Question

You have $200,000 of cash. The riskless interest rate is 3%. The market index fund has an expected return of 10% and a standard deviation of 20%. A and B below are unrelated. a. You decide to invest your $200,000 as follows: $60,000 invested in the riskless asset (riskless interest rate), and $140,000 in the market index portfolio. Calculate the expected return and standard deviation of this investment portfolio? b. You decide to borrow $100,000 at the riskless interest rate, and you then invest all $300,000 ($200,000 of your own cash and the $100,000 borrowed cash) in the market index fund. Calculate the expected return and standard deviation of this investment portfolio?

Answer 1

A. % in riskless asset = 60/200 = 30%

so expected return = 0.30*3% + (1-0.3)*10% = 7.90%

standard dev = 0.70*20% = 14%

B. % in riskless = -100/200 = -50%

investment in market index = 150%

expected reutrn = 1.50*10% + -0.5*3% = 13.50%

standard dev = 1.50*20% = 30.00%