Farmer Alf Alpha has a pasture located on a sandy hill. The return to him from this pasture is a random variable depending on how much rain there is. In rainy years the yield is good; in dry years the yield is poor. The market value of this pasture is $5,000. The expected return from this pasture is $500 with a standard deviation of $100. Every inch of rain above average means an extra $100 in profit and every inch of rain below average means another $100 less profit than average. Farmer Alf has another $5,000 that he wants to invest in a second pasture. There are two possible pastures that he can buy.
(a) One is located on low land that never floods. This pasture yields an expected return of $500 per year no matter what the weather is like. What is Alf Alpha’s expected rate of return on his total investment if he buys this pasture for his second pasture? _________.What is the standard deviation of his rate of return in this case? _________.
(b) Another pasture that he could buy is located on the very edge of the river. This gives very good yields in dry years but in wet years it floods. This pasture also costs $5,000. The expected return from this pasture is $500 and the standard deviation is $100. Every inch of rain below average means an extra $100 in profit and every inch of rain above average means another $100 less profit than average. If Alf buys this pasture and keeps his original pasture on the sandy hill, what is his expected rate of return on his total investment? _________.What is the standard deviation of the rate of return on his total investment in this case? _________.
(c) If Alf is a risk averter, which of these two pastures should he buy and why? He should choose the second pasture since it has the same expected return and lower risk.