The yields to maturity on three government bonds (assume default-free) with maturities
of 1, 2 and 3 years are respectively: 3%, 4% and 6%. The bonds all pay an annual coupon
and have the same coupon rate of 1% and a face value of $1,000.
(a) What are the prices of the three bonds? [5 marks]
(b) What are the implied forward rates, 1f1 (the forward rate between year 1 and year
2) and 2f1 (the forward rate between year 2 and year 3)? [5 marks]
(c) What is the Macaulay duration of the 3-year coupon bond? [5 marks]
(d) According to the expectations hypothesis, what is the expected 1-year interest rate
in 1 year’s time? Explain. [2 marks]
(e) How would your answer to (d) change if you believed the liquidity preference
hypothesis instead? Explain. [3 marks]
(f) The price of a security that pays $100 if the 1-year interest rate is above 2% three
years from now and zero otherwise is $70. What is the price of a security that
pays $100 if the 1-year rate is less than or equal to 2% three years from now, and
otherwise pays zero? [5 marks]
FN2190 Asset Pricing & Financial Markets Page 3 of 5
You are an investment professional advising your client in regards his future retirement.
Your client is 30 years of age today, defined as t = 0, and has just started a new job. His
salary for the first year which he will receive at the end of the year, t = 1 will be $50,000.
You forecast that your client’s salary will increase at the steady rate of 4% per year until
your client retires at age 60.
(a) If the annual discount rate is 6%, what is the PV of these future salary payments?
(b) If your client saves 10% of his salary each year and invests these savings at an
annual interest rate of 6%, how much will he have saved by age 60? [5 marks]
(c) If your client plans to spend these savings in even annual amounts when he retires
at age 60, over the subsequent 20 years in retirement, how much can he spend at
the end of each year? This implies your client spends his first payment at the end
of his first retirement year when he turns 61 years of age. [5 marks]
Please answer the following questions. You must give clear and concise explanations to
support your answers.
(d) Explain the three forms/levels of the efficient market hypothesis. [5 marks]
(e) What are the main differences between forward and future contracts? [5 marks]
FN2190 Asset Pricing & Financial Markets Page 4 of 5
For this question, unless otherwise indicated, assume that the CAPM holds. Consider two
stocks (A and B) and a risk-free asset with annual return of 3%. The expected returns and
standard deviations of returns of the two stocks are given in the following table. The two
stocks’ return correlation is 0.3.
The market expected return is 8%, and the standard deviation of the market return is
Expected Return Standard Deviation
Stock A 10% 50%
Stock B 6% 40%
(a) What is the maximum attainable Sharpe ratio? Explain. [5 marks]
(b) What are the betas of stocks A and B? [5 marks]
(c) What portfolio achieves an expected return of 10% with the minimum volatility
(standard deviation)? [5 marks]
(d) If investors are unable to borrow what alternative investment strategy achieves an
expected return of 10% at higher volatility than the portfolio in your answer to
part (c)? (Assume investors are unable to short sell.) [3 marks]
(e) What are the assumptions of the CAPM? What is the only risk priced in the
CAPM and how is it measured? [7 marks]
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