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%
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:
The expected return of this portfolio = 13.50%
standard deviation of this portfolio = 30.00%
Explanation:
From the information given:
The percentage of riskless = -100000/200000
The percentage of riskless = -0.50%
Now; the investment in market index = 1.50%
The expected return of this portfolio = 1.50 × 10% + ( - 0.5 ×3 %)
The expected return of this portfolio = 1.50 × 0.1 - 0.5 × 0.03
The expected return of this portfolio = 0.15 - 0.015
The expected return of this portfolio = 0.135
The expected return of this portfolio = 13.50%
standard deviation of this portfolio = the investment in market index × market index standard deviation
standard deviation of this portfolio = 1.50 × 20%
standard deviation of this portfolio = 30.00%
