Question

Rocession 9 5. Use the following information to answer the question assuming the equal probability of each scenario: Security 1(%) Security 2(%) 13 Normal 13 10 Boom 26 -2 E(R)-10%; E(R.) 7%; 0, -14.45%; 0, 6.48%; a) Calculate Covariance between Security 1 and Security 2. (6 points) b) Calculate Correlation between Security I and Security 2. (3 points) e) Calculate expected portfolio rate of return investing 60% of the wealth in Security I and the remaining in Security 2. (3 points) d) Calculate standard deviation of portfolio investing 60% of the wealth in Security the remaining in Security 2. (5 points) and

Answer 1

	Scenario	Probability	Return 1 [%]	Return 2 [%]	Deviation from mean d1	Deviation from mean d2	d1*d2	p*d1*d2
	Recession	0.3333	-9	13	-19	6	-114	-38
	Normal	0.3333	13	10	3	3	9	3
	Boom	0.3333	26	-2	16	-9	-144	-48
a]	Covariance =							-83
b]	Correlation coefficient = Covariance/Product of standard deviations = -83/(14.45*6.148) =							-0.93
c]	Expected return = 10*60%+7*40% =							8.80
d]	SD of the two portfolio asset = (w1^2*sd1^2+w2^2*sd2^2+2*w1*w2*sd1*sd2*Cor(1,2))^0.5 =
	= (0.6^2*14.45^2+0.4^2*6.48^2+2*0.6*0.4*14.45*6.48*-.93)^0.5 =							6.33