Assume that the economy can experience high growth, normal growth, slow down or

Question

Assume that the economy can experience high growth, normal growth, slow down or severe recession. Under these condtions you expect the following stock market returns for the coming year:

state of the economy probability return

high growth

- probability .25

- return 30%

normal growth

-probability .4

- return 10%

slow down

- probability .2

- return 2%

severe reession

- probability .15

- return -10%

a. compute the expected value of a $1000 ivestment over the coming year. What is the expected return on investment

b. compute the standard deviation of the return as a percentage over the coming year.

c. if the risk free return is 9%, what is the risk premium for a stock market investment?

Explanation / Answer

X' = Mean

A) Return = 10.4 % i.e $104 ( 1000*10.4%), Value= 1104

B) Standard Deviation = 13.13 %

C) Risk Premium = (Rm- Rf)

= (10.4 - 9) = 1.4 %

State of Economy Probability P(x) Return (x) x.P (x) (x-x') (x-x') * (x-x') Px . (x-x') * (x-x') High Growth 0.25 30 7.5 19.6 384.16 96.04 Normal Growth 0.4 10 4 -.4 .16 .064 Slow down .2 2 .4 -8.4 70.56 14.112 Severe Recession .15 -10 -1.5 -20.4 416.16 62.424 172.64 Return x' = 10.4% SD = 13.13 %

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