V ariance copy
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SAPM Prof. Saptarshi Mukherjee
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Transcript of V ariance copy
SAPM
Prof. Saptarshi Mukherjee
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%.
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%.
Risk Calculator
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%.
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……
