Question

You are in a world where there are two assets: gold and stocks. You are interested in investing your money in one or both of these assets. You collect the following data on the returns of these two assets over the past six years: Gold Market Average Return = 10% Stock Average Return = 18%, Gold Standard Deviation = 30% Stock Market Standard Deviation 22% Your estimate of the correlation between gold and stocks is negative -0.40. What is the average return and standard deviation of the portfolio composed of gold and stocks that has the lowest possible risk?

Select one:

a. 39% in gold and 61% in stocks

b. 43% in gold and 57% in stocks

c. 61% in gold and 39% in stocks

d. 57% in gold and 43% in stocks

e. 33% in gold and 67% in stocks

Answer 1

Given :

	Average Return	Standard Deviation
Gold Market	0.1	0.3
Stock Market	0.18	0.22
Correlation Coefficient		-0.4

Step1 : Calculation of Optimal Weight

Formula for Calculation of Optimal Weights in case of two asset portfolio

Where, WG = Weight of gold
Standard deviation of Gold Market & Stock Market respectively
rGS = correlation Coefficient

WG = (0.22^2 - 0.3*0.22*-0.4) / (0.3^2 + 0.22^2 - 2*0.3*0.22*-0.4)

WG = (0.0484 + 0.0264) / (0.09 + 0.0484 + 0.0528)

WG = 0.0748 / 0.1912

WG = 0.3912134 or 39% approx

Weight of stock WS = 100% - WA = 100% - 39% = 61%

So, the composition of weight selected is a) 39% of Gold & 61% of Stock

Step 2 : Calculation of Expected Return of Portfolio

WG = 39%
WS = 61%

ERp = ER(G) * WG + ER(S) * WS

Where ER (G) & ER(S) are expected returns of gold market & stock market respectively
WG & WS are weights of gold  & stock  respectively

ERp = 0.10*0.39 + 0.18*0.61

ERp = 0.039 + 0.1098

ERp = 0.1488 or 14.88%

Expected Return of Portfolio = 14.88%

Step 3 : Calculation of Standard Deviation of portfolio

0.1383384 OR 13.83% approx.

Standard Deviation of portfolio = 13.83%