Barbara is considering investing in a stock and is aware that the return on that

Question

Barbara is considering investing in a stock and is aware that the return on that investment is particularly sensitive to how the economy is performing. Her analysis suggests that four states of the economy can affect the return on the investment. Using the table of returns and probabilities below find:

1) What is the expected return on Barbara's investment?

2) What is the standard deviation of the return on Barbara's investment?

               Probability    Return

Boom         0.3            25.00%

Good         0.2            15.00%

Level          0.3            10.00%

Slump        0.2            -5.00%

Explanation / Answer

E[X] = x*P[X=x]
= 0.3*25 + .. + 0.2*-5
= 12.5

E[X2] = x2*P[X=x]
= 0.3*252 + .. + 0.2*(-5)2
= 267.5

i) Expected Return = E[X] = 12.5%

ii) Standard Deviation = {E[X2] - E2[X]}0.5
= [267.5 - 12.52]0.5
= 10.5475%

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