55.1
1. You invest 60% of your money in Amazon.com and 40% in General Motors. Assume that the standard deviation of Amazon.com is 80% and the standard deviation of GM is 30%. The correlation coefficient between Amazon.com and GM is 0.2.
a. What is the standard deviation of your portfolio?
First calculate the variance and then take the square root to get the standard deviation. The weights are .6 and .4 for AMZN and GM (60% and 40%) and the standard deviations of the individual stocks are .8 and .3 (80% and 30%). rho (r ) =.2.
b. Is this standard deviation different from just the simple weighted (60% in Amazon.com and 40% in GM) average of the standard deviations of the two stocks? If so, why?
Yes, it is different. The reason is because the two stocks are not perfectly positively correlated. That is, you get some diversification benefit from holding them together (they sometimes move in different directions, dampening the overall movement of your portfolio). This diversification results in a lower portfolio variance than just the weighted average of the individual stock variances would produce. You can see in the formula that the third term includes the correlation coefficient, which is adjusting the risk of the portfolio to account for the comovement of the stocks.