Frogs reproductive
Section A:
Question 1
i. Consider the following four risk-free government bonds: A, B, C, and D. All four
bonds have a face value of £100 and pay annual coupons, but the coupon rates are
different. Bond A has a coupon rate of 6%, B 7%, C 8%, and D 9%. Both A and B
mature in two years while C and D mature in four years. Bonds A, B, C, and D are
currently trading at £102.78, £104.65, £112.62, and £116.22, respectively.
a. Calculate the 1-year, 2-year, 3-year, and 4-year spot rate. What is the shape of
the term structure?
b. Which theory of the term structure can explain the shape above? Explain the
intuition. [5 marks]
ii. Suppose the price of espresso machines is risky, with a CAPM beta of 0.8. The
monthly storage cost is $10, and the current spot price is $1,000. However, one can
also rent out the machine to earn $5 per month. Storage costs and rent are paid at the
end of each month. The expected rate of return on the market is 1.5% per month, with
a risk-free rate of 0.5% per month.
a. What is the required monthly return on an asset with the espresso machine’s
beta?
b. Using your answer above, work out what price the espresso machine should
sell for in 3 months .
c. Suppose that you need an espresso machine in 3 months. You believe that the
price of the espresso machine in 3 months will be $1,050. Which of the
following would be cheaper overall: buying the espresso machine today or
buying it in 3 months?
Question 2
i. The following table lists prices of options on Apple’s stock.
a. Using the information above, derive the two missing prices.
b. How can you produce a bear call spread using the two calls above? What is
the price of this bear call spread?
ii. Read the following statements. For each statement, first state whether it is true or
false. Then explain your reasoning.
a. XYZ reported a profit of $270 million for 2020. At the same time, their share
price dropped by 10% in the same year. The fact that the stock market reacted
Stock Time to
Exercise
Exercise
Price
Stock
Price
Put
Price
Monthly
Interest
rate
Call
Price
Apple 1 120 126 2 1% ?
Apple 1 122 126 ? 1% 6
© LSE IRDAP 2021/FM213 Page 3 of 5
negatively to positive earnings suggests that it is not informationally efficient.
b. Your friend Jonny made a total return of 100% in 2020 by investing in
GameStop, beating the market return by a big margin. In the same year, your
friend Sammy made a total return of 5% by investing in government bonds,
much lower than the market return in 2020. Given that Jonny outperformed
Sammy substantially, Jonny must be a better investor.
c. Managers make superior returns on their purchases of their company’s stock.
This violates the strong form of market efficiency.
iii. Both Firm A and Firm B earn £20 per share every year. Firm A’s equity has a beta
of 0.5 and Firm B’s equity has a beta of 1.5. The expected market return is 10%
per year and the risk-free rate is 2% per year. Firm A pays out all its earnings to
equityholders. Firm B retains half its earnings and pays out the other half to
equityholders.
a. What are the required rates of return for A and B’s equity?
b. Suppose that the ROE is 15% for Firm B. The first dividend will be paid one
year from today. Calculate the current share price for both Firm A and Firm B.
Why are the two prices different?
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