Question

Problem 2 The Lubin’s Investment Team is considering investmenting in two securities, A and B, and the relevant information is given below:

State of the economy	Probability	Return on A(%)	Return on B(%)
Trough	0.05	-20%	2%
Recession	0.4	-10%	2%
Expansion	0.5	15%	2%
Peak	0.05	20%	2%

1. Calculate the expected return and standard deviation of two securities.

2. Suppose the Team invested $7000 in security A and $3,000 in security B. Calculate the expected return and standard deviation of the Team’s portfolio.

Answer 1

1)	State of the economy	Probability	Return on A (%)	p*r	r-E[r] =d	d^2	p*d^2
	Trough	0.05	-0.20	-0.010	-0.235	0.055225	0.002761
	Recession	0.40	-0.10	-0.040	-0.135	0.018225	0.007290
	Expansion	0.50	0.15	0.075	0.115	0.013225	0.006613
	Peak	0.05	0.20	0.010	0.165	0.027225	0.001361
	Expected Return = ?(p*r) = 3.5%			0.035			0.018025
	Standard deviation = [?(p*d^2)]^(1/2) = (0.018025)^(1/2) =				13.43%
	State of the economy	Probability	Return on B(%)	p*r	r-E[r] =d	d^2	p*d^2
	Trough	0.050	0.02	0.001	0	0	0.000000
	Recession	0.400	0.02	0.008	0	0	0.000000
	Expansion	0.500	0.02	0.010	0	0	0.000000
	Peak	0.050	0.02	0.001	0	0	0.000000
	Expected Return = ?(p*r) = 2.00%			0.02			0.000000
	Standard deviation = [?(p*d^2)]^(1/2) = 0
2)	Expected return = 3.5*0.7+2*0.3 =		3.05	%
	Standard deviation = 3.5*0.7 =		2.45	%