Question

What is the standard deviation of a portfolio of two stocks given the following data: Stock A has a standard deviation of 18%. Stock B has a standard deviation of 14%. The portfolio contains 40% of stock A, and the correlation coefficient between the two stocks is -.23.

Multiple Choice

A. 9.7%

B. 12.2%

C. 14%

D. 15.6%

Answer 1

Ans:- SD of a Portfolio is given by

( Wa^2 * SDa^2 + Wb^2 * SDb^2 + 2 * Wa * Wb * r * SDa * SDb ) ^ 1 / 2, where Wa and Wb are the weights of stock A and Stock B, SDa and SDb are the Standard deviations of Stock A and Stock B and r is the correlation coefficient between two stocks.

Wa = 0.40, Wb = (1 - 0.40) = 0.60, SDa = 0.18, SDb = 0.14 and r = -.23.

= ( 0.40^2 * 0.18^2 + 0.60 ^2 + 0.14^2 + 2 * 0.40 * 0.60 * (-.23) * 0.14 * 0.18 ) ^ 1/2

= 0.097 * 100 = 9.7% (approx).

Therefore option (A) is the correct answer.

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