Question

A firm's stock has 50% chance of a 9% rate of return and a 50% chance...

A firm's stock has 50% chance of a 9% rate of return and a 50% chance of a 27% rate of return. What is the standard deviation of return for this stock? Answer as a percent return to the nearest hundredth of a percent as in xx.xx without entering a percent symbol.

Homework Answers

Answer #1

Given,

Probability (P) = 50% or 0.50

First return (R1) = 9% or 0.09

Second return (R2) = 27% or 0.27

Solution :-

Expected return = (P x R1) + (P x R2)

= (0.50 x 0.09) + (0.50 x 0.27)

= 0.045 + 0.135 = 0.18

Variance = P(R1 - expected return)2 + P(R2 - expected return)2

= 0.50(0.09 - 0.18)2 + 0.50(0.27 - 0.18)2

= 0.50(-0.09)2 + 0.50(0.09)2

= 0.50(0.0081) + 0.50(0.0081)

= 0.00405 + 0.00405 = 0.0081

Standard deviation = (variance)1/2

= (0.0081)1/2 = 0.09 or 9.00%

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