Question

After studying the economy, you forecast that there is a 70% chance of a good economy next year and a 30% chance of a poor economy. If the economy is good, you estimate that a stock you have been following would have a 19% return. Likewise, if the economy is poor, you estimate a -7% return for that same stock. The risk-free rate is 4.3%. What is the standard deviation of the expected returns for this stock? (Answer to the nearest tenth of a percent, but do not use a percent sign). Probability Return Good Economy 70% 19% Poor Economy 30% -7% Risk-Free Rate = 4.3

Answer 1

Probability of Good Economy = 70%
Expected Return during Good Economy = 19%
Probability of Poor Economy = 30%
Expected Return during Poor Economy = -7%

Expected Return = 70% * 19% + 30% * (-7%)
Expected Return = 11.20%

Variance = 0.70 * (0.19 - 0.112)^2 + 0.30 * (-0.07 - 0.112)^2
Variance = 0.014196

Standard Deviation = (0.014196)^(1/2)
Standard Deviation = 0.119 or 11.9%

So, standard deviation of the expected returns for this stock is 11.9%