Question

A project has a 0.62 chance of doubling your investment in a year and a 0.38 chance of halving your investment in a year. What is the standard deviation of the rate of return on this investment? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Answer: 72.8%

Explanation:

Doubling my investment would mean increasing by 100% so that is the first return.

Halving my investment would mean reducing it by 50% so the second return is -50%.

Expected return is a weighted average based on the probabilities of the returns and is calculated as:

= (0.62 * 100%) + (0.38 * -50%)

= 0.43

Variance = (0.62 * (100% - 0.43)²) + (0.38 * (-50% - 0.43)²)

= 0.201438 + 0.328662

= 0.5301

Standard deviation = √0.5301

= 72.8%