Question

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.

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%