Question

1. You are working in a financial intermediary and your manager asks you to analyze stocks of two different companies trading on Borsa İstanbul. The first company is called R&H Inc. (RHI) and the second company is called M&L Corp. (MLC). Both of these companies are in consumer's goods industry and founded at the beginning of the 20th century. You do not know what the returns on these company stocks will be for the next year but you have some expectations regarding their returns under different states of the economy. You have prepared the table presented below State Probability Return of RHI Stock Return of MLC Stock 38% Boom 35% Neutral 20% 14% 0.5 Recession 12% 6% 0.2 a. Calculate the expected return and standard deviation of RHI Stock. b. Calculate the expected return and standard deviation of MLC Stock. c. You have a client and your client has saved $25,000. You plan to invest $14,000 in Stock RHI and the rest in Stock MLC to form a portfolio. Calculate the expected return and the standard deviation of this portfolio d. Suppose you also find another stock from healthcare industry, SVC Inc. (SVCI). You calculate its expected retum, standard deviation of its returms and covariance of SVCI with RHI Expected Retum of SVCI = 18.7% Standard Deviation of SVC1-1 1 .091% Covariance of the returns of SVCI and RHI0.0108415 You have already decided to have Stock of RHI in your portfolio but you are not sure whether you should invest in Stock of MLC or Stock of SVCI. (You cannot invest in both of them and you have to choose one based on its characteristics.). State which one of these stocks you should choose and briefly explain why e. Suppose your goal is to minimize the total risk of your portfolio. Calculate the weights you should allocate to the two assets you have chosen for your portfolio in part (d) of this question to create a portfolio with minimum total risk. f. You also collected some market information and beta of these three stocks. This information is summarized in the table below SVCI MLC RHI 0.5052 5% 0.6131 0.8017 Correlation with the Market Portfolio 5% 5% Risk Free Rate 10% 10% 10% Return on the Market Portfolio 8% 8% 890 Standard Deviation of the Market Portfolio Evaluate your decision in part (e) given the information summarized in the table above. Briefly discuss if you still want to select the security you selected in part (e) if your goal is to create a portfolio with lower systematic risk

Answer 1

		RHI STOCK ANALYSIS
			P	R	P*R	D=(R-23.8)	E=D^2	F=E*P
		State	Probability	Return	Probabilty *Return	Deviation from Mean	Deviation Squared	Deviation Squared*Probability
		Boom	0.3	38	11.4	14.2	201.64	60.492
		Neutral	0.5	20	10	-3.8	14.44	7.22
		Reccession	0.2	12	2.4	-11.8	139.24	27.848
				SUM	23.80		SUM	95.56
		Mean Return	23.8
		Variance of Return	95.56
		Standard Deviation	9.78	(Square Root (95.56)
	a	Expected Return of RHI	23.80%
		Standard Deviation of RHI	9.78%
		MLC STOCK ANALYSIS
			P	R	P*R	D=(R-18.7)	E=D^2	F=E*P
		State	Probability	Return	Probabilty *Return	Deviation from Mean	Deviation Squared	Deviation Squared*Probability
		Boom	0.3	35	10.5	16.3	265.69	79.707
		Neutral	0.5	14	7	-4.7	22.09	11.045
		Reccession	0.2	6	1.2	-12.7	161.29	32.258
				SUM	18.70		SUM	123.01
		Mean Return	18.70
		Variance of Return	123.01
		Standard Deviation	11.09	(Square Root (123.01)
	b	Expected Return of MLC	18.70%
		Standard Deviation of MLC	11.09%
		COVARIANCE BETWEEN RETURN OF RHI and MLC
			P	D1	D2	P*D1*D2
		State	Probability	Deviation from Mean of RHI	Deviation from Mean of MLC	Deviation RHI*DeviationMLC*Probability
		Boom	0.3	14.2	16.3	69.438
		Neutral	0.5	-3.8	-4.7	8.93
		Reccession	0.2	-11.8	-12.7	29.972
					SUM	108.34
		Covariance (RHI,MLC)	108.34
	c	Weight of stock RHI	0.56	(14000/25000)
		Weight of stock MLC	0.44	(1-0.56)
		Expected Portfolio Return :
		(Weight of RHI*Mean Return of RHI)+(Weight of MLC*Mean Return of MLC)
		Expected Portfolio Return :	21.56%	(0.56*23.8)+(0.44*18.7)
		Standard Deviation Of Portfolio:
		Vp=Portfolio Variance =(w1^2)*(S1^2)+(w2^2)*(S2^2)+2*w1*w2*Covariance(1,2)
		w1=weight of stock 1=	0.56
		w2=weight of stock 2=	0.44
		S1=Standard Deviation of Stock1=	9.78
		S2=Standard Deviation of Stock2=	11.09
		Covariance(1,2)=	108.34
		Portfolio Variance=	107.172304
		Portfolio Standard Deviation	10.35%	(Square Root of 107.17)
		Expected Return of SVCI 18.70% Standard Deviation 11.09% (0.0108415) Covariance of Return Expected return of MLC 18.70% Standard Deviation of MLC 11.09% SVCI has same expected return and Standard Deviation But, SVCI has negative Covariance with RHI Hence SVCI should be selected instead of MLC This willreduce the Portfolio Standard Deviation Vp-Portfolio Variance (w12)*(S1 2)+(w2n2)*(S2 2)+2*w1*w2*Covariance(1,2) If Covariance is negative it reduces portfolio Variance and consequently Standard deviation is reduced