Question

Explosive BetaSML Funds is a fund management company that has created a family of exchange traded (mutual) funds that are designed to put investors at various points along the Security Market Line. One of Explosive's products, called the Market Bull Plus fund, is designed to provide a return that is twice the market index's return. The Market Bull Plus fund is constructed by borrowing money at the risk-free rate and then buying market index units (exchange traded funds which mimic the market index). If the cost of borrowing is 3 % and the expected return on the market is 10.10 % , then what is the portfolio weight of the market index for the Market Bull Plus fund?

Correct answer is 242.25%

Please explain in detail, not in excel. Thanks in advance!

Answer 1

Expected return on the market index = r_m = 10.10%

Expected return of Market bull Plus fund = 2 x Expected return on market index = 2 x 10.10% = 20.20%.

Cost of borrowing = r_b = 3%

Let w be the weight of market index in Market bull plus fund, Then weight of amount borrowed money in Market bull plus fund = (1 - w)

Expected return of on Market bull plus fund = weight of market index x expected return on market index + weight of amount borrowed x cost of borrowing

20.20% = w x r_m + (1-w) x r_b

20.20% = w x 10.10% + (1 - w ) (3%)                                                   

0.2020 = 0.1010w + 0.03 - 0.03w

0.2020 - 0.03 = 0.1010w - 0.03w

0.1720 = 0.0710w

w = 0.1720 / 0.0710 = 2.4225 = 242.25%

Hence weight of market index in Market bull plus fund = 242.25%