Question

You are considering investing in a project with the following possible outcomes: Calculate the expected rate of return and standard deviation of returns for this investment, respectively.

Probabilities: Boom: 0.15 Normal: 0.4 Decline: 0.25 Depression: 0.2
Returns: Boom: 12% Normal: 7% Decline: 1% Depression: -8%
Answers:
A) 3.05%, 8%
B) 2.9%, 5.78%
C) 4.88%, 7.63%
D) 3.25%, 6.61%

Answer 1

The expected rate of return is 3.25% and the standard deviation of returns is 7.01%.

Step-by-step explanation:

To calculate the expected rate of return, we multiply each return by its corresponding probability and sum them up. Using the given probabilities and returns:

Expected rate of return = (0.15 * 12%) + (0.4 * 7%) + (0.25 * 1%) + (0.2 * -8%) = 1.8% + 2.8% + 0.25% - 1.6% = 3.25%

To calculate the standard deviation, we need to calculate the variance first. The variance is calculated by subtracting the expected return from each return, squaring the result, multiplying it by its corresponding probability, and summing them up. The standard deviation is the square root of the variance. Using the given probabilities and returns:

Variance = [(0.12 - 0.0325)^2 * 0.15] + [(0.07 - 0.0325)^2 * 0.4] + [(0.01 - 0.0325)^2 * 0.25] + [(-0.08 - 0.0325)^2 * 0.2] = 0.00148125 + 0.000708125 + 0.000724375 + 0.00101375 = 0.0049275

Standard deviation = sqrt(0.0049275) = 0.0701225 = 7.01%