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 (R _{1}) = 9% or 0.09**

**Second return (R _{2}) = 27% or 0.27**

**Solution :-**

**Expected return = (P x R _{1}) + (P x
R_{2})**

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

**= 0.045 + 0.135 = 0.18**

**Variance = P(R _{1} - expected
return)^{2} + P(R_{2} - 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%**

MT
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