Question

You are in a world where there are only two 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 two assets over the past six years.

                                               Gold            Stock Market

Average return                         8%                               20%

Standard deviation                    25%                             22%

Correlation                               -0.4

Compute the expected return and standard deviation of a portfolio consisting of

1. 0% stocks
2. 25% stocks
3. 50% stocks
4. 75% stocks
5. 100% stocks

(the rest in gold).

Answer 1

Expected Return = Wg*Rg + Ws*Rs

SD =√( Wg²SDg²+Ws²SDs²+2*Wg*Ws*COVgs)

A. 0% stock =100% gold ie, Expected Return = 8%, SD = 25%

B. Expected Return = 8%*0.75 + 20%*0.25 = 11%

SD= √((0.75)^2*(25)^2+(0.25)^2*(20)^2+2*0.75*0.25*(-0.4)) = 19.40%

C. Expected Return = 0.5*8% + 0.5*20% = 14%

SD =√( 0.5^2*25%^2 + 0.5^2*20^2 + 2*0.5*0.5*(-0.4)) = 16%

D. Expected Return = 0.25*8% + 0.75*20% = 17%

SD=√( 0.25^2*25%^2+0.75^2*22%^2+2*0.25*0.75*(-0.4)) = 17.64%

E. 100% stock. So Expected return = 20%, SD = 22%