EXAMINATION II:
Fixed Income Analysis and Valuation
Derivatives Analysis and Valuation
Portfolio Management
Questions
Final Examination
September 2010
Question 1: Fixed Income Analysis and Valuation
(31 points)
Investment Advisory Service X has not previously included Consumer Price Index (CPI)linked government bonds in its bond fund portfolio. However, as a bond analyst, you want to
recommend that they should be included because prices on the CPI-linked government bond
market experienced a much greater decline during last year's financial market upheavals than
prices for ordinary government bonds.
a) Many developed-country governments began issuing CPI-linked government bonds in the
1990s. Provide and briefly explain two reasons why CPI-linked government bonds were
considered beneficial to government fund-raising and debt policy.
(5 points)
Table 1 contains the real yield of a CPI-linked government bond with a 10 year maturity, the
breakeven inflation rate and the nominal yield of an ordinary "benchmark" government bond
with the same maturity as the CPI-linked government bond. The CPI-linked government bond
has a fixed coupon, and principal slides according to the cumulative rate of change for the
consumer price index between the time of issue and each interest payment (and maturity). The
coupon payment and redemption price are based on the adjusted principal. However, the CPIlinked government bond also has a "floor," and its principal will not decline below the value
at issue even if the cumulative rate of change for consumer prices is negative.
Nominal yield of benchmark government bond
(10 year maturity)
Breakeven inflation rate
Real yield of CPI-linked government bond
(10 year maturity)
2.95%
1.13%
1.82%
Table 1: Market yields for a CPI-linked government bond (maturity of 10 years) and
benchmark government bond
b) The real yield of any CPI-linked government bond is defined as the internal rate of return
of cash flow assuming the consumer CPI growth rate is zero; the breakeven inflation rate
is defined as the difference between the yield to maturity of the benchmark government
bond and the real yield of the CPI-linked government bond. Explain why this is called the
"breakeven inflation rate".
(5 points)
c) What impact does the floor have on the real yield on the CPI-linked government bond
required by investors?
(4 points)
d) You want to create a position that will benefit from an increase in the breakeven inflation
rate of the CPI-linked government bond. What combination of long positions and short
positions in the CPI-linked government bond and benchmark government bond will you
use so that 1) your portfolio is neutral with respect to changes of the same degree in the
benchmark government bond yield and CPI-linked government bond real yield and 2) you
will have a profit of 10,000 currency units per an immediate increase of 1 basis point
(= 0.01%) in the breakeven inflation rate? How much (value) of each bond will you trade
to achieve this (rounding to the nearest 1,000 currency units)? Use the modified durations
for the CPI-linked government bond and benchmark government bond provided in
Table 2.
(6 points)
ACIIA® Questions Examination Final II – September 2010
Page 1 / 11
CPI-linked government bond (10 year maturity)
Benchmark government bond (10 year maturity)
8.98
8.55
Table 2: Modified durations of the CPI-linked government bond and
benchmark government bond
To measure the risk associated with a portfolio that contains CPI-linked government bonds,
you collect historical data on CPI-linked bond real yields, breakeven inflation rates and
benchmark government bond yields to maturity and calculate the correlation coefficients with
standard deviations for the daily changes in each of these figures (Table 3).
Standard
deviation
Correlation coefficient
(%)
Δ it
Δ rt
Δ beit
Δ it
0.065
Δ it
1.000
0.810
0.405
Δ rt
0.061
Δ rt
0.810
1.000
-0.208
Δ beit
0.039
Δ beit
0.405
-0.208
1.000
Δit: Change (in %) from the previous day in the nominal yield of the benchmark government bond
Δrt: Change (in %) from the previous day in the real yield of the CPI-linked government bond
Δbeit: Change (in %) from the previous day in the breakeven inflation rate
Table 3: Daily changes in market yields and breakeven inflation rates
e) In order to understand the relationship between changes in the yield to maturity of the
benchmark government bond and changes in the CPI-linked government bond (the "yield
beta"), use the calculation results found in Table 3 to derive the value of β in Equation (1)
assuming that measurement is made with a regression equation shown below for the same
period as covered in Table 3. You should calculate beta rounding the value to two decimal
places.
Δrt = α + β Δ it + ξt
Equation (1)
where:
Δit: Change (in %) from the previous day in the nominal yield of the benchmark
government bond.
Δrt: Change (in %) from the previous day in the real yield of the CPI-linked government
bond.
ξt: independent and identically distributed (i.i.d.) error term with zero mean.
(5 points)
f) The yield to maturity of the benchmark government bond will not on average change by
the same amount as the real yield of the CPI-linked government bond unless β in Equation
(1) is equal to 1. Therefore, the profit or loss on the position created in Question d) will be
statistically correlated to the nominal interest rate level, for which the yield to maturity of
the benchmark government bond serves as a proxy. Your supervisor tells you that yield
beta should be used to adjust the correlation when building the position in Question d).
What do you think about this idea?
(6 points)
ACIIA® Questions Examination Final II – September 2010
Page 2 / 11
Question 2: Fixed Income Analysis and Valuation
(27 points)
You are the Executive Assistant to the Chief Risk Officer of a regional bank in Europe.
Whilst the turbulences in the financial markets decreased over the last months, your boss has
asked you to conduct risk analysis and stress tests based on the bank’s balance sheet given
below (the balance sheet is very simplified, as there is no loan item in spite of being the one
of a bank. Ignore credit risk).
(Amounts: in EUR billions)
Assets
Instrument
Bond A
Bond B
Bond C
Liabilities & Equity
Notional
amount
Value
amount
Maturity
[years]
Instrument
5.000
3.000
7.000
Total
4.682
2.602
5.322
12.606
3
5
8
Deposit
Bond D
Equity
Notional
amount
Value
amount
Maturity
[years]
3.000
10.000
Total
2.963
8.672
0.971
12.606
1
5
perpetual
Note: yield convention: 30/360, annual compounding
All Bonds A, B, C and D are zero-coupon bonds.
a) Calculate the discount rates and discount factors for maturities of 1 and 8 years [round the
discount rates to 3 decimal places, the discount factors to 5 decimal places].
(5 points)
b) What is the net duration of the balance sheet, above? (Assume a zero duration for the
Equity position. Net duration is defined as the difference between assets’ and liabilities’
Macauley duration).
(5 points)
c) Calculate the Tier 1 capital ratio of the given bank [Note: Tier 1 capital ratio = Equity /
Risk Weighted Assets, whereas risk weightings for all asset values stand at 100%].
(3 points)
d) Risk weightings for the values of Zero-Bonds A, B and C are assumed to increase to
125%, 150% and 200% respectively under Basel II in line with a deteriorating economic
environment. Determine the new Tier 1 ratio.
(3 points)
You are now asked to conduct a capital stress test based on the bank’s balance sheet.
According to Basel II the Total Minimum Capital Requirements for credit, market and
operational risk must be no lower than 8% of risk-weighted assets. Tier 2 capital
[= Undisclosed reserves, Revaluation reserves, General provisions, Hybrid debt capital
instruments and Subordinated term debt] is limited to 100% of Tier 1 capital [= Equity capital
and disclosed reserves], therefore the regulatory minimum Tier 1 ratio is 4%.
e) Your assistant quantifies the equity loss triggered by a 200 bp (i.e. 2%) parallel shift of all
discount rates in EUR 0.4 billion. Calculate the bank’s Tier 1 ratio after the 200 bp
parallel shift effect in the equity and under the higher risk weightings as in question d).
You can assume no changes in asset values. Is the bank passing the combined stress test in
the light of Basel II?
(5 points)
ACIIA® Questions Examination Final II – September 2010
Page 3 / 11
f) Lastly, you are asked for your view on the bank’s liquidity risk position [due to assetsliabilities mismatching] in terms of having to raise new liabilities once the existing ones
expire. How do you judge the bank’s liquidity risk exposure? (compare the bank’s longterm assets by corresponding liabilities). What kind of measures do you have in mind in
order to mitigate the bank’s liquidity risks? Mention 2 key measures.
(6 points)
ACIIA® Questions Examination Final II – September 2010
Page 4 / 11
Question 3: Derivatives Valuation and Analysis
(59 points)
In September 2010 you are analyzing S&P 500 (Symbol: SPX) index options traded at the
CBOE in Chicago. These SPX options will expire in 12 month from now and are European
type. The contract size is 100 USD per index point. Note that the dividend yield on the
S&P 500 index is approximately 3.3% per annum, while the riskless rate of interest is 0.5%
per annum (both continuously compounded). The volatility of the S&P 500 is 20% per
annum. The S&P 500 is currently at 990 points. You have got the following data from the
trading room:
Contract
Strike
K
Option
Prices
Delta

SPX Call
Sep 2011
950
86.0
0.54761
SPX Call
Sep 2011
975
70.8
SPX Call
Sep 2011
1000
SPX Call
Sep 2011
1025
Contract
Strike
K
Option
Prices
Delta

SPX Put
Sep 2011
950
69.7
- 0.41993
0.49777
SPX Put
Sep 2011
975
83.1
- 0.46977
60.6
0.44896
SPX Put
Sep 2011
1000
97.8
- 0.51858
51.6
0.40188
SPX Put
Sep 2011
1025
113.6
- 0.56566
Options do not necessarily trade at their theoretical prices.
[Hint: the present value “D” of the cash-dividends which are expected over the next year on
the stocks of the S&P 500 index is 32.14 index points (D = 32.14). The Delta  is derived
from Black-Scholes (B-S) formula; for example, the delta of the call is given by:
C

 e  y  N (d1 ) ].
S
a) Show whether put-call parity does hold for the options with strike 950.
(4 points)
b) Given there is an index tracker instrument available, an exchange traded fund (ETF) with
current value of 990 USD per unit, which mimics the total return of the S&P 500
perfectly, i.e. including dividends, how would you exploit a violation of put-call parity
trading 100 puts and/or calls with strike 950? Describe in detail which transactions are
necessary today to implement a riskless arbitrage, and detail the final value of the
positions in 12 months time depending on the index value at maturity ST [Hint: consider
separately the cases ST ≤ 950 and ST > 950]. How much would you earn from this
opportunity, if there are no transaction costs and you can invest/borrow at the riskless rate
of interest?
For your answer you can refer to the table below. You can either fill the table or derive
your answer in your own way.
ACIIA® Questions Examination Final II – September 2010
Page 5 / 11
TODAY
POSITION
Sample
Buy 100 calls with strike 975
index points
(per unit)
-70.8
USD
-708,000
IN 12 MONTHS
Value in index points
(per unit)
ST ≤ 950
ST > 950
0
ST-975
1.
2.
3.
4.
5.
Total:
(Hint: You can use numbers, ST, and/or words in “IN 12 MONTHS” columns.)
(14 points)
c) Your client, who is a strategic options investor, wants you to recalculate the “probability
of ending up in-the-money” for the SPX call and put with strike 1000. She claims that using the data from above - this probability is 34.2% for the call and 65.8% for the put.
Verify her calculations using the B-S-formula. [Hint: the risk neutral probability of a call
(7 points)
ending up in-the-money is: P(ST > K) = N(d2)]
d) Your client expects decreasing stock price quotations and wants to establish a long
position in a bear spread with calls. Using the SPX calls with strike 950 and 1025, this
means she buys 100 calls with strike 1025 and writes 100 calls with strike 950. Calculate
the initial investment, the maximum profit and/or loss, and the break even points at
expiration, if applicable. Draw the profit/loss-diagram of the strategy at expiration; ignore
interest on the option premiums.
(13 points)
e) Just after having established the bear spread with calls, your client wants to neutralize this
position for a short period of time using the index tracker ETF from question b). How
much of the index tracker fund should be bought/sold to neutralize the position? (4 points)
f) You mention that futures might be advantageous with respect to transaction costs
compared to the index tracker ETF. Given that S&P 500 futures contracts traded at the
CME in Chicago have a contract size of USD 250 times the futures price, how many
futures contracts should be bought/sold to neutralize the bear spread with calls? [Hint:
Consider the theoretical futures price formula.]
(5 points)
g) Assume that after neutralizing her position, the S&P 500 would suddenly soar more than
150 points. Briefly explain what adjustments would be necessary to her ETF position (if
she follows question e)) or S&P 500 futures position (if she follows question f)) to keep
the entire position neutral? (No further calculations are needed here.)
(4 points)
ACIIA® Questions Examination Final II – September 2010
Page 6 / 11
h) You explain to your client that there is still another possibility for a bearish spread in this
situation which could also be used to neutralize the bear spread with calls. Using 100 puts
with strikes 950 and 1025 instead of the ETF could be advantageous here. Show that
adding a short position in a bear spread with puts (in other words, a long bull spread with
puts) to her already established long position in that bear spread with calls from e) results
in a riskless position. Show that this so-called box spread is independent of the index
value at expiration. How much has to be invested in the entire box spread and how much
can be earned from it at expiration of the options? [Interest on option premiums should be
considered here.]
(8 points)
ACIIA® Questions Examination Final II – September 2010
Page 7 / 11
Question 4: Portfolio Management
(31 points)
In a defined benefit pension plan, enrollees are guaranteed pension benefits after retirement.
From the perspective of the pension fund offering the defined benefit pension plan, this
constitutes a liability, and the pension plan sponsor must therefore take account of this
liability when investing its assets. In other words, it must practice pension ALM (asset
liability management). In the following questions, we define pension liabilities and
investigate asset management methods suitable for meeting these liabilities.
Figure 1 illustrates the cash flow pattern for a defined pension plan that provides 1 million
yen in benefits per year for a period of 20 years. It also shows the present value of the cash
flow.
Figure 1: Pension cash flow pattern and present value
16
Amount (million yen)
14
Present value
12
10
8
Discounted calculation
6
4
Pension benefit (cash flow)
2
0
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
Ye ar
Assume that all returns are simple returns.
a) Assuming the discount rate is 4% per annum, what is the total present value of the pension
plan which pays 1 million yen every year (starting one year from now) for 20 years?
(4 points)
b) Assuming the discount rate moves to 5% per annum, what is the new total present value of
the pension plan discussed under a)? Describe the relationship between the discount rate
and the present value of pension liabilities.
(4 points)
It is possible to pay pension benefits by holding assets equivalent to the present value of
pension obligations, taking into account the premium revenue from enrollees in the pension
fund. The following scenario assumes that a discount rate changes according to the market
interest rate.
ACIIA® Questions Examination Final II – September 2010
Page 8 / 11
c) What kinds of assets do you think would be suitable investment assets for the pension
liabilities? Explain your reasons.
(4 points)
d) In general, asset management performance is measured against a market benchmark, even
for bonds. Describe two problems in using the bond market index as a benchmark for
pension liabilities such as those in Figure 1. Describe the characteristics of the bonds you
would invest in (focus your answer on the duration of the bonds).
(4 points)
Table 1 shows the expected returns, risks (standard deviation of returns) and correlation
coefficients for the pension fund's assets and liabilities. The pension fund is 100% funded
because the value of assets and the value of liabilities are equal at 10 billion yen. The surplus
returns of each asset against liabilities can be calculated by subtracting the return of the
liability from the return of the asset. The surplus risk can be calculated using the correlation
coefficient between asset and liability returns.
Short-term
instruments
Bonds
Equities
Liabilities
Amount
Expected
return
Risk
Correlation coefficient
(100 million
yen)
(%)
(%)
Short-term
Bonds Equities Liabilities
instruments
10
1
0
1.0
0.0
0.0
0.0
50
40
100
4
8
5
5
20
10
0.0
0.0
0.0
1.0
0.3
0.8
0.3
1.0
0.2
0.8
0.2
1.0
Table 1: Expected returns, risks and correlation coefficients for pension fund assets
and liabilities
e) Calculate the expected surplus returns and surplus risks for short-term assets and bonds,
and explain why they differ from the original risks.
e1) Expected surplus return and surplus risk for short-term instruments.
(3 points)
e2) Expected surplus return and surplus risk for bonds.
(3 points)
e3) Reasons for the difference with respect to the original risks.
(3 points)
f) The idea of investing pension assets in consideration of liabilities has a long history and
recently liability driven investment (LDI) has been drawing much attention.
f1) Discuss the need of LDI. Use two key words: “maturity” of pension fund (as measured
by benefit payments / premium receipts) and “risk tolerance”.
(3 points)
f2) IASB is proposing immediate recognition of change of net pension liabilities on the
balance sheet. Discuss the influence of the proposal on LDI.
(3 points)
ACIIA® Questions Examination Final II – September 2010
Page 9 / 11
Question 5: Portfolio Management
(32 points)
a) You are consulting for a pension fund. Your task is to pick a new active manager for
European equities. You base your analysis on the “Fundamental Law of Active
Management” [FLAM, originally stated by R. Grinold], which relates the expected
Information Ratio (IR) to the Information Coefficient (IC) and the number of independent
forecasts made per year (N), often called “breadth”. The Information Coefficient is
defined as the correlation coefficient between return forecasts and return realisations (that
is, actual returns). More specifically, the FLAM states that
IR  IC  N
In words, FLAM states that the productivity of an active manager will depend both on his
level of skill and how often that skill is put into use.
The following table contains some useful information on two active investment
management firms, HIGHTIME and PIXXAM:
HIGHTIME
PIXXAM
IC
0.12
0.01
Number of Analysts
3
30
The 3 analysts of HIGHTIME are needed to produce a monthly updated equity market
forecast, as a team, with information coefficient 0.12, according to which HIGHTIME
does market timing for their European equity mandates.
The task of the PIXXAM analysts is to produce forecasts for single stocks. Each analyst
does forecasts for 10 stocks, which are updated on a quarterly basis. This is the basis for
PIXXAM’s stock picking approach.
a1) Define briefly the activities “Market Timing” and “Stock Selection”.
(4 points)
a2) Define briefly, in general, “Information Ratio” with respect to its benchmark.
(3 points)
a3) Calculate the expected Information Ratios based on the FLAM and indicate which
asset manager you would prefer.
(4 points)
a4) Give some arguments why it could be advantageous to opt for active management.
(3 points)
b) You are consulting for a pension fund on strategic asset allocation. The client gives you
his investment goals:
- minimum cumulated return (over 4 years): 4% (with confidence of 95%)
- optimize expected returns subject to the minimum return requirement.
ACIIA® Questions Examination Final II – September 2010
Page 10 / 11
You have the following investment assets at your disposal:
- a global equity fund with expected return 10% p.a. and volatility 20% p.a.
- government Zero Coupon bonds with returns 3% p.a. at all maturities (which you may
assume as risk-free):
You assume returns as normally distributed and therefore calculate the VaR (value at risk)
of your portfolio return r to be:
VaR(r) = E(r) - ·(r)
with
E(r):
(r):
:
expected return p.a.
volatility (standard deviation) of returns p.a.
confidence parameter (for 95% confidence: 1.645)
Furthermore, for multi-year returns (for individual investments as well as for your overall
portfolio) cumulated over n years you assume that
E(rn) = E(r) · n
(rn) = (r) ·
and
n
[all returns are continuously compounded]
b1) How do you have to strategically allocate your overall portfolio into global equities
and zero bonds?
(7 points)
b2) What is the expected return p.a. of this asset allocation?
(2 points)
b3) The expected return of this recommendation is deemed too low by the client. The
client is now willing to relieve the restriction of 4% cumulated minimum returns. He
now formulates:
- lose no more than 10% (VaR after 4 years) with confidence of 95%.
- provide a solution which yields an expected return of 30% (cumulated over 4 years).
Can you find an asset allocation that fulfils these two requirements? If yes, give the
portfolio weights of global equities and zero bonds.
(9 points)
ACIIA® Questions Examination Final II – September 2010
Page 11 / 11