Question

Suppose that the entire security market is made of only three types of assets: a risk-free asset, with a return of 3%, and two risky stocks A and B. There are 500 A stocks trading in the market, at a price of $10 per stock. Stock A has an expected return of 8% and a volatility of 10%. There are 375 B stocks trading in the market at a price of $8 per stock. Stock B has a volatility of 16%. The correlation between the returns of stock A and stock B is 0.15. 1. Compute the volatility of the market portfolio. (8 points) 2. Compute the β of stock B. (8 points) 3. Compute the expected return of stock B. (8 points)

Answer 1

		Portfolio Variance=(w1^2)*(S1^2)+(w2^2)(S2^2)+2w1w2*Cov(1,2)
		w1=Weight of Stock1
		S1=Standard Deviation of Stock1
		w2=Weight of stock 2
		S2=Standard Deviation of stock2
		Cov(1,2)=Covariance of Stock 1 and Stock2
		Cov(1,2)=Corrl(1,2)*S1*S2
		Corrl(1,2)=Correlation of Stock1 and 2
	A	Market value of Stock A	$5,000	(500*10)
	B	Market value of Stock B	$3,000	(375*8)
	C=A+B	Total Market Value	$8,000
	w1=A/C	Weight of Stock A	0.625
	w2=B/C	Weight of Stock B	0.375
	S1	Standard Deviation of stock A	10%
	S2	Standard Deviation of stock B	16%
	Corrl(1,2)	Correlation of return of A&B	0.15
	Cov(1,2)	Covariance of Stock A & stock B	24	(0.15*10*16)
	Vp	Market Portfolio Variance=	(w1^2)*(S1^2)+(w2^2)(S2^2)+2w1w2*Cov(1,2)
	Vp	Market Portfolio Variance=	86.3125	(0.625^2)*(10^2)+(0.375^2)*(16^2)+2*0.625*0.375*24
	Sp	Market Portfolio Standard Deviation= Square Root of Vp
	Vp	Standard Deviation of market Portfolio	9.290452	(86.3125^2)
		Volatility of market portfolio	9.3%
		Beta of Stock B=Beta2=Correlation (1,2)*(S2/S1)
		Beta of Stock B=Beta2=Correlation (1,2)*(S2/S1)
		Beta of Stock B=	0.24	0.15*(16/10)
		Expected Return of Stock B=Rf +Beta*(Rm-Rf)
	Rm	Market Return =0.625*R1+0.375*R2
		R1=Return of stock A=	8%
		R2=return of Stock B
		Rf=Risk free Rate=3%
		Rm=0.625*8+0.375R2….Eqn(1)
		R2=3+0.24*(Rm-3)
		0.24 Rm=R2-3+(0.24*3)
		0.24Rm=R2-2.28
		Rm=(R2/0.24)-(2.28/0.24)
		Rm=(R2/0.24)-9.5…Eq(2)
		Subtracting Equan(1) from Eqn(2)
		(R2/0.24)-9.5-0.375R2-(8*0.625)=0
		4.1667R2-9.5-0.375R2-5=0
		3.79R2=14.5
		R2=14.5/3.79=	3.825858
		Return of StockB	3.80%