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%**