Question

Rate of Return if State Occurs State of Economy Probability of State of Economy Stock A Stock B Recession .25 .03 −.15 Normal .55 .13 .13 Boom .20 .16 .33 a. Calculate the expected return for the two stocks. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) b. Calculate the standard deviation for the two stocks. (Do not round your intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Answer 1

Part A:

Expected Ret = Sum [ Prob * ret ]

Stock A:

Scenario	Prob	Ret	Prob * Ret
Receision	0.2500	0.0300	0.0075
Normal	0.5500	0.1300	0.0715
Boom	0.2000	0.1600	0.0320
Expected Ret			0.1110

Expected Ret from stock A is 11.10%

Stock B:

Scenario	Prob	Ret	Prob * Ret
Receision	0.2500	(0.1500)	(0.0375)
Normal	0.5500	0.1300	0.0715
Boom	0.2000	0.3300	0.0660
Expected Ret			0.1000

Expected ret from stock B is 10.00%

Part B:

SD:
Standard deviation is a measure of amount of variation or dispersion of set of values. It spcifies the risk of set of values.
SD = SQRT [ SUm [ Prob * (X-AVgX)^2 ] ]

Stock A:

State	Prob	Ret (X)	(X-AvgX)	(X-AvgX)^2	Prob * (X-Avg X)^2
Recision	0.2500	0.0300	(0.0810)	0.0066	0.0016
Normal	0.5500	0.1300	0.0190	0.0004	0.0002
Boom	0.2000	0.1600	0.0490	0.0024	0.0005
Sum[ Prob * ( X-AvgX)^2 ) ]					0.00232
SD = SQRT [ [ Sum[ Prob * ( X-AvgX)^2 ) ] ] ]					0.04816

SD of Stock A is 4.82%

Stock B:

State	Prob	Ret (X)	(X-AvgX)	(X-AvgX)^2	Prob * (X-Avg X)^2
Recision	0.2500	(0.1500)	(0.2500)	0.0625	0.0156
Normal	0.5500	0.1300	0.0300	0.0009	0.0005
Boom	0.2000	0.3300	0.2300	0.0529	0.0106
Sum[ Prob * ( X-AvgX)^2 ) ]					0.02670
SD = SQRT [ [ Sum[ Prob * ( X-AvgX)^2 ) ] ] ]					0.16340

SD of Stock B is 16.34%