The standard deviation of returns on Warchester stock is 20% and on Shoesbury stock it is 16%. The coefficient of correlation between the stocks is .75. The standard deviation of any portfolio combining the two stocks will be less than 20%.

Question

Quizplus · Accepted Answer

The formula for the standard deviation of a portfolio is (w1^2 * σ1^2 + w2^2 * σ2^2 + 2w1w2σ1σ2ρ12)^0.5, where w1 and w2 are the weights of the two stocks in the portfolio, σ1 and σ2 are their standard deviations, and ρ12 is the coefficient of correlation between them. Substituting the given values, we get (0.5 * (20%)^2 + 0.5 * (16%)^2 + 2 * 0.5 * 0.5 * 20% * 16% * 0.75)^0.5 = 17.24%. Therefore, the standard deviation of any portfolio combining the two stocks will be less than 20%.

The Standard Deviation of Returns on Warchester Stock Is 20