Question

290 Treasury bonds for each scenario. The of return on 10-year zero and returns are shown here: Return on a 10-Year Zeno Coupon Treasury Bond during the Next Year Probability of 0.10 Worst C Poor Case Most Likely Good Case Best Case 0.40 You have also gathered historical returns for the past 10 years for Blandy, Gourman Corporation (a producer of gourmet specialty foods), and the stock market. Historical Stock Returns 18 -22 15 Standard deviation: Correlation with the market: 20.1% 1.00 1.00 ? 38.6% 0.678 1.30 Beta: a. What are investment returns? What is the return on an investment that costs $1.00 b. Graph the probability distribution for the bond returns based on the 5 scenarios Wht The risk-free rate is 4% and the market risk premium is 5% and is sold after 1 year for $1,060 might the graph of the probability distribution look like if there were an infinite c. Use the scenario data to calculate the expected rate of return for the 10-year aem d. What is stand-alone risk? Use the scenario data to calculate the standard deviation of e. Your client has decided that the risk of the bond portfolio is acceptable and wishes to number of scenarios (ie, if it were a continuous distribution and not a discrete coupon Treasury bonds during the next year the bond's return for the next year. leave it as it is. Now your client has asked you to use historical returns to estimate the for each scenario. The of return on 10-year zero coupon Treasury bonds and returns are shown here Return on a 10-Year Zere during the Next Year -14% Probability of Coupon Treasury Bond Scenario Worst Case Poor Case Most Likely Good Case Best Case 0.10 6% 16% 26% 0.40 You have also gathered historical returns for the past 10 years for Blandy, Gour tion (a producer of gourmet specialty foods), and the stock market. Historical Stock Returns Market Blandy Gourmange 26% 15 Year 47% 30% -14 15 18 -22 -18 42 30 -32 28 10 26 10 75 Average return: Standard deviation: Correlation with the market: Beta: 8.0% 20.1% 1.00 1.00 9.2% 38.6% 0.678 1.30 The risk-free rate is 4% and the market risk premium is 5%. a. What are investment returns? What is the return on an investment that costs $1,000 and is sold after 1 year for $1,060? Graph the probability distribution for the bond returns based on the 5 scenarios. What might the graph of the probability distribution look like if there were an infinite number of scenarios (ie, if it were a continuous distribution and not a discrete distribution)? b. c. Use the scenario data to calculate the expected rate of return for the 10-year coupon Treasury bonds during the next year. d. What is stand-alone risk? Use the scenario data to calculate the standard deviation of the bond's return for the next year. e. Your client has decided that the risk of the bond portfolio is acceptable and wishes leave it as it is. Now your client has asked you to use historical returns to estimate to the

Answer 1

Historical stock returns
Year	Market	Blandy	Gourmange
1	30%	26%	47%
2	7%	15%	-54%
3	18%	-14%	15%
4	-22%	-15%	7%
5	-14%	2%	-28%
6	10%	-18%	40%
7	26%	42%	17%
8	-10%	30%	-23%
9	-3%	-32%	-4%
10	38%	28%	75%
Avg return	8%	6%	9.20%
std dev	20.10%	23.90%	38.60%
Correlation with market	1	0.481	0.678
Beta	1	0.60	1.3
Covariance with market	0.03642	0.02195	0.04738

a. For question a. the average return is calculated with mean. The covariance of Blandy is calculated with respect to market and the covariance of market with market is nothing but the variance of the market.

The formula to calculate covariance with market is Covariance Rs, Rm= (Rs-meanRs)(Rm-meanRm)

Jo-mean(RS))(Rm-mean(Rm)) Covariance (Rs,Rm)

where Rs is the return of stock Blandy. Rm is return of market. The return on investment for a stock that returns 1060 dollars for an investment of 1000 dollars is 6% (1060 - 1000)/1000.

b. The probability graphs were drawn by plotting the different points in the zero coupon yield.

b.

Probability of scenario 0.45 0.35 02 0.1 05 0 -20% -15% -10% -5% 0% 5% 10% 15% 20% 25% 30% Axis Title

Probability of scenario 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 -15% 10% 5% 10% 15% 20% 25% 30% Axis Title

c. Expected rate of zero coupon treasury bond using the different probabilities and different expected treasury rates = 0.1 * -14% + 0.2 * -4% + 0.4* 6% + 0.2 * 16% + 0.1 * 26% = 6%.

d. To calculate the standalone risk, the formula to calculate variance is Variance Bond returns= p=1np*Bond return-Mean Bond return2

Variance (Bond returns) - p * (Bond return -Mean Bond return)2 PF1

Variance = 0.1*(-14-6)²+ 0.2*(-4-6)²+ 0.4*(6-6)²+ 0.2*(16-6)²+ 0.1*(26-6)² = 1.2

Risk = sqrt(1.2) = 10.95%