Asset Pricing
Semester Semester 1, 2023
Exam type Online, non-invigilated, end-of-semester examination
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Semester One Examinations, 2023 FINM2416 Asset Pricing
Page 2 of 5
Question 1 (20 Marks).
a. A corporate bond with a coupon rate of 10% makes semi-annual coupon payments on
January 15 and July 15 of each year. The Wall Street Journal reports the ask price for
the bond on February 15 at 102% of the par value. The par value of the bond is 1000.
What is the invoice price of the bond? The coupon period has 182 days.
(4 marks)
b. A 12.75-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective
annual yield) has convexity of 150.3 and modified duration of 11.81 years. A 30-year
maturity 6% coupon bond making annual coupon payments also selling at a yield to
maturity of 8% has nearly identical duration—11.79 years—but considerably higher
convexity of 231.2.
i. Suppose the yield to maturity on both bonds increases to 9%. What will be the
actual percentage capital loss on each bond? What percentage capital loss would
be predicted by the duration-with-convexity rule?
ii. Repeat part (a), but this time assume the yield to maturity decreases to 7%.
iii. Compare the performance of the two bonds in the two scenarios, one involving an
increase in rates, the other a decrease. Based on the comparative investment
performance, explain the attraction of convexity.
(10 marks)
c. The following table summarizes prices of various default-free, zero-coupon bonds
(expressed as a percentage of face value):
Maturity (years) 1 2 3 4
Price (per $100 face value) $96.21 $91.83 $87.16 $82.51
i. Compute the yield to maturity for each bond.
ii. Plot the zero-coupon yield curve (for the first five years).
iii. Is the yield curve upward sloping, downward sloping, or flat?
(6 marks)
Question 2 (20 Marks).
You have information on several possible investments as laid out in the table below. A, B,
and C are individual risky securities. F is the risk-free asset. M is the market portfolio. All
returns are annual returns.
Correlation
Matrix
Investment Expected
Return
Standard
Deviation
A B C F M
A 19.20% 36% 1.0000 0.7000 0.6000 0.0000 0.5
B 21.90% 35% 1.0000 0.5000 0.0000 0.6
C 12.00% 25% 1.0000 0.0000 0.4
F 3.00% 0% 1.0000 0.0
M 12.00% 10% 1.0
Semester One Examinations, 2023 FINM2416 Asset Pricing
Page 3 of 5
a. Using the correlation matrix, compute the covariance of asset A with the market and
B with the market.
(3 marks)
b. Using the correlation matrix, compute the beta of asset C.
(2 marks)
c. Assume that you want to form a portfolio that consist of a long position of $18,000
in asset C and a short position of $6,000 in asset A. What is the expected return and
risk of this portfolio?
(6 marks)
d. You have $100,000 to invest. You would like use a combination of M and F to obtain
a standard deviation of 4% on your overall portfolio. How much (in dollars) do you
invest in F if you choose the most efficient portfolio possible? What is the return of
this portfolio?
(6 marks)
e. Which one of the portfolios (A with M or B with M or C with M) are efficient? Explain.
(3 marks)
Question 3 (20 Marks).
A portfolio contains 45% of Bond I, 25% of Bond II, 15% of Bond III and 15% of Bond
IV. Details of the four bonds are given below:
I. 10-year zero coupon government bond, par value $1000, current price = $613.91
II. 10-year zero coupon corporate bond, par value $1000, default premium= 3%
III. 5 year 15 % coupon corporate bond, par value $1000, annual coupon payments,
default premium = 9% and YTM for similar government bond is 6%
IV. 5 year 15% government coupon bond, par value $1000, annual coupon payments,
YTM=7%
a. Find the prices of Bond II, Bond III, and Bond IV.
(3 marks)
b. What are the Macaulay’s durations of Bond III and Bond IV?
(6 marks)
c. What is the duration of the portfolio?
(3 marks)
d. What is the convexity of Bond I?
(4 marks)
e. If Bond I’s yield decreases by 2.5%, what is the price of Bond I based on duration-with-
convexity rule?
(4 marks)
Semester One Examinations, 2023 FINM2416 Asset Pricing
Page 4 of 5
Question 4 (20 marks):
a. Assume an institutional investor writes a March put option on shares of the DBS with
an exercise price of 280 and a March expiry date at a price of 10. Calculate the profit
and loss at the expiry date for this investor with the prices of 320 and 265. Draw the
profit graph of this option
(6 marks)
b. Assume an investor takes 2 positions: first, a long position in a call option with an
exercise price of 55 and a premium of 10; second, a long position in a put option with
the exercise price of 55 and a premium of 9. What is the name of this combination
strategy? When do investors make profit from this strategy? Show the profit diagrams
for both the positions and also for the combination strategy. Calculate the breakeven
points.
(8 marks)
c. Determine the lower bound of the price (minimum price) for a six month call when the
share price is 115, the put’s exercise price is 100, and the interest rate for the six month
period is 6.5 per cent.
(3 marks)
d. Draw a profit and loss diagram that shows an investment in two long puts, given an
exercise price of 40 for the puts and a price for a put option of 6.
(3 marks)
Question 5 (20 marks):
a. “An investor can control the level of systematic risk in a portfolio, but not the level of
unsystematic risk.” Do you agree with this statement? Explain.
(4 marks)
b. Stocks offer an expected rate of return of 18%, with a standard deviation of 22%.
Gold offers an expected return of 10% with a standard deviation of 30%. In light of
the apparent inferiority of gold with respect to both mean return and volatility, would
anyone hold gold? If so, demonstrate graphically why one would do so.
(6 marks)
c. Considering the following information regarding the performance of a portfolio
manager in a recent quarter:
Manager’s
Return
Manager’s
Weight
Benchmark
weight
Benchmark
Return
Stocks 1% 0.50 0.30 2%
Bonds 2% 0.30 0.30 1.5%
Treasury bills 0.75% 0.20 0.40 0.5%
i. Identify the Alpha of the manager's portfolio
ii. Identify the contributions of asset allocation and security selection to relative
performance.
(6 marks)
d. Traditional finance theories are criticised in light of the dominant role of behavioural
biases. List two points how traditional finance is different from behavioural finance.
(4 marks)
END OF EXAMINATION
Semester One Examinations, 2023 FINM2416 Asset Pricing
Page 5 of 5
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