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Sample Examination Paper
Final Examination
Questions
Portfolio Management
Derivative Valuation and Analysis
Fixed Income Valuation and Analysis
Exam Guide
Subject Area Question Number Weight
Fixed income valuation and analysis Q 1 20 points
Fixed income valuation and analysis Q 2 25 points
Derivative valuation Q 3 25 points
Derivative valuation Q 4 33 points
Portfolio management Q 5 30 points
Portfolio management Q 6 20 points
Portfolio management Q 7 7 points
Portfolio management Q 8 20 points
180 points
Time allowed : 180 minutes
Exam Guide
Answer all questions
Question 1: Bond Valuation and Analysis (20 points)
You are considering investing in a bond for the next twelve months. You are limiting your
choice of bond to one of the following, both of which pay annual coupons at year end and
have identical credit risk:
Bond Maturity Coupon YTM
A 2 years 8% 7.842%
B 3 years 9% 8.027%
(a) If the one year, two year and three year spot rates are 7.65%, 7.85% and 8.05%
respectively, determine the prices of bond A and bond B. (4 points)
(b) Estimate, using duration, the expected change in price of bond B for a 0.2% change
in yield to maturity. (5 points)
(c) Calculate the difference in the one year holding period return on the bonds, assuming
that spot rates will fall in twelve months’ time by 0.2% across the maturity spectrum. (6 points)
(d) When estimating holding period return, what are the implications of each of the
following assumptions?
(i) the yield to maturity or spot rate curve will remain constant; and
(ii) the forward rate curve correctly estimates future spot rates (5 points)
Exam Guide
Question 2: Bond Valuation and Analysis (25 points)
A pension fund is currently showing a surplus in its asset/liability position (see table below).
Under International Accounting Standards (IAS), which were recently adopted, pension
liabilities must be valued at market interest rates, and, if they are larger than fund assets, the
difference must be posted to the corporate balance sheet as a liability. You have been asked
to invest in bonds in such a way as to avoid this happening. Answer the following questions
about your investment strategy.
Pension Fund Asset/Liability Position
Value
($1 million)
Modified
duration (years)
Pension assets
Bonds
Equities
Pension liabilities
Surplus
120
80
40
110
10
6
7
4
12
–
(a)
(b)
Assume that the amount of future pension benefits is fixed in nominal terms and that
you want to maintain a surplus even if there is a movement in interest rates that
causes a change in the liability. You may also assume for the following questions that
interest-rate movement is parallel and that the convexity effect can be ignored.
(i) If you keep your current asset mix, how many percentage points up or down
will interest rates need to move before the surplus is negative?
(ii) You want to keep the current asset mix ($80 million in bonds, $40 million in
equities), but change the composition of the bond portion so that the current
surplus is maintained even if interest rates move. How many years should the
bonds’ modified duration be?
(iii) If you put all of your assets into bonds, what modified duration will enable you
to maintain the current surplus even if interest rates move?
(iv) Referring to the previous two cases, i.e. (a)(ii) and (a)(iii), discuss the pros and
cons of lengthening the duration of your bond investments.
Pension benefit amounts will be usually indexed to inflation, and you need to take
this factor into account in valuing pension liabilities and in managing bond
portfolios.
(i) Assume the kind of investments described in Question (a)(iii). If there is
inflation, what effect will it have on assets and liabilities and on the surplus?
(ii) If pension benefit amounts are indexed to inflation, what discount rate should
you use to value liabilities?
(iii) Discuss the kind of bonds you should invest in if pension benefit amounts are
indexed to inflation.
(3 points)
(3 points)
(3 points)
(4 points)
(4 points)
(4 points)
(4 points)
Exam Guide
Question 3: Derivative Valuation and Analysis (25 points)
You are currently managing a well-diversified stock portfolio with a beta of 1.2 on the
TOPIX* index of Tokyo Stock Exchange stock prices. The TOPIX is now at 1600, one-
year (riskless) interest is 3%, and the aggregate market value of your portfolio is ￥16 billion.
Ignoring dividends, answer the following questions. (Where calculations are necessary,
include the calculations clearly in your answer sheet.)
*TOPIX: The weighted average stock price index of all TSE 1st Section listed stocks.
(a) Given a TOPIX value of T one year from now, what will be the Value V of your
portfolio at this time? Express V as a function of T. (4 points)
(b) (i) Assume the prices and deltas of a put option on the TOPIX with one year to
maturity are as follows:
Exercise Price 1600 1608 1616 1624 1632 1640 1648
Put Price 72.8 76.3 80 83.3 87.6 91.6 95.7
Delta –0.393 –0.406 –0.419 –0.431 –0.444 –0.457 –0.470
Depending on the TOPIX value one year hence, your portfolio may suffer a
loss and you have thought of hedging with a purchase of puts capable of
maintaining the minimum portfolio value (before put premium, of ￥16
billion). Assuming that one TOPIX option corresponds to an amount 10,000
times that of the index, how many puts should you buy at what exercise price? (5 points)
(ii) How much will this hedge cost? (2 points)
(c) Since it is difficult to buy puts with one year to maturity on the market, you think of
achieving the same results as in Question 2 by using futures for dynamic hedging.
(i) Assuming that one-month (risk-free) interest is now 3% (at an annual rate) and
that the TOPIX futures with one month to maturity are at their theoretical
price, how many futures should you sell for the purpose of dynamic hedging?
Assume that the trading unit of the TOPIX futures is 10,000 times the index
and that the amount corresponding to the costs required for the puts purchased
in Question 2 is invested at the risk-free interest rate. (5 points)
(ii) Assume that immediately afterwards, stock prices rise and TOPIX hits 1632.
Now how many futures should you sell in order to effect dynamic hedging?
The prices and deltas of a put with one year to maturity when TOPIX is at
1632 are as follows: (5 points)
(iii) The put prices and deltas given in the table for Question (c)(ii) above are the
figures given an estimated volatility of 15%. Explain what the results of
dynamic hedging would be if volatility were actually greater than 15% and
TOPIX fell. (4 points) | 
