(Computing the standard deviation for an individual investment) James Fromholtz is considering whether to invest in a newly formed investment fund. The fund's investment objective is to acquire home mortgage securities at what it hopes will be bargain prices. The fund sponsor has suggested to James that the fund's performance will hunge on how the national economy performs in the coming year. Special, he suggested the following possible income: Rapid expansion and recovery Probability 5%, Fund Returns 100%. Modest growth, Probability 40%, Fund Returns 45%. Continued recession, Probability 50%, Fund Returns 15%. Falls into depression, Probability 5%, Fund Returns -100%.
a. Based on these potential outcomes, what is your estimate of the expected rate of return from this investment opportunity?
b. Calculate the standard deviation in the anticipated returns found in part a.
c. Would you be interested in making such an investment? Note that you lose all your money in one year if the economy collapses into the worst state or you double your money if the economy enters into a rapid expansion.