Assume that as an investor, you decide to invest part of your wealth in a risky...

Assume that as an investor, you decide to invest part of your wealth in a risky asset that has an expected return of 11%, and a standard deviation of 15%. You invest the rest of your capital in the risk-free rate, which offers a return of 3%. You want the resulting portfolio to have an expected return of 5%. What percentage of your capital should you invest in the risky asset?

Expert Solution

25%

WORKING:

Total percentage of Investment is 100% or 1

Investment in risky asset is "x"
so, investment is risk free assets is (1-x)

Return of risky asset		11%	0.11
Return of risk free assets		3%	0.03

Now, as per question,

Expected Return of Portfolio		=	(0.11x)+(0.03(1-x))
	0.05	=	(0.11x)+(0.03(1-x))
	0.05	=	0.11x+0.03-0.03x
	0.05	=	0.08x+0.03
	0.02	=	0.08x
	x	=	0.25

Thus, Investment in risky asset					0.25
Investment in risk free asset			1-0.25	=	0.75

jeff jeffy answered 2 years ago

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