What is the standard deviation of returns on a stock priced today at $10 that has a 25.0% probability of increasing to $13, a 50.0% probability of increasing to $12, a 15.0% probability of increasing by 5.0%, and a 10.0% probability of decreasing to $ 7?
A)0.0094
B)0.0286
C)0.0968
D)0.1692

Question

Quizplus · Accepted Answer

To calculate the standard deviation of returns, we first need to find the expected return and then use it to calculate the variance before taking the square root to get the standard deviation.1. Calculate the expected return (mean):- Increase to $13: $3 increase on $10, or 30% return, with a 25% probability.- Increase to $12: $2 increase on $10, or 20% return, with a 50% probability.- Increase by 5%: $0.50 increase on $10, or 5% return, with a 15% probability.- Decrease to $7: $3 decrease on $10, or -30% return, with a 10% probability.Expected return = (0.25 * 0.30) + (0.50 * 0.20) + (0.15 * 0.05) + (0.10 * -0.30) = 0.075 + 0.10 + 0.0075 - 0.03 = 0.1525 or 15.25%2. Calculate the variance:Variance = Σ[P(x) * (x - mean)^2]= 0.25*(0.30 - 0.1525)^2 + 0.50*(0.20 - 0.1525)^2 + 0.15*(0.05 - 0.1525)^2 + 0.10*(-0.30 - 0.1525)^2= 0.25*(0.1475)^2 + 0.50*(0.0475)^2 + 0.15*(-0.1025)^2 + 0.10*(-0.4525)^2= 0.00543125 + 0.00113125 + 0.001573125 + 0.02050625= 0.0286418753. Calculate the standard deviation:Standard deviation = sqrt(variance) = sqrt(0.028641875) ≈ 0.1692Therefore, the correct answer is D) 0.1692.

What Is the Standard Deviation of Returns on a Stock