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

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

 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%