A project has a 0.44 chance of doubling your investment in a year and a 0.56 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.)

74.46%

Explanation:

Since the project has a chance of doubling investment, it has a chance of making a + 100% return. The project also have a chance of losing half of its investment that is - 50% return. The expected return E (r) is given by:

E (r) = chance of doubling investment + chance of losing half of its investment

E (r) = 0.44 (100%) + 0.56 (-50%) = 0.44 (1) + 0.56 (-0.5) = 0.44 - 0.28 = 0.16

σ² = 0.44 (100% - E (r)) ² + 0.56 (-50%-E (r)) ² = 0.44 (1 - 0.16) ² + 0.56 (-0.5 - 0.16) ² = 0.310464 + 0.243936 = 0.5544

σ = √σ² = √0.5544 = 0.7446 = 74.46%

The standard deviation is 74.46%