Question

Suppose your expectations regarding the stock price are as follows:

State of the Market	Probability				Ending Price				HPR (including dividends)
Boom		0.23			$	140				44.5	%
Normal growth		0.29				110				11.5
Recession		0.48				80				−21.5

Use the equations E(r)=Σsp(s)r(s)E(r)=Σsp(s)r(s) and σ2=Σsp(s)[r(s)−E(r)]2σ2=Σsp(s) [r(s)−E(r)]2 to compute the mean and standard deviation of the HPR on stocks. Do not round intermediate calculations. Round your answers to 2 decimal places.)

a .Mean% [___]

b. Standard deviation% [____]

Answer 1

a. Mean %

Mean % = E(r)=Σsp(s)r(s) where

E(r) = Expected return

s = State of the market, s(b) = Boom; s(n) = Normal; s(r) = recession

p(s) = probability of the state of the market, p(s(b)) = 23%; p(s(n)) = 29%;p(s(r)) = 48%

r(s) = HPR of the state of the market; r(s(b)) = 44.50%; r(s(n)) = 11.50%;r(s(r)) = -21.50%

E(r) = (23%*44.50%)+(29%*11.50%)+(48%*-21.50%) = 0.10235+0.03335-0.10320 = 0.0325 or 3.25%

Expected return = 3.25%

b. Standard Deviation %

Standard Deviation % = σ2=Σsp(s)[r(s)−E(r)]2 where

σ2 = variance^(1/2) = Standard Deviation %

s = State of the market, s(b) = Boom; s(n) = Normal; s(r) = recession

p(s) = probability of the state of the market, p(s(b)) = 23%; p(s(n)) = 29%;p(s(r)) = 48%

r(s) = HPR of the state of the market; r(s(b)) = 44.50%; r(s(n)) = 11.50%;r(s(r)) = -21.50%

E(r) = 3.25%

σ2 = (23%*((44.50%-3.25%)^2)+29%*((11.50%-3.25%)^2)+48%*((-21.50%-3.25%)^2))^(1/2)

=(23%*0.170156+29%*0.006806+48%*0.061256)^(1/2)

=(0.039136+0.001974+0.029403)^(1/2) = 0.070513^(1/2) = 0.2655 or 26.55%

Standard Deviation % = 26.55%