Question

A potential venture investment has the following possible outcomes:

Performance Probability of Rate of
Outcome Occurrence Return
Home Run (Success) .15 500.0%
Breakeven .35 15.0
Strikeout (Failure) .50 -100.0
A. What is the expected rate of return on the venture?
B. Calculate the variance and standard deviation of the rates of return for the venture.
C. Calculate the coefficient of variation of the rates of return for the venture. If the coefficient of variation of rates of return for your prior venture investments is 4.0, would the new venture be considered as being less or more risky?

Answer 1

The expected rate of return on the venture is 75.0%. The variance and standard deviation of the rates of return can be calculated using the squared differences between each rate of return and the expected rate of return. The coefficient of variation can be calculated by dividing the standard deviation by the expected rate of return.

Step-by-step explanation:

A. To calculate the expected rate of return on the venture, we need to multiply each possible outcome by its corresponding probability, and then sum up the results. In this case, the expected rate of return can be calculated as:

Expected Rate of Return = (Probability of Home Run x Rate of Return for Home Run) + (Probability of Breakeven x Rate of Return for Breakeven) + (Probability of Strikeout x Rate of Return for Strikeout)

Expected Rate of Return = (0.15 x 500.0%) + (0.35 x 15.0%) + (0.50 x -100.0%)

Expected Rate of Return = 75.0%

B. To calculate the variance and standard deviation of the rates of return, we need to first calculate the expected rate of return (which we've already done). Then, for each possible outcome, we subtract the expected rate of return from the corresponding rate of return, square the result, multiply it by the probability of occurrence, and sum up the results. The variance is the sum of these squared differences, and the standard deviation is the square root of the variance.

C. To calculate the coefficient of variation, we divide the standard deviation by the expected rate of return. If the coefficient of variation for the prior venture investments is 4.0, and the coefficient of variation for the new venture is lower than 4.0, the new venture would be considered less risky.