The document discusses the expected rates of return, standard deviations, variances, and coefficient of correlation for two stocks, A and B. It provides the calculations to determine: 1) The expected rates of return for Stock A is 13.2% and Stock B is 7.7%. 2) The standard deviations of Stock A is 1.5% and Stock B is 1.1%. 3) The variances of Stock A is 0.0225% and Stock B is 0.0121%. 4) The coefficient of correlation between Stock A and B is 0.47.

1. SAPM
Prof. Saptarshi Mukherjee

2. Return Problems
 Consider the following probability
distribution for stocks A and B:
1. The expected rates of return of stocks A and B are
E(RA) = 0.1(10%) + 0.2(13%) + 0.2(12%) + 0.3(14%) + 0.2(15%) = 13.2%;
E(RB) = 0.1(8%) + 0.2(7%) + 0.2(6%) + 0.3(9%) + 0.2(8%) = 7.7%.

3.  1. Consider the following probability
distribution for stocks A and B:
2. The standard deviations of stocks A and B are
sA = [0.1(10% - 13.2%)^2 + 0.2(13% - 13.2%)^2 + 0.2(12% - 13.2%)^2 +
0.3(14% - 13.2%)^2 + 0.2(15% - 13.2%)^2]^(1/2) = 1.5%;
sB = [0.1(8% - 7.7%)^2 + 0.2(7% - 7.7%)^2 + 0.2(6% - 7.7%)^2 + 0.3(9%
- 7.7%)^2 + 0.2(8% - 7.7%)^2 ]^(1/2) = 1.1%.
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4. Contd……
 1. Consider the following probability
distribution for stocks A and B:
3. The variances of stocks A and B are
VAR(A) = 1.5%^2=0.0225%;
VAR(B) = 1.1%^2=0.0121%.

5.  1. Consider the following probability
distribution for stocks A and B:
4. The coefficient of correlation between A and B is
Cov(A,B) = 0.1(10% - 13.2%)(8% - 7.7%) + 0.2(13% - 13.2%)(7% -
7.7%) + 0.2(12% - 13.2%)(6% - 7.7%) + 0.3(14% - 13.2%)(9% - 7.7%) +
0.2(15% - 13.2%)(8% - 7.7%) = 0.76;
Corr(A,B) = 0.76/[(1.1)(1.5)] = 0.47.
Contd……

6.  1. Consider the following probability
distribution for stocks A and B:
4. The coefficient of correlation between A and B is
Cov(A,B) = 0.1(10% - 13.2%)(8% - 7.7%) + 0.2(13% - 13.2%)(7% -
7.7%) + 0.2(12% - 13.2%)(6% - 7.7%) + 0.3(14% - 13.2%)(9% - 7.7%) +
0.2(15% - 13.2%)(8% - 7.7%) = 0.76;
Corr(A,B) = 0.76/[(1.1)(1.5)] = 0.47.
Contd……