Question

There is a probability of 0.38 that there will be extremely cold weather this coming Winter. If it does, we expect investors of Star & Bucks to achieve a return of 0.16. Else, investors may expect a lower return of 0.07. Can you estimate the variance of this rate of return?

Answer 1

To estimate the variance of the rate of return for Star & Bucks, one should calculate the expected return with the given probabilities and returns, and then use this to find the variance through the appropriate formulas.

Step-by-step explanation:

The question involves determining the variance of the rate of return for an investment in Star & Bucks, given different probabilities for returns based on weather conditions. Given a probability of 0.38 for extremely cold weather leading to a return of 0.16, and a probability of 1 - 0.38 (0.62) for a return of 0.07, we can calculate the expected return (E[R]) and then use it to find the variance (Var[R]).

The expected return is calculated as:

• E[R] = 0.38 * 0.16 + (1 - 0.38) * 0.07

Then, the variance is found using the formula:

• Var[R] = 0.38 * (0.16 - E[R])^2 + 0.62 * (0.07 - E[R])^2

To get the actual numerical value, you have to substitute the expected return you calculated into the variance formula and compute the result.