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)
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.
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 = 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%
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