Question

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?

Answer 1

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			=	(0.11*x)+(0.03*(1-x))
	0.05		=	(0.11*x)+(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