Question

Consider the following information:

State of the Economy	Probability of State of the Economy	Return on A %	Return on B %
Boom	0.40	10	4
Growth	0.20	-4	0
Normal	0.20	24	16
Recession	0.20	16	20

a)         What is the expected return for A? For B?                                         

b)         What is the standard deviation for A? For B?                                    

c)         What is the expected return on a portfolio of A and B that is 30% invested in A and the remainder in B?       

Answer 1

Part A:

Expetced Return:
Avg Ret = Sum [ Prob * ret ]

Stock A:

Scenario	Prob	Ret	Prob * Ret
Boom	0.4	10.00%	4.00%
Growth	0.2	-4.00%	-0.80%
Normal	0.2	24.00%	4.80%
Recision	0.2	16.00%	3.20%
Expected Ret	11.20%

STock B:

Scenario	Prob	Ret	Prob * Ret
Boom	0.4	4.00%	1.60%
Growth	0.2	0.00%	0.00%
Normal	0.2	16.00%	3.20%
Recision	0.2	20.00%	4.00%
Expected Ret	8.80%

Part B:

SD:
It spcifies the risk of Stock

SD = SQRT [ SUm [ Prob * (X-AVgX)^2 ] ]

STock A:

State	Prob	Ret (X)	(X-AvgX)	(X-AvgX)^2	Prob * (X-Avg X)^2
Boom	0.4000	10.00%	-1.20%	0.000144	0.00006
Growth	0.2000	-4.00%	-15.20%	0.023104	0.00462
Normal	0.2000	24.00%	12.80%	0.016384	0.00328
Recsion	0.2000	16.00%	4.80%	0.002304	0.00046
Sum[ Prob * ( X-AvgX)^2 ) ]					0.00842
SD = SQRT [ [ Sum[ Prob * ( X-AvgX)^2 ) ] ] ]					0.09174

I.e SD is 9.17 %

STock B:

State	Prob	Ret (X)	(X-AvgX)	(X-AvgX)^2	Prob * (X-Avg X)^2
Boom	0.4000	4.00%	-4.80%	0.002304	0.00092
Growth	0.2000	0.00%	-8.80%	0.007744	0.00155
Normal	0.2000	16.00%	7.20%	0.005184	0.00104
Recsion	0.2000	20.00%	11.20%	0.012544	0.00251
Sum[ Prob * ( X-AvgX)^2 ) ]					0.00602
SD = SQRT [ [ Sum[ Prob * ( X-AvgX)^2 ) ] ] ]					0.07756

I.e SD is 7.76 %
Part C:

Portfolio Ret is weighted Avg ret of securities in portfolio.

Stock	Weight	Ret	WTd Ret
A	0.30	0.1120	0.0336
B	0.70	0.0880	0.0616
Portfolio Ret Return			0.0952

Portfolio Ret is 0.0952 i.e 9.52%