A stock has a beta of 1.4, an expected return of 17.2 percent, and lies on...

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A stock has a beta of 1.4, an expected return of 17.2 percent,and lies on the security market line. A risk-free asset is yielding3.2 percent. You want to create a portfolio that is comprised ofthe stock and the risk free and will have a portfolio beta of 0.8.What is the expected return on this portfolio?
a) 12.33% b) 13.87% c) 11.20% d) 14.41%

Answer & Explanation Solved by verified expert

4.1 Ratings (769 Votes)

c) 11.20%

Step-1:Calculation of weight of both investment

Risk free asset as its name suggest has zero risk and hence has beta of 0.
Suppose, weight of risk free asset is "w" and so weight of stock is "1-w"



So, as per question,

Beta of portfolio	=	Sum of weighted beta of portfolio
0.8	=	(w0)+((1-w)1.4)
0.8	=	0+((1.4-1.4w)
0.8	=	1.4-1.4w
1.4w	=	0.6
w (Risk free asset)	=	0.4286
1-w (Stock)	=	0.5714

Step-2:Calculation of portfolio return

		Weight	Return
		a	b	a*b

Stock		0.5714	17.20%	9.83%
Risk free asset		0.4286	3.20%	1.37%

Portfolio return				11.20%

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Transcribed Image Text

A stock has a beta of 1.4, an expected return of 17.2 percent,and lies on the security market line. A risk-free asset is yielding3.2 percent. You want to create a portfolio that is comprised ofthe stock and the risk free and will have a portfolio beta of 0.8.What is the expected return on this portfolio?a) 12.33% b) 13.87% c) 11.20% d) 14.41%