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The standard deviations of Stock (K) and Stock (L) are 10% and 40%, respectively
The standard deviations of Stock (K) and Stock (L) are 10% and 40%, respectively. The correlation between these two stocks is 54%. what would be the APPROXIMATE standard deviation of a portfolio if we invest 40% for Stock K and 60% for Stock L?
A)18%
B)26%
C)32%
D)48%
Expert Solution
Ans) B) 26%
Standard deviation of portfolio = [(Weight in stock K2 x Standard deviation of stock K2) + (Weight in stock L2 x Standard deviation of stock L2) + 2 x Weight in stock K x Weight in stock L x Standard deviation of stock K x Standard deviation of stock L x co relation between stocl L and stock K)]0.5
Weight in stock K = 40%
Weight in stock L = 60%
Standard deviation of stock K = 10%
Standard deviation of stock L = 40%
co relation between stocl L and stock K = 0.54
Thus Standard deviation of portfolio =[(0.42 x 10^2) + (0.62 x 402) + 2 x 0.4 x 0.6 x 10 x 40 x 0.54]0.5
= [(0.16 x 100) + (0.36 x 1600) + 103.68]0.5
= [ 16 + 576 + 103.68]0.5
= 695.680.5
= 26.38%
Thus APPROXIMATE standard deviation of a portfolio = 26%
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