Question

Suppose your expectations regarding the stock market are as follows:

State of the Economy	Probability	HPR
Boom	0.2	43%
Normal growth	0.4	14
Recession	0.4	-17

Use above equations to compute the mean and standard deviation of the HPR on stocks. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

Mean :

It is simple arithmatical average of returns generated over period of time.

Mean = Sum [ Prob * ret ]

Scenario	Prob	Ret	Prob * Ret
Boom	0.2000	0.4300	0.0860
Normal Growth	0.4000	0.1400	0.0560
Recesion	0.4000	(0.1700)	(0.0680)
Mean			0.0740

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 ] ]

State	Prob	Ret (X)	(X-AvgX)	(X-AvgX)^2	Prob * (X-Avg X)^2
Boom	0.2000	0.4300	0.3560	0.126736	0.02535
Normal Growth	0.4000	0.1400	0.0660	0.004356	0.00174
Recesion	0.4000	(0.1700)	(0.2440)	0.059536	0.02381
Sum[ Prob * ( X-AvgX)^2 ) ]					0.05090
SD = SQRT [ [ Sum[ Prob * ( X-AvgX)^2 ) ] ] ]					0.22562

SD is 22.56%