Question

You have $219,485 to invest in a stock portfolio (this amount is your original wealth). Your choices are Stock H, with an expected return of 14.21 percent, and Stock L, with an expected return of 8.55 percent. Legal constraints require you to invest at least $43.580 in stock L. If your goal is to create a portfolio with an expected return of 19.92 percent on your original wealth, what is the minimum amount you must borrow (and subsequently repay) at the risk free rate of 2.77 percent to achieve your goal? Answer in $ to two decimals.

Answer 1

Let the amount borrowed be x

Portfolio return is equal to weighted average return.

The minimum amount will be invested in L as it provides lower return.

Hence, 19.92%*219485 = 43580*8.55% + (175905+x)*14.21% - x*2.77%

43,721.412 = 3726.09 + 24,996.1005 + 0.1421x - 0.0277x

14,999.2215 = 0.1144x

x = $131,112.08

Hence, amount required to be borrowed = $131,112.08