Question

This is previously answered wrong - hopefully someone can try again taking into account the risk free asset as well as Stock R and Stock S

You have $10,000 to invest in a portfolio containing Stock R, Stock S, and a risk - free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 15% and that has only 120% of the risk of the overall market. If Stock R has an expected return of 25% and a beta of 1.6, Stock S has an expected return of 17.5% and a bet a of 1.3, and the risk - free rate is 6%, how much money will you invest in Stock R? Explain your answer.

Answer 1

Answer

• Money you will invest in Stock R = - $3333

Note : It is negative it denotes it is being borrowed instead of investment.

Working

Let theWeight of investment in Stock R be X and Weight of Investment in Stock S be Y

Weight of Investment in Risk free Asset = 1-X-Y

Beta of Portfolio = 120%

Weight of investment in Stock R*Beta of Stock R + Weight of investment in Stock S*Beta of Stock S + Weight of Risk free Asset*Beta of Risk free asset = 1.20

X*1.6 + Y*1.3 + (1-X-Y)*0 = 1.20

1.6X + 1.3Y = 1.20

Y = (1.20-1.6X)/1.3

Expected Return of Portfolio = 15%

Weight of investment in Stock R*Expected Return of Stock R + Weight of investment in Stock S*Expected Return of Stock S + Weight of Risk free Asset*Expected Return of Risk free asset = 15%

X*25% + (1.20-1.6X)/1.3 * 17.5% + (1-X-(1.20-1.6X)/1.3) *6% = 15%

0.25X + 0.161538 - 0.215385X + 0.06 - 0.06X - 0.0553846+ 0.073846X = 15%

0.048461X + 0.166154 = 0.15

X = (0.15-0.166154)/0.048461

X = -33.33%

Y = (1.20-1.6*-33.33%)/1.3

Y = 133.33%

Weight of Investment in Risk free asset = 1-(-33.33%)-133.33%

Weight of Investment in Risk free asset = 0%

Money you will invest in Stock R = X*Total Investment

Money you will invest in Stock R = -33.33%*10000

Money you will invest in Stock R = -3333