Final answer:
To find the standard deviation of an investment, calculate the expected return and variance. The expected return is the weighted average of the possible returns, and the variance is the weighted average of the squared deviations from the expected return. For this investment, the standard deviation is approximately 28.67%.
Step-by-step explanation:
To find the standard deviation of an investment, we need to calculate the expected return and the variance of the investment. The expected return is the weighted average of the possible returns, where the weights are the probabilities of each return.
For this investment, there is a 40% chance of earning a 10% rate of return, a 50% chance of earning a 6% rate of return, and a 10% chance of losing 5%. Using these probabilities, we can calculate the expected return as:
Expected return = (40% * 10%) + (50% * 6%) + (10% * -5%) = 4%
The variance is the weighted average of the squared deviations from the expected return. We can calculate the deviations as: -6%, -2%, and -9%. Squaring these deviations gives us: 36%, 4%, and 81%.
Using the probabilities, we can calculate the variance as:
Variance = (40% * 36%) + (50% * 4%) + (10% * 81%) = 8.2%
The standard deviation is the square root of the variance, so the standard deviation of this investment is:
Standard deviation = √(8.2%) ≈ 28.67%