Question

You are in a world where there are only 2 assets: gold and stocks. You are interested in investing your money in one, the other or both assets. Consequently, you collect the following data on the returns on the 2 assets over the last 6 years. Gold Stock market Average return 8% 20% Standard deviation 25% 22% Correlation -0.4 a. If you were constrained to pick just one, which one would you choose? b. How would a portfolio composed of equal proportions in gold and stocks do in terms of mean and variance?

Answer 1

a, The stock Return to Risk ratio = Return/ Standard deviation =20%/22% =20/22

Gold Return to Risk Ratio = Return/Standard Deviation =8%/20% =8/22
Since Return to risk ratio of stock is higher than gold hence stocks should be chosen

b. Return of Portfolio = weight of Gold* return of Gold+Weight of Stock* Return of Stock =0.5*8%+0.5*20% =14%

Standard Deviation of Portfolio =( Weight of Gold* Standard Deviation of Gold)^2+( Weight of Stock* Standard Deviation of Stock)^2+2* weight of Gold* Weight of Stock* Standard Deviation of Stock * Standard Deviation of Gold*Correlation)^0.5
=((0.5*25%)^2+(0.5*22%)^2+2*0.5*0.5*25%*22%*-0.4))^0.5 =12.93%