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MN-3505 Asset Management

Problem Set

1. During a period of severe inflation, a bond offered a nominal HPR of 80% per year. The inflation rate was 70% per year.

a. What was the real HPR on the bond over the year?

b. Compare this real HPR to the approximation r_real ≈ r_nom − i.

2. Use the following scenario analysis for Stocks X and Y to answer the following questions (round to the nearest per cent).

a. What are the expected rates of return for Stocks X and Y?

b. What are the standard deviations of returns on Stocks X and Y?

c. Assume that of your $10,000 portfolio, you invest $9,000 in Stock X and $1,000 in Stock Y. What is the expected return on your portfolio?

3. Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with an 8% coupon if it is currently selling at par and the probability distribution of its yield to maturity a year from now is as follows:

For simplicity, assume the entire 8% coupon is paid at the end of the year rather than every 6 months.

4. A stock has returns of 3%, 18%, -24%, and 16% for the past four years. Based on this information, what is the 95% probability range for any given year?

5. Over the past five years, a stock produced returns of 14%, 22%, -16%, 2%, and 10%. What is the probability that an investor in this stock will NOT lose more than 8% nor earn more than 21% in any one given year?

6. What are the arithmetic and geometric average returns for a stock with annual returns of 4%, 9%, -6%, and 18%? 

Arithmetic average = (.04 + .09 - .06 + .18) ÷ 4 = 6.25%;

Geometric return = (1.04 × 1.09 × .94 × 1.18)^.25 - 1 = 5.89%

7. Banco Santander has a monthly mean return of 2.13 per cent and a standard deviation of 9.03 per cent. Assume you have invested 1 million in the bank. Calculate the analytical VaR for Banco Santander using a monthly holding period and a 1% probability of loss.