Question

Highland Investment, a venture investor, is considering investing in a software venture opportunity. However, the rate of return to be realized next year is likely to vary with the economic climate that actually occurs. Following are three possible economic outcomes, the probability that each one will occur, and the rate of return projected for each outcome:

                    Economic             Probability of                     Rate of

                        Climate                 Occurrence                         Return

                        Recession                    .25                                -20.0%

                        Normal                         .50                               15.0%

                        Rapid Growth            .25                               30.0%

1. What is the expected rate of return on the software venture?

2. Calculate the variance and standard deviation of the rates of return for the software venture?

3. Calculate the coefficient of variation of the rates of return for the software venture. If the coefficient of variation of rates of return for Highland’s prior venture investments is 1.5, would the software venture be considered as being less or more risky?

Answer 1

State of Economy	Probability of Economy(X)	Return
recession	0.25	-20.00%
normal	0.5	15.00%
boom	0.25	30%
Expected return E(X)=sum of(x*P(X))		10.00%
E(X^2)		0.04375
Variance=E(X^2)-E(X)^2		0.03375
Standard deviation=sqrt(Variance)		18.37%
coefficient of variation = std/expected return		1.84

It is more risky