Question

Use the following information for the problem.

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               State of        Probability of              Returns if State Occurs

               Economy      State of Economy       Stock S          Stock T

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               Boom           0.10                            12%                 4%

               Normal         0.65                          9%                   6%

               Recession     0.25                          2%                   9%

               ____________________________________________________

      a)   Find the expected return of each stock.

Use at least seven decimal places in computations of (b), (c) and (d) below to avoid significant rounding errors.

      b) Calculate the variance and standard deviation of returns of each stock.

      c)   Compute the covariance and correlation of returns between the two stocks.

      d)   Assume that you invest $4,500 in Stock S and $3,000 in Stock T. Find the expected return on the portfolio and the standard deviation of the portfolio’s return.

           

Answer 1

	STOCK S	P	R1	A=P*R1	B1=R1-7.55	C=B1^2	D=C*P
	State of Economy	Probability	Return(%)	Probability*return	Deviation from mean	Deviation squared	Deviation Squared*Probability
	Boom	0.1	12	1.2	4.45	19.80	1.98025
	Normal	0.65	9	5.85	1.45	2.10	1.36663
	Recession	0.25	2	0.5	-5.55	30.80	7.70063
			Total	7.55		Total	11.04750
	Expected (Mean) Return of StockS	7.55%
	Variance of return of stock S	11.04750
	Standard Deviation of Return of stockS	3.32378	Percent	(Square Root of Variance)
	STOCK T	P	R2	A=P*R2	B2=R2-6.55	C=B2^2	D=C*P
	States	Probability	Return(%)	Probability*return	Deviation from mean	Deviation squared	Deviation Squared*Probability
	Boom	0.1	4	0.4	-2.55	6.50	0.65025
	Normal	0.65	6	3.9	-0.55	0.30	0.19663
	Recession	0.25	9	2.25	2.45	6.00	1.50063
			Total	6.55		Total	2.34750
	Expected (Mean) Return of stock T	6.55%
	Variance of return of stockT	2.34750
	Standard Deviation of return of Stock T	1.53216	Percent	(Square Root of Variance)
	COVARIANCE BETWEEN STOCK S AND STOCK T
		P	R1	R2	B1=R1-7.55	B2=R2-6.55	E1,2=B1*B2*P
	States	Probability	Return(%)	Return(%)	Deviation S from mean	Deviation T from mean	DeviationS*DeviationT*Probability
	Boom	0.1	12	4	4.45	-2.55	-1.13475
	Normal	0.65	9	6	1.45	-0.55	-0.518375
	Recession	0.25	2	9	-5.55	2.45	-3.399375
						SUM	-5.05250
	Covariance(S,T)	-5.05250
	Correlation (S,T)=Covariance (S,T)/((Standard Deviation S)*(Standard Deviation T))
	Correlation (S,T)=	-0.9921367
		Expected Return	Variance
	STOCK S	7.55%	11.04750
	STOCK T	6.55%	2.34750
	Covariance(S,T)	-5.0525
	Correlation (S,T)	-0.9921367
	Investment in StockS	$4,500
	Investment in StockT	$3,000
	Total Investment	$7,500
	Weight of S in Portfolio=4500/7500	0.60
	Weight of T in Portfolio=300/7500	0.40
	Portfolio Return =0.6*Expected Return of S+0.4*Expected Return of S
	Portfolio Variance =(0.6^2)*Variance of S+(0.4^2)*Variance of T+2*0.6*0.4*Covariance(S,T)
	EXPECTED RETURN OF PORTFOLIO	7.15%	0.6*7.55+0.4*6.55
	PORTFOLIO VARIANCE	1.92750	(0.6^2)*11.04750+((0.462)*2.34750+2*0.6*0.4*(-5.05250)
	PORTFOLIO STANDARD DEVIATION	1.38834	%	(Square Root (1.9275)