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

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The standard deviation of a portfolio combining two assets depends not only on their individual standard deviations but also on their correlation. The formula for the standard deviation of a portfolio is σp = √(wA^2σA^2 + wB^2σB^2 + 2wAwBσAσBρAB), where wA and wB are the weights of the two assets, σA and σB are their individual standard deviations, ρAB is their correlation coefficient. Since the coefficient of correlation between Warchester and Shoesbury shares is positive, the last term of the formula is positive and reduces the overall standard deviation of the portfolio. Therefore, it is possible for the standard deviation of a portfolio combining two assets with individual standard deviations of 20% and 16% and a correlation coefficient of 0.75 to be less than 20%.

The Standard Deviation of Returns on Warchester Shares Is 20