Question

You invest $100 in a risky asset with an expected rate of return of 9% and a standard deviation of 0.15 and a T­-bill with a rate of return of 5%. What percentages of your money must be invested in the risky asset to form a portfolio with an expected return of 9%?

Answer 1

Solution:
	Percentages invested in the risky asset	100%
Working Notes:
	Let W be the weight of risky asset in the port folio having expected return of 9%
		Returns
	Risky assets = W	9%
	Risk free assets (T-bill) = 1-W	5%
	Expected return of portfolio	9%
	Expected return of portfolio = Weighted average expected return of Individual assets
	Expected return of portfolio = W1 x r1 + W2 x r2
	9% =( W x 9%) + ((1-W) x 5%)
	9% =9% W + 5% - 5% W
	4% = 4%W
	W=4%/4%
	W=1
	W= 100%
Hence	100% should be invested in Risky assets
Lets check	Expected return of portfolio = W1 x r1 + W2 x r2
	Expected return of portfolio = 100% x 9% + 0% x 5%
	Expected return of portfolio = 9%
Please feel free to ask if anything about above solution in comment section of the question.