Question

Consider the following information: State of Economy, Probability of State of Economy, Portfolio Return if State Occurs.

Recession: 0.19, -0.13
Normal: 0.55, 0.15
Boom: 0.26, 0.35
Calculate the expected return. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places.)

Options:
a) 15.06%
b) 9.21%
c) 11.74%
d) 13.89%

Answer 1

The expected return, after multiplying each possible return by its probability and summing these values, is 14.98%.

Step-by-step explanation:

To calculate the expected return of a portfolio, we multiply each possible return by its corresponding probability and sum these products. Given the information provided:

• Recession: Probability = 0.19, Return = -0.13 (or -13%)
• Normal: Probability = 0.55, Return = 0.15 (or 15%)
• Boom: Probability = 0.26, Return = 0.35 (or 35%)

We perform the following calculation:

(0.19 * (-0.13)) + (0.55 * 0.15) + (0.26 * 0.35) = -0.0247 + 0.0825 + 0.091 = 0.1498 or 14.98%.

After rounding to two decimal places, the expected return is 14.98%.