Question

• Troy wants to form a portfolio of four different stocks. Summary data on the four stocks appears below. The average standard deviation (found simply by summing the standard deviations and dividing by 4 which is the same as the weighted average in this example) across the four stocks is 17.25%. If Troy forms a portfolio by investing 25% of his money in each of the stocks in the table, it is very likely that the standard deviation of this portfolio’s return will be (more than, less than, equal to) 17.25%. Choose one of the options (more than, less than, equal to) and explain WHY? (You are not asked to calculate portfolio standard deviation or correlation. You do not need to do any math at all to answer this.)

Stock     Return Standard deviation

#1          12%       20%

#2          -5%        29%

#3          7%         13%

#4          2%         7%

Answer 1

Troy forms a portfolio by investing 25% of his money in each of the stocks, it is very likely that the standard deviation of this portfolio’s return will be less than 17.25%.

It is because of the reason that when you choose different stocks for investments rather than investing in only one stock, diversification benefit occurs. It means, if you invest in different stocks, your return get averaged but your risk get reduced. Risk is reduced because stocks may have positive, less positive or negative correlation with one another. Due to correlation between them, diversification benefit occurs and due to diversification benefit portfolio risk is reduced.

So it is very likely that actual standard deviation of portfolio of this portfolio's return will be less than weighted average of standard deviation of stocks i.e. less than 17.25%.