Question

Use the following information for Stock K and Stock M to solve the following problems

State of Economy	Probability of state of the economy	Rate of return if the state occurs
Boom	.10	Stock K: .25	Stock M: .18
Growth	.20	.10	.20
Normal	.50	.15	.04
Recession	.20	-.12	.00

What is the expected return for stock K? For stock M?

What is the variance for Stock K? For Stock M?

What is the standard deviation for Stock K? For Stock M?

An individual plans to invest $5,000: $3,000 in Stock K and $2,000 in Stock M. What are the portfolio weights for this portfolio?

Using the portfolio weights just computed, what is the expected return for the portfolio?

Given the weight, computer the variance and standard deviation of the portfolio?

Answer 1

1,2,3]	Stock K
	State of Economy	Probability of state of the economy [p]	Rate of return if the state [r] occurs	E[r] = p*r	d = r-E[r]	d^2	p*d^2
	Boom	0.1	25	2.50	15.4	237.16	23.716
	Growth	0.2	10	2.00	0.4	0.16	0.032
	Normal	0.5	15	7.50	5.4	29.16	14.58
	Recession	0.2	-12	-2.40	-21.6	466.56	93.312
				9.60			131.64
	Expected return			9.60
	Variance			131.64
	SD = 131.64^0.5 =			11.47
	Stock M:
	State of Economy	Probability of state of the economy	Rate of return if the state occurs	E[r] = p*r	d = r-E[r]	d^2	p*d^2
	Boom	0.1	18	1.80	10.2	104.04	10.404
	Growth	0.2	20	4.00	12.2	148.84	29.768
	Normal	0.5	4	2.00	-3.8	14.44	7.22
	Recession	0.2	0	0.00	-7.8	60.84	12.168
				7.80			59.56
	Expected return			7.80
	Variance			59.56
	SD = 59.56^0.5 =			7.72
4]	Portfolio weights:
	Stock K = 3000/5000 = 0.6
	Stock M = 2000/5000 =0.4
5]	Expected return for the portfolio = 9.6*0.6+7.8*.4 =					8.88
6]	Correlation [K,M]:
	State of Economy	Probability of state of the economy	dk*dm	dk*dm*p
	Boom	0.1	157.08	15.708
	Growth	0.2	4.88	0.976
	Normal	0.5	-20.52	-10.26
	Recession	0.2	168.48	33.696
	Covariance [k,m]			40.120
	Correlation [k,m] = 40.12/(11.47*7.72) =				0.49636
	Variance of the portfolio = (0.6^2*11.47^2+0.4^2*7.72^2+2*0.6*0.4*11.47*7.72*0.49636)=								77.99
	SD of the portfolio = 77.99^0.5 =								8.83

Formula for Variance of a two asset portfolio = [wa^2*sda^2+wb^2*sdb^2+2*wa*wb*sda*sdb*cor(a,b)]

Where

wa and wb are the weights of the two assets a and b, sda and sdb their standard deviations and cor(a,b) their correlation.