Question

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.)

Answer 1

74.46%

Step-by-step 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%