Question

A stock is expected to return 15% in a normal economy, 20% in a boom, and lose 10% in a recession. there is a 25% chance the economy will boom and a 25% chance of a recession. what is the standard deviation of the expected returns?

- 11.73%
-8.36%
-10.0%
-12.53%

Answer 1

The standard deviation of the expected returns is 11.73%.

Step-by-step explanation:

To find the standard deviation of the expected returns, we can calculate the weighted average of the returns for each scenario and then calculate the standard deviation using the formula for weighted standard deviation.

Let's calculate the weighted average returns:

• Expected return in a normal economy (15%) * Probability of a normal economy (50%): 0.15 * 0.5 = 0.075
• Expected return in a boom (20%) * Probability of a boom (25%): 0.2 * 0.25 = 0.05
• Expected return in a recession (-10%) * Probability of a recession (25%): -0.1 * 0.25 = -0.025

The weighted average return is the sum of these values: 0.075 + 0.05 - 0.025 = 0.1 (or 10%).

To calculate the standard deviation, we need to find the variance of each scenario:

• Normal economy: (0.15 - 0.1)^2 * 0.5 = 0.0025 * 0.5 = 0.00125
• Boom: (0.2 - 0.1)^2 * 0.25 = 0.01 * 0.25 = 0.0025
• Recession: (-0.1 - 0.1)^2 * 0.25 = 0.04 * 0.25 = 0.01

The variance is the sum of these values: 0.00125 + 0.0025 + 0.01 = 0.01375.

Finally, the standard deviation is the square root of the variance: sqrt(0.01375) = 0.1173 (or 11.73%).