Question

You are considering investing $10,000 in a complete portfolio. The complete portfolio is composed of treasury bills that pay 6% and a risky portfolio, P, with expected return of 12% and standard deviation of 20%.  How much you should invest of your complete portfolio in the risky portfolio P to form a complete portfolio with an expected rate of return of 9%?

		$5000
		$0
		$10000
		$20000

Answer 1

Let the weight of risk free asset be x

Hence, the weight of the risky portfolio =(1-x)

Expected return of Portfolio = Weight of Risk free Asset* Expected return of Risk free Asset + Weight of Risky Portfolio * Expected return of Risky Portfolio

9% = x* 6% + (1-x)*12%

9% = x*6% + 12%-12%*x

6%*x = 3%

x = 3%/6%

= 0.50

The weight of the risky portfolio =(1-x)

= 0.50

Total Amount invested = $ 20,000

Hence, the amount to be invested in the risky portfolio =$ 20,000 * 0.50

= $ 10,000

Answer = $10000