Question

You have $234,267 to invest in a stock portfolio (this amount is your original wealth). Your choices are Stock H, with an expected return of 15.23 percent, and Stock L, with an expected return of 10.67 percent. Legal constraints require you to invest at least $42,668 in stock L. If your goal is to create a portfolio with an expected return of 20.5 percent on your original wealth, what is the minimum amount you must borrow (and subsequently repay) at the risk free rate of 3.23 percent to achieve your goal? Answer in $ to two decimals.

Answer 1

Total amount invested = $234,267

Return of Stock H, R(H) = 12.23%

Return of Stock L, R(L) = 10.67%

Weight of Stock L in portfolio = $42,668/$234,267 = 0.1821

Risk free Return, R(RF) = 3.23%

let weight of Stock H in porttfolio be X

& Weight of Risk Free asset be (1-X-0.1821)

Expected Return of Portfolio = 20.5

Expected Return of Portfolio = [Weight of H*R(H)]+[Weight of L*R(L)]+[Weight of RF*R(RF)]

20.5 = (X)(15.23)+(0.1821)(10.67)+(1-X-0.1821)(3.23)

20.5 = 15.23X + 1.9430 + 3.23 - 3.23X -0.588183

15.915183 = 12X

X = 1.3263

So, weight of Stock H be 1.3263

Weight of Risk Free Asset be (1-1.3263-0.1821) = -0.5084

So, risk free asset is borrowed which is to be repay is = $234267*(-0.5084)

= $119101.34

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