### 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%.

**Question 1**

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?

(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)?

(c) What is the Macaulay duration of the 3-year coupon bond?

(d) According to the expectations hypothesis, what is the expected 1-year interest rate in 1 year’s time? Explain.

(e) How would your answer to (d) change if you believed the liquidity preference hypothesis instead? Explain.

(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

**Question 2**

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 a 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?

(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.

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.

(e) What are the main differences between forward and futures contracts?

**Question 3**

For this question, unless otherwise indicated, assume that the CAPM holds. Consider two stocks (A and B) and a risk-free asset with an 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 20%.

(a) What is the maximum attainable Sharpe ratio? Explain.

(b) What are the betas of stocks A and B?

(c) What portfolio achieves an expected return of 10% with the minimum volatility (standard deviation)?

(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.)

(e) What are the assumptions of the CAPM? What is the only risk priced in the CAPM and how is.

**Question 4**

(a) Stock ABC has a required return of 10%. Its earnings are expected to grow at 5% per year forever and Stock ABC has a constant dividend payout ratio of 25%. If the next dividend is to be paid in a year’s time and the earnings per share in a year’s time are expected to be $40, what is its current stock price?

(b) Using the information below derive the implied annual risk-free interest rate.

(c) Using the information below is there any mispricing in the options? If so explain the arbitrage strategy in detail showing all associated cash flows. The annual risk-free is 10%.

(d) Explain intuitively how volatility in the underlying stock price affects the prices of both call and put options written on the underlying stock.