
PROCESSES
AND INVESTMENT PROCESSES
Bailard, Biehl, and Kaiser Five-Way Model
- Adventurer: Confident and willing to take
chances, so often hold undiversified portfolio
- Celebrity: Like to be center of attention,
but recognizes weaknesses so may seek
- Individualist: Independent and confident;
make decisions after careful analysis
- Guardian: Cautious and concerned about
the future; common for older people
approaching retirement
- Straight Arrow: Sensible and secure; willing
to take on some risk for extra return
Description of the Four
Behavioral Investor Types
- Passive Preservers want to preserve wealth
rather than take risk to generate more wealth.
- Friendly Followers are passive investors that
- An Independent Individualist is an active
investor that is typically strong-willed
and independent.
- Active Accumulators are aggressive,
confident and strong-willed.
How Behavioral Factors Affect
Portfolio Construction
- Inertia and Default
- Na&iuml;ve Diversification
- Investing in the Familiar Stocks
o Familiarity and overconfidence
o Na&iuml;ve extrapolation of past returns
o Framing and status quo
o Loyalty
o Financial incentives
- Home Bias
Behavioral Finance and Analyst Forecasts
Overconfidence in Forecasting Skills
- Investment analysts are often overconfident in
their abilities and information, which is referred
to as the illusion of knowledge bias.
- Analysts also exhibit self-attribution bias,
in which they take credit for success and
assign responsibility for failure.
- Availability bias causes the analysts to give
too much weight to accessible and readily
recalled information.
- Hindsight bias inclines the analyst to
think past events are predictable.
Influence of Company’s Management on Analysis
- Company management can present
information in such a way to exploit biases.
and availability are all cognitive biases
that can play a role.
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Analyst Biases in Conducting Research
- Collecting too much information can lead to the
illusion of control and representativeness.
- Stories can be weaved that are created
to fit the data.
- Confirmation bias can lead analysts to
become entrenched in their prior beliefs.
- The gamblers’ fallacy is another cognitive bias
that can affect analysts. It is a wrong belief that
probabilities must revert to a long-term mean.
- Endowment bias and confirmation bias can lead
to analysts recommending financially sound
companies even if the current stock price does
not justify the investment.
How Behavioral Factors Affect Committee
Decision Making
- Social proof is a bias in which individuals
tend to follow the group beliefs.
- Group discussions can lead to an
overconfidence bias.
- Committees often perform poorly because
they are usually composed of individuals
with similar backgrounds who have
debates to arrive at a consensus.
How Behavioral Finance
Influences Market Behavior
Momentum
- Most markets exhibit short-term positive
correlation and long term negative correlation.
- Availability bias could also explain why
investors rely so much on recent information.
- Regret aversion could drive investors to
purchase mutual funds that have performed
well in the previous year to avoid regretting
again not owning it the next year.
- The disposition effect encourages
investors to hold onto losers just
to avoid recognizing the loss.
Bubbles and Crashes
and lack of diversification.
- Bubbles can be linked to confirmation,
Value and Growth
- Value stocks outperform growth stocks.
- Overconfidence can affect growth rate
predictions. Emotional investors may be
attracted to growth.
TOPICS IN
WEALTH MANAGEMENT
MANAGEMENT
TOPICS
IN PRIVATE
PRIVATE WEALTH
After-Tax Returns
- A pre-tax holding period return is calculated as
follows:
ππ. − ππ' + πΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌ
ππ =
ππ'
- An after-tax holding period return is a pre-tax
ππ. − ππ' + πΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌ − ππππππ
ππ′ =
ππ'
- The Modified Dietz formula can be used to better
estimate returns when tax payments have been
ππππππ
ππ [ = ππ −
πΆπΆY (ππ − ππ)
ππ' + ∑
ππ
- The after-tax post-liquidation return is calculated
as the geometrically linked sub-period returns
less the embedded tax liability that would be
due if accumulated unrealized gains were
realized upon liquidation:
&amp;
πΏπΏπΏπΏπΏπΏ. ππππππ &quot;
~ −1
πΉπΉπΉπΉπΉπΉπΉπΉπΉπΉ ππππππππππ
πΏπΏπΏπΏπΏπΏ. ππππππ = (πΉπΉπΉπΉπΉπΉπΉπΉπΉπΉ π£π£π£π£π£π£π£π£π£π£ − ππππππ ππππππππππ)
&times; πΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆ ππππππππ π‘π‘π‘π‘π‘π‘ ππππππππ
= πΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈπΈ ππππππππππππππ ππππππππ
&times; πΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆ ππππππππ π‘π‘π‘π‘π‘π‘ ππππππππ
- Tax alpha is simply the pre-tax excess return
(relative to a benchmark) less the after-tax
excess return.
- The tax efficiency ratio (TER) is a portfolio’s
after-tax return as a percentage of its
pre-tax return.
ππ?4 = }(1 + ππ&amp;[) … (1 + ππ&quot;[ ) −
Capital Accumulation
- The future value of an investment held in a taxexempt account is:
πΉπΉππ.(G,%G%BO\$ = (1 + ππ)&quot;
- If the same investment were held in a taxable
account, its future value would be:
πΉπΉππ.(G(U8% = [1 + ππ(1 − π‘π‘)]&quot;
- Holding an investment in a tax-deferred account
allows it to accumulate gains that are untaxed
until they are realized:
πΉπΉππ.(G,I%#%++%I = (1 + ππ)&quot; (1 − π‘π‘)
Potential Capital Gain Exposure (PCGE)
ππππππππ
πΊπΊπΊπΊπΊπΊπΊπΊπΊπΊ − πΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆπΆ πΊπΊπΊπΊπΊπΊπΊπΊπΊπΊ π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π· − πΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏπΏ
=
ππππππππππ ππππππ π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄
Estate Planning
- The relative value of transferring assets as gifts
during the donor's lifetime rather than as
bequests can be calculated using the following
formula:
&quot;
.1 + ππJ 21 − π‘π‘J 45 (1 − ππJ )
πΉπΉππ\7#\$
=
πΉπΉππE%];%A\$ [1 + ππ% (1 − π‘π‘% )]&quot; (1 − ππ% )
- If annual returns are taxed at the same rate for
the recipient and donor and the assets can be
transferred as tax-free gifts, the relative value is
formula shown above simplifies to:
1
1 − ππ%
ππππ =
6
RISK
RISK MANAGEMENT
MANAGEMENT FOR
FORINDIVIDUALS
INDIVIDUALS
Economic Balance Sheet
- The assets on an individual's economic (holistic)
balance sheet include both their human capital
and their financial capitalγ
- Human capital is the present value of expected
future employment income.
- Financial capital includes both personal assets
and investment assets, which can be classified
based on marketability and whether they are
PORTFOLIO
PORTFOLIOMANAGEMENT
MANAGEMENTFOR
FOR
INSTITUTIONAL INVESTORS
INSTITUTIONAL INVESTORS
Common Characteristics
Institutions tend to share the following
characteristics that distinguish this class of
investors from individuals:
- Large Scale
- Long Investment Horizons and
Low Liquidity Needs
- Regulatory Framework
- Formal Governance Framework
- Principal-Agent Problems
DB Pension
Liabilities
Benefit payments are determined by a formula
based on inputs such as tenure and final salary.
Estimates of future payments must account for
unknowns such as mortality and inflation.
Stakeholders
The primary stakeholders are participants,
Investment Objectives
Primarily to meet obligations to participants.
Secondary objectives may include limiting surplus
volatility or minimizing the sponsor's need to
Legal/Regulatory Constraints
Governments tend to establish high regulatory
requirements for pensions, often based on the
principles of prudential supervision, capital
protection. Trustees may be held personally liable
if they fail to meet their fiduciary duty to
participants.
Tax Constraints
DB pension plans are typically tax-exempt
investors.
Risk Considerations
- Investment Horizon: Typically long-term for
plans that remain open to new participants.
Workforce characteristics, such as a higher
average age of participants, will shorten a plan's
investment horizon.
- Liquidity Needs: Funds are required to make
benefit payments. Plan features, such as options
to accept lump-sum payments, will increase
liquidity needs.
- Other Risk Considerations: A DB pension plan's
risk tolerance may be limited by factors such as
common risk exposure with the sponsor,
financial status.
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Asset Allocation
Pension plans have traditionally held large fixedincome allocations with some equities as a source
of growth. Recently, alternative assets have
become more common in pension portfolios,
although asset allocations can be subject to
regulatory requirements and limitations.
DC Pensions
Liabilities
Plan sponsors are only liable for their promised
contributions and the plans themselves have no
liabilities beyond allowing participants to access
the assets in their accounts.
Stakeholders
Plan participants are the primary stakeholders.
Investment Objectives
Individual participants have their own specific
objectives. The investment firms and insurance
companies that manage DC plans will want to show
that their portfolio options perform well.
Legal/Regulatory Constraints
Plan sponsors are typically required to provide
regular financial education courses for
participants. Other legal requirements may include
offering a glide path fund as a default option.
Tax Constraints
Assets held in DC pension plan accounts are
allowed to accumulate tax-free until they are
withdrawn, after which they are taxed at the
participant's applicable rate.
Risk Considerations
- Investment Horizon: DC plans must provide a
range of investment options that account for
differences in the time horizons of individual
participants. All else equal, older participants
and larger balances are associated with shorter
investment horizons.
- Liquidity Needs: DC plans receive regular
contributions from participants, but must
maintain sufficient liquidity to meet
withdrawals.
Asset Allocation
While each participant has their own allocation
preferences, the aggregate scale of DC plans may
otherwise be unavailable to them. Plans must offer
participants a menu of different allocations.
Sovereign Wealth Funds
SWFs - Budget Stabilization Funds
- Typically created by governments that rely
heavily on natural resource revenues to provide
fiscal support if commodity prices fall.
- The primary objective is to preserve the real
value of assets and liabilities are relatively
unpredictable, so risk tolerance is relatively low
with large allocations to highly-liquid, low-risk
debt securities.
SWFs - Development Funds
- Given a broad mandate to spur economic
growth, these funds invest in a variety of
opportunities — from infrastructure projects to
venture capital investments in emerging sectors.
- Liabilities are ill-defined and it is difficult to
generalize about asset allocations for these
types of funds. However, they tend to be longterm investors with low liquidity needs and an
objective to earn a real return in excess of GDP
or productivity growth.
SWFs - Savings Funds
- The purpose of these funds is to transfer wealth
to future generations.
- Liquidity needs are relatively low, typically
determined by a fixed spending rate.
- An objective to achieving intergenerational
equity produces a very long-term time
horizon with a correspondingly high level
of risk tolerance.
- Portfolio allocations are dominated by equities
and alternatives, with relatively few fixedincome assets.
SWFs - Reserve Funds
- These funds are used by export-intensive
economies to absorb their local currency while
accumulating excess foreign currency reserves
as assets.
- The return objective is a rate in excess of the
yield on the monetary stabilization bonds issued
by the central bank.
- A very long-term time horizon allows for high
allocations to equity-like alternatives, but
some liquid fixed-income securities are also
held in order to meet relatively unpredictable
liquidity needs.
SWFs - Pension Reserve Funds
- Used to pre-fund future pension and health care
costs, these funds are supported by government
budget surpluses.
- Liquidity needs are minimal during an initial
accumulation phase, allowing for very high
allocations to equities and illiquid alternatives
such as infrastructure, real assets, and
hedge funds.
- In the subsequent decumulation phase, the
investment horizon shortens and funds are
allocated to more fixed-income assets to help
meet growing liquidity needs.
Foundations
Liabilities
Foundations are typically required to give out a
certain percentage of assets as grants every year.
Stakeholders
A private foundation's primary stakeholders are
the individual benefactor (or founding family) and
the groups that receive grants. Tensions may exist
between increasing current grants and preserving
assets for future grants.
Investment Objectives
Foundations with infinite lives typically seek to
maintain the real value of their assets by setting a
return target equal to the sum of the spending rate,
expected inflation, and any management fees.
7
Legal/Regulatory Constraints
Foundation directors are typically required to
exercise a fiduciary standard of care and adhere to
the principles of modern portfolio theory when
making investment decisions.
Tax Constraints
Foundations are tax-exempt investors, provided
that they meet minimum annual spending
requirements.
Risk Considerations
- Investment Horizon: Most foundations expect to
continue operating in perpetuity. However,
limited life foundations are given a specific date
by which they must distribute their assets and
cease operating.
- Liquidity Needs: Foundations have relatively
low liquidity needs. They are not required to
make any payments in excess of the minimum
threshold to maintain tax-exempt status.
However, foundations may be subject to flowthrough rules requiring them to spend
donations during the year in which they are
Asset Allocation
- Small allocations to cash and highly liquid
securities are maintained in order to meet
immediate spending needs, but long investment
horizons and low liquidity needs allow for high
allocations to equities and alternatives
(particularly for larger foundations).
- Limited life foundations hold increasingly large
allocations of low-risk liquid assets as they
move toward winding down their operations.
Endowments
Liabilities
- Endowments do not have specific, legally
enforceable liabilities.
- An endowment’s liabilities are the informal
spending commitments that have been made to
future students.
- When an endowment uses a fixed spending
rate, the amount of its spending in the upcoming
year (Year 1) can be calculated based on the
spending rate (S), inflation (i), the amount
of spending in the previous year (Year 0),
and the average value of assets under
management (AUM):
ππππππππ 1 π π π π π π π π π π π π π π π π
= [π€π€ &times; ππππππππ 0 π π π π π π π π π π π π π π π π  &times; (1 + ππ)]
+[(1 − π€π€) &times; ππ &times; π΄π΄π΄π΄π΄π΄]
o Market value rule: Set w to 0.
o Constant growth rule: Set w to 1.
o Hybrid rule (a.k.a. Yale spending rule):
Set w between 0 and 1.
Stakeholders
The two most important stakeholder groups
for university endowments are current and
future students.
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Investment Objectives
- A university endowment’s main investment
objective is to achieve intergenerational equity
between current and future students.
- The primary component of an endowment’s
return objective is the spending rate. Other
components of a return target that is sufficient
to maintain purchasing power include inflation
and management fees.
Legal/Regulatory Constraints
Investment committees of endowments are often
required to invest on a total return basis and
achieve sufficient diversification.
Tax Constraints
- Endowments are typically tax-exempt investors.
- Unlike foundations, endowments tend not to be
subject to minimum spending requirements in
order to maintain this status.
Risk Considerations
- Investment Horizon: Because university
endowments are continually accounting for the
interests of future students, their investment
horizon is perpetual.
- Liquidity Needs: Have lower liquidity needs
than foundations.
- When assessing an endowment’s ability to
tolerate investment risk, consider the
degree to which the university depends
on its contributions.
Asset Allocation
- Small allocations to cash and highly liquid
securities are maintained in order to meet
immediate spending needs.
- Larger endowments have relatively high
allocations to illiquid alternative assets.
- The share of alternatives in endowment
portfolios has been increasing over time at the
expense of equities and fixed income securities.
Banks
Liabilities
- Demand deposits have effectively zero duration
as they can be withdrawn at any moment.
- Time (term) deposits, such as savings accounts
and certificates of deposit, have slightly longer
duration because funds cannot be withdrawn
- Banks can also access short-term wholesale
funding, but this is a higher cost source of
funds than deposits, which are perceived
as more stable.
Stakeholders
- The primary stakeholders of banks are the
customers who deposit their funds and the
- Counterparties to derivative contracts and
shareholders also have a strong interest in the
ongoing operations of banks.
Investment Objectives
Banks typically use their investment portfolios to
manage their exposure to interest rate risk.
Insurers
Liabilities
- Life Insurer:
o Due to the long-term nature of their liabilities,
investment horizons of 20 to 40 years.
However, this has changed as insurers have
diversified into new product lines.
o For certain products (e.g., term life insurance,
fixed annuities), the insurer bears the
investment risk.
o Certain life insurance liabilities are highly
sensitive to interest rates.
- Property and Casualty Insurers:
o P&amp;C insurers have shorter duration, more
volatile liabilities. As a result, P&amp;C insurers
tend to allocate a higher proportion of their
portfolios to cash and short-term fixedincome instruments.
- Regulators typically require insurers to have a
reserve portfolio to meet policy liabilities.
- A surplus portfolio is used to earn higher
returns. Insurers are more willing to accept
liquidity risk in this portfolio, including
allocations to alternative assets.
Stakeholders
The main stakeholders of insurance companies
are the policyholders who pay premiums for
protection and expect to be compensated
for insured events.
Investment Objectives
- An insurance company’s investment objectives
will be consistent with the expected timing and
amount of policyholders’ claims.
- In general, insurers use their investment
portfolios to meet their liquidity needs as well
as to manage their exposure to interest rate risk,
credit risk, and exchange rates.
Banks and Insurers
Legal/Regulatory Constraints
- Banks and insurers are subject to a relatively
high level of regulatory and legal constraints
compared to other institutional investors.
- Regulators want to ensure that financial
intermediaries have sufficient equity capital to
provide a buffer against losses on assets (e.g.,
loan defaults, negative investment returns) to
preserve their ability to meet their obligations
to depositors, lenders, and policyholders.
- Regulators also focus on ensuring that financial
intermediaries have sufficient liquidity.
Tax Constraints
Banks and insurance companies are fully
taxable for-profit entities.
Balance Sheet Management
- Banks and insurance companies use the liability
driven investing (LDI) model, which
recommends asset allocations based explicitly
on their ability to hedge liabilities.
- To calculate the change in equity in percentage
terms, we must account for leverage using the
following formula:
π΄π΄
π΄π΄
%π₯π₯π₯π₯ = O P %π₯π₯π₯π₯ − O − 1 P %π₯π₯π₯π₯
πΈπΈ
πΈπΈ
8
Managing Interest Rate Risk
- Sensitivity to interest rates is captured by the
modified duration measure.
- The duration of the financial intermediary's
equity is calculated as follows:
π΄π΄
π΄π΄
π₯π₯π¦π¦4
π·π·H = O P π·π·: − O − 1 P π·π·4
πΈπΈ
πΈπΈ
π₯π₯π¦π¦:
Managing Equity Volatility
- Equity volatility (standard deviation) is
π΄π΄ π΄π΄
ππH- = O P ππ:- + O − 1 P ππ4πΈπΈ
πΈπΈ
π΄π΄ π΄π΄
− 2 O P O − 1 P ππππ: ππ4
πΈπΈ πΈπΈ
- Actions that can reduce the asset volatility and,
by extension, equity volatility, include:
o Holding higher quality fixed-income
securities to reduce credit risk
o Holding more cash and short-term securities
to reduce liquidity risk
o Matching the durations of assets and
liabilities to reduce interest rate risk
- For insurance companies, actions that decrease
the volatility of liabilities include imposing
penalties on surrenders, having more
predictable underwriting losses, and
diversifying into different product lines to take
advantage of the law of large numbers.
PORTFOLIO
MANAGEMENT
(PART(PART
II) II)
PORTFOLIO
MANAGEMENT
OVERVIEW
OF ASSET
OVERVIEW OF
ASSETALLOCATION
ALLOCATION
Approaches to Asset Allocation
- Asset-only: Focus is solely on the assets, with
mean-variance optimization the most common
approach. Liabilities are not explicitly modelled.
- Liability-relative: Assets are chosen to fund
the liabilities. Surplus optimization is
a common approach.
- Goals-based: Assets are divided into
sub-portfolios to meet specified goals. Each
goal specifies the cash flows, time horizon,
and risk tolerance.
Asset Classes
The following five criteria helps
specify asset classes:
- Assets within a class should be
relatively homogenous.
- Asset classes should be mutually exclusive.
- Asset classes should be diversifying
to avoid redundancy.
- The asset classes collectively should cover most
of the available world investable assets.
- The asset class should be able to absorb a
significant portion of the investor’s portfolio
without undue liquidity impairments.
A Framework for Rebalancing
- Calendar rebalancing rebalances on a schedule.
- Percent-range rebalancing rebalances if the
portfolio drifts out of a specified range.
www.saltsolutions.com
Strategic Considerations in Rebalancing
- Higher transaction costs, less risk-averse
investors, more correlated assets, beliefs in
momentum, illiquidity, and taxes lead to wider
rebalancing ranges.
- Belief in mean reversion leads to tighter
rebalancing bands.
- Illiquid assets can create a problem.
- Tax issues can create asymmetric bands.
PRINCIPLES OF
PRINCIPLES
OFASSET
ASSETALLOCATION
ALLOCATION
Developing Asset-Only Allocations
Mean-Variance Optimization (MVO)
The investor’s utility, U, from an asset
allocation mix, m, can be calculated
with the following formula:
ππB = πΈπΈ[ππB ] − 0.005ππππB
where ππ is the investor’s degree of risk aversion.
Criticisms of MVO
- The outputs are very sensitive to the inputs,
especially expected returns.
- The optimal allocations are very concentrated in
a subset of available assets.
- Investors are concerned about more than the
mean and variance of returns.
- Sources of risk may not be diversified, even if
using many asset classes.
- MVO allocations are not directly related to the
liabilities being funded.
- MVO is a single-period framework that does not
weights that are assumed to be optimal, along
with covariance and risk aversion estimates.
Then, the expected returns are solved for.
from reverse optimization, then applies a
method to incorporate the investor’s views.
- Resampled Mean-Variance Optimization:
Combine MVO with Monte Carlo simulation.
to Illiquid Assets
- Exclude them from the asset allocation decision,
but use them for the target strategic asset
allocation.
- Include the less liquid assets and attempt to
model the inputs for the specific risk of assets
likely to be used.
- Include the less liquid assets and model the
highly diversified characteristics with the true
asset classes.
Risk Budgeting
The marginal contribution to total risk (MCTR) and
the absolute contribution to total risk (ACTR) can
be calculated as:
- ππππππππ7 =
(π΅π΅π΅π΅π΅π΅π΅π΅ ππππ ππ π€π€. ππ. π‘π‘. ππππππππ. )(ππππππππ. π£π£π£π£π£π£π£π£π£π£π£π£π£π£π£π£π£π£π£π£)
- π΄π΄π΄π΄π΄π΄π΄π΄7 = (ππππππππβπ‘π‘7 )ππππππππ7
Developing Liability-Relative Asset Allocations
Characterizing the Liabilities
Characteristics of liabilities that affect
asset allocation in liability-relative asset
allocation include:
- Fixed or contingent liabilities
- Legal liabilities and quasi-liabilities
- Duration and convexity of liability cash flows
- Size relative to organization
- Factors driving the liability, timing,
and regulations
Approaches to Liability-Relative Asset Allocation
- Surplus optimization substitutes surplus
return for the asset return in traditional
mean-variance optimization.
4V
= πΈπΈ.ππA,B 5 − 0.005ππππ - .ππA,B 5
ππB
o Surplus return is:
πΆπΆβππππππππ ππππ ππππππππππ π£π£π£π£π£π£π£π£π£π£ − πΆπΆβππππππππ ππππ ππππππππππππππππππ π£π£π£π£π£π£π£π£π£π£
πΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌ ππππππππππ π£π£π£π£π£π£π£π£π£π£
o Simple, linear correlation, all risk levels, any
funded ratio, single period
- A hedging/return-seeking portfolios approach
assigns assets to one of two portfolios. The
objective of the hedging portfolio is to hedge the
investor’s liability stream. Any remaining funds
are invested in the return-seeking portfolio.
o Simple, linear or non-linear correlation,
conservative risk levels, positive funded ratio,
single period
- An integrated asset-liability approach integrates
the asset and liability decisions when optimizing
a portfolio.
o Complex, linear or non-linear correlation, all
risk levels, any funded ratio, multiple periods
ASSET ALLOCATION
ASSET
ALLOCATIONWITH
WITH REAL-WORLD
CONSTRAINTSCONSTRAINTS
REAL-WORLD
Constraints in Asset Allocation
- Asset Size
- Liquidity
- Time Horizon
- Regulatory and Other External Constraints
Asset Allocation for the Taxable Investor
- The after-tax return is the pre-tax return
ππ(\$ = ππO\$ (1 − π‘π‘)
- For equity assets, the typical return includes
dividend income and capital gains:
ππ(\$ = ππI ππO\$ (1 − π‘π‘I ) + ππ( ππO\$ 21 − π‘π‘CJ 4
ππI is the proportion of ππO\$ from
dividends ππ( is the proportion of ππO\$ from
price appreciation
- The after-tax standard deviation is also affected
by the tax rate:
ππ(\$ = ππO\$ (1 − π‘π‘)
Strategies to Reduce Tax Impact
Other strategies can be used to reduce
the tax impact:
- Tax-loss harvesting is intentionally realizing
capital losses to offset capital gains in another
part of the portfolio.
- Strategic asset location is placing less taxefficient assets in accounts with more favorable
tax treatment such as tax-exempt or taxdeferred accounts.
9
In general, to minimize overall taxes:
- Equities are placed in taxable accounts
because they incur lower tax rates.
- Taxable bonds and high-turnover
strategies should be in tax-exempt or
tax-deferred accounts.
- Assets held for liquidity purposes should
be placed in taxable accounts.
Short-Term Shifts in Asset Allocation
- Strategic asset allocation (SAA) is for long-term
investment policy.
- Tactical asset allocation (TAA) attempts to
deviate in the short term from SAA to take
o Discretionary TAA depends on a qualitative
interpretation of political, economic, and
financial market conditions. It relies on
manager skills in predicting and timing shortterm market moves.
o Systematic TAA depends on qualitative signals
to exploit persistent anomalies in the market,
such as value and momentum.
STRATEGIESAND
ANDEXECUTION
EXECUTION
Implementation Shortfall
- IS is calculated as the difference between a
trade’s paper return and its actual return.
- The paper return is the return that would
have been earned if all shares were transacted
at the decision price without any associated
costs or fees:
ππππππππππ ππππππππππππ = (ππ&quot; − ππI )ππ
where
o S is the total order shares (value is positive
for buy orders and negative for sell orders)
o ππI is the decision price
o ππ&quot; is the current price
- The actual return of the portfolio
is calculated as:
π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄ ππππππππππππ = &ccedil;&Eacute; π π Y &eacute; ππ&quot; − &Eacute; π π Y ππY − πΉπΉπΉπΉπΉπΉπΉπΉ
where
o π π Y represents the number of shares executed
o ππY represents the transaction price
o ∑π π Y represents the total number
of shares executed
o Fees include all costs paid by the fund to
complete the order
- Rearranging the basic IS formula allows us to
decompose the total trade costs into three parts:
o Execution cost: Cost that arises due to the
&Eacute; π π Y ππY − &Eacute; π π Y ππI
o Fixed fees: Includes all fees such as
commissions, exchange fees, and taxes
o The restated formula is:
πΌπΌππ = πΈπΈπΈπΈπΈπΈπΈπΈ. ππππππππ + ππππππππππ. ππππππππ + πΉπΉπΉπΉπΉπΉπΉπΉπΉπΉ ππππππππ
Expanded Implementation Shortfall
- The execution cost can be further decomposed
into two parts:
ππππππππππππππ ππππππππ = &Eacute; π π Y ππY − &ccedil;&Eacute; π π Y &eacute; ππ'
π·π·π·π·π·π·π·π·π·π· ππππππππ = &ccedil;&Eacute; π π Y &eacute; ππ' − &ccedil;&Eacute; π π Y &eacute; ππI
- Trade costs can be stated in absolute
terms or on a per share basis, but investment
professional typically express these costs
in terms of basis points (bps) using the
following formula:
ππ&egrave; − ππ ∗
&times; 10,000 ππππππ
πΆπΆπΆπΆπΆπΆπΆπΆ (ππππππ) = ππππππππ &times;
ππ ∗
where
o Side has a value of +1 for a buy order of a -1
for a sell order
o ππ&egrave; is the average execution price of the order
o ππ ∗ is the reference price
- Market-adjusted cost can be calculated
using the following formula:
ππππππππππππ − ππππππππππππππππ ππππππππ (ππππππ)
= π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄ ππππππππ (ππππππ) − π½π½ &times; πΌπΌπΌπΌπΌπΌπΌπΌπΌπΌ ππππππππ (ππππππ)
where
o πΌπΌπΌπΌπΌπΌπΌπΌπΌπΌ ππππππππ (ππππππ) = ππππππππ &times;
K&quot;I%G L^:?,K&quot;I%G (++7_(8 O+7C%
K&quot;I%G (++7_(8 O+7C%
&times; 10,000 ππππππ
o π½π½ is the stock’s beta relative to
the underlying index
- The formula for calculating the
π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄ (ππππππ)
= π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄ ππππππππ (ππππππ) − πΈπΈπΈπΈπΈπΈ. ππππππ
− π‘π‘π‘π‘π‘π‘π‘π‘π‘π‘ ππππππππ (ππππππ)
PORTFOLIO PERFORMANCE
PORTFOLIO
PERFORMANCEEVALUATION
EVALUATION
- Transaction-based attribution: It uses both
portfolio holdings and transaction data to fully
explain excess return, including the impact of
trading costs. Most comprehensive and accurate.
- Holdings-based attribution: It compares a
portfolio’s holdings at the beginning and end of
a period. Holdings are valued at the end of a
period and a return is calculated relative to their
value at the end of the previous period.
- Returns-based analysis: It can be used when
complete data on a portfolio’s holdings are
unavailable. Least accurate.
- When an arithmetic attribution approach is used
excess return is defined as the difference
between a portfolio’s return (R) and the return
on its benchmark (B).
- When a geometric attribution approach
is used, geometric excess return (G) is
calculated as follows:
ππ − π΅π΅
1 + ππ
−1=
πΊπΊ =
1 + π΅π΅
1 + π΅π΅
Equity Return Attribution – The Brinson Model
- Returns for the portfolio and its benchmark
are calculated as the weighted average of
sector returns:
&quot;
ππππππππππππππππππ ππππππππππππ: ππ = &Eacute; π€π€7 ππ7
7T&amp;
&quot;
π΅π΅π΅π΅π΅π΅π΅π΅βππππππππ ππππππππππππ: π΅π΅ = &Eacute; ππ7 π΅π΅7
7T&amp;
where
o π€π€7 : portfolio weight of the ith sector
o ππ7 : portfolio asset return in the ith sector
o ππ7 : benchmark weight of the ith sector
o π΅π΅7 : benchmark asset return in the ith sector
- Under the Brinson model, there are
three sources of excess return for an
equity investment:
o Asset allocation effect: π΄π΄7 = (π€π€7 − ππ7 )π΅π΅7
o Security selection effect: ππ7 = ππ7 (ππ7 − π΅π΅7 )
o Interaction effect: πΌπΌ7 = (π€π€7 − ππ7 )(ππ7 − π΅π΅7 )
Return Attrition
- A common factor model used for equity
attribution analysis is the Carhart model:
ππO − ππ# = ππO + ππO&amp; ππππππππ + ππO- ππππππ
+ππO` π»π»π»π»π»π» + ππOa ππππππ + πΈπΈO
- Exposure Decomposition – Duration Based: Topdown approach that breaks down the portfolio
risk exposures based on certain characteristics
such as bond duration and sector.
- Yield Curve Decomposition – Duration Based:
Can be either top-down or bottom-up. It
estimates the return on investment using the
relationship between duration and the change
in yield to maturity (YTM).
%ππππππππππ ππππππ. = %πΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌπΌ ππππππ. +%ππππππππππ ππππππ.
where
%ππππππππππ ππππππ. ≈ −π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π· &times; πΆπΆβππππππππ ππππ ππππππ
- Yield Curve Decomposition – Full Repricing:
A bottom-up technique that measures the
contributions from the change in spot rates
and the quality of active management.
o Opportunity cost: Cost that arises when an
order cannot be fully executed due to adverse
price movement or a lack of liquidity during
&ccedil;ππ − &Eacute; π π Y &eacute; (ππ&quot; − ππI )
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10
Benchmarking Investments and Managers
Properties of a Valid Benchmark
- Investable: It is possible to invest passively
in the benchmark as an alternative accepting
the portfolio’s active risk exposures.
- Appropriate: The benchmark is consistent
with a manager’s style and any constraints
imposed by the client.
- Measurable: The benchmark’s performance
can be easily measured.
- Specified in advance: The identity of
the benchmark is known before the
evaluation period begins.
- Owned/Accountable: The manager owns
the benchmark and agrees to be held
accountable to it.
- Unambiguous: The composite securities
and their weights in the benchmark are
clearly identifiable.
- Reflective of opinions: The manager knows
and has opinions on all of the securities
in the benchmark.
Decomposing Portfolio Returns
- A portfolio’s total return, R, can be decomposed
into the benchmark return, B, and the manager’s
active return, A.
ππ = π΅π΅ + π΄π΄
- The benchmark return can be further
decomposed into the market index return, M,
and the style return, S.
π΅π΅ = ππ + ππ
- Using these formulas, we can think of portfolio
return as the sum of three components:
ππ = ππ + ππ + π΄π΄
o If a portfolio’s benchmark is a broad market
index, the S is zero and R = M + A.
o If a portfolio is meant to replicate the
performance of a broad market index with
zero tracking error (e.g., an index ETF), then
both S and A are zero and R = M.
Performance Appraisal
Measure
Sharpe ratio
Numerator
ππ? − ππ#
Denominator
ππ?
Sortino ratio
ππ? − ππ.
ππ6
Information rat.
ππ? − ππE
ππ(+',+()
Treynor ratio
Appraisal ratio
ππ? − ππ#
πΌπΌ
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π½π½?
ππb
Capture ratios measure a portfolio’s
return relative to its benchmark in
different market conditions.
o The upside capture (UC) ratio measures
benchmark return in periods when the
benchmark return is positive.
o The downside capture (DC) ratio expresses
the same relationship in down markets.
o The upside and downside ratios combine
to give a single capture ratio (CR) that is
calculated as UC divided by DC.
- Drawdown is a portfolio’s cumulative
peak-to-trough loss over a continuous period.
Investors measure drawdowns in terms
of both money and time.
o The financial impact of drawdown is
measured by maximum drawdown, which
is a portfolio’s largest peak-to-trough loss
(in percent).
o The time component of a drawdown is
captured by drawdown duration, which is
the amount of time that extends from when a
portfolio starts to fall from its peak until it
returns to that level.
INVESTMENT MANAGER
INVESTMENT
MANAGER SELECTION
SELECTION
Actual Performance
Hire/Retain
Not hire /
Fire
Below
Expectations
Above
Expectations
Type I error
Correct
decision
Correct
decision
Type II error
The active share measure is based on the difference
between the weights given to securities in a
portfolio and their benchmark weights.
π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄π΄ ππβππππππ =
P
1
&Eacute;|ππππππππππππππππππ ππππππππβπ‘π‘7
2
7T&amp;
− π΅π΅π΅π΅π΅π΅π΅π΅βππππππππ ππππππππβπ‘π‘7 |
ETHICAL AND PROFESSIONAL STANDARDS
ETHICAL AND PROFESSIONAL STANDARDS
I(A) Knowledge of the Law
Obey strictest applicable law. Disassociate
immediately from any illegal or unethical activity.
I(B) Independence and Objectivity
Do not offer or accept gifts that might impair
independence and objectivity. Gifts from clients
may be permissible.
I(C) Misrepresentation
Cite sources. Do not plagiarize or omit important
information. Act quickly to correct any errors.
I(D) Misconduct
Does not apply to personal behavior unless it
reflects poorly on the investment profession.
II(A) Material Nonpublic Information
Do not act or cause others to act on material
nonpublic information. Seek public dissemination.
II(B) Market Manipulation
Do not take any actions that distort prices or
trading volume. Market making and legitimate
III(A) Loyalty, Prudence, and Care
Place clients’ interest above yours. Disclose
policies on proxy voting and soft commissions.
III(B) Fair Dealing
Treat all clients fairly. Treat non-immediate family
like other clients. Communicate investment
recommendations and changes simultaneously.
III(C) Suitability
Use a regularly updated IPS during investment
decisions. Evaluate decisions in a portfolio context.
III(D) Performance Presentation
Performance data should be fair, accurate, and
complete. Do not promise returns for risky assets.
III(E) Preservation of Confidentiality
Keep all client information confidential unless:
client is involved in illegal activity, you are legally
required, or you have the client’s permission.
11
IV(A) Loyalty
Get permission before taking outside work (even
unpaid) that competes with employer. Abide by
non-compete agreement (if applicable) and do not
take employer’s property.
Obtain written permission from all parties before
receiving any compensation for outside work.
IV(C) Responsibilities of Supervisors
Supervisors must adequately train and monitor
subordinates. Responsibilities may be delegated.
V(A) Diligence and Reasonable Basis
Exercise diligence and thoroughness. Support
actions with research and investigation.
V(B) Communication with Clients and
Prospective Clients
Make appropriate disclosures. Distinguish between
fact and opinion in analysis and recommendations.
V(C) Record Retention
Maintain records to support recommendations and
decisions. 7-year retention period recommended.
VI(A) Disclosure of Conflicts
Disclose any matters that may impair
independence and objectivity, prominently
and in plain language.
VI(B) Priority of Transactions
Execute clients’ transactions before accounts
in which you have a beneficial interest.
BA II PLUS CALCULATOR TIPS
BA II PLUS CALCULATOR TIPS
Basic Operations
2ND : Access secondary functions (in yellow)
ENTER : Send value to a variable
2ND + ENTER : Toggle between options
↑ ↓ : Navigate between variables/options
STO + 0 - 9 : Store current value into memory
RCL + 0 - 9 : Recall value from memory
Time Value of Money (TVM)
For annuity, loan, and bond calculations
N : Number of periods
I/Y : Effective interest rate per period (in %)
PV : Present value
PMT : Payment/coupon amount
FV : Future value/redemption value
CPT + one of the above : Solve for unknown
2ND + BGN : Toggle between ordinary annuity
and annuity due
2ND + CLR TVM : Clear TVM worksheet
Cash Flow Worksheet ( CF , NPV , IRR )
For non-level payments
Input ( CF )
CF0: Initial cash flow
C01: 1st distinct cash flow after initial cash flow
F01: Frequency of CO1
C0n: nth distinct cash flow
F0n: Frequency of C0n
Note:
- Always clear the CF worksheet before starting
a new calculation
- The use of F0n is optional. You can leave them as
1 and input repeating cash flows multiple times. If
you do so, C01 will be the cash flow at time 1, C02
will be the cash flow at time 2, and so on.
Output ( NPV , IRR )
I: Effective interest rate per period (in %)
NPV + CPT : Solve for net present value
IRR + CPT : Solve for internal rate of return
Note:
- Always clear the TVM worksheet before
starting a new calculation
- For bonds, PMT and FV should have the same
sign, and opposite signs to PV
VI(C) Referral Fees
Disclose referral fees to clients and employer,
including non-monetary arrangements.
VII(A) Conduct as Participants in
CFA Institute Program
Do not share confidential exam details. Expressing
opinions about CFAI policies is permissible.
VII(B) Reference to CFA Institute, the CFA
Designation, and the CFA Program
Do not misrepresent the meaning of CFA Institute
membership, designation, or candidacy.
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