Question

**Please answer ASAP

You are responsible for managing a portfolio of two investments for the coming year. You have read all of the latest financial news and according to your favourite reputable financial analysts, the probability of another recession occurring is 30% and the probability of a boom is 20%; otherwise the economy will be behaving normally. Common shares of Firm A are expected to earn a return of 30% during boom times, but lose 10% during a recession. Normally, the firm’s common shares would earn a 20% return. The price of Firm B’s common shares is expected to decline 10% during boom times, but increase by 6% during a recession. Normally the firm’s common shares would earn a 9% return.

Questions:

G) Compare the return versus risk of a portfolio 100% invested in Firm B's shares with the return versus risk of the portfolio consisting of 30% invested in Firm A and 70% in Firm B. Which would you prefer? Why?                                                                                     

h. Find the Minimum Variance Portfolio (MVP) consisting of some combination of shares of both Firm A and Firm B. What proportion of the portfolio must be invested in Firm A's common shares and what proportion in those of firm B to achieve the MVP? (Use the "Solver" tool in Excel.)                                                                                     

I) Calculate the standard deviation of expected returns on the MVP?                                                                                     

J) Calculate the expected return on the MVP?                                                                                  

Answer 1

		COMMON SHARES OF FIRM A
			A	B	C=A*B	D=B-13	E=D^2	F=E*A
		Scenario	Probability	Return	Return *probability	Deviation	Deviation	Deviation squared*Probability
				Percent		fromexpected	Squared
		Recession	0.3	-10	-3	-23	529	158.7
		Normal	0.5	20	10	7	49	24.5
		Boom	0.2	30	6	17	289	57.8
				SUM	13		SUM	241
		Expected Return	13	percent
		Variance	241
		Standard Deviation	15.52	Percent	(Square Root of 241)
		COMMON SHARES OF FIRM B
			A	B	C=A*B	D=B-4.3	E=D^2	F=E*A
		Scenario	Probability	Return	Return *probability	Deviation	Deviation	Deviation squared*Probability
				Percent		fromexpected	Squared
		Recession	0.3	6	1.8	1.7	2.89	0.867
		Normal	0.5	9	4.5	4.7	22.09	11.045
		Boom	0.2	-10	-2	-14.3	204.49	40.898
				SUM	4.3		SUM	52.81
		Expected Return	4.3	percent
		Variance	52.81
		Standard Deviation	7.27	Percent	(Square Root of 52.81)
			Return	Risk
		Share of Firm A	13	15.52
		Share of Firm B	4.3	7.27
		Correlation of A&B
		Scenario	Return A	Return B
		Recession	-10	6
		Normal	20	9
		Boom	30	-10
		CORRELATION	-0.58004	(USING "CORREL "function of Excel)