Gavin Jones\'s friend is planning to invest $1 million in a rock concert to be h
ID: 3149782 • Letter: G
Question
Gavin Jones's friend is planning to invest $1 million in a rock concert to be held 1 year from now. The friend figures that he will obtain $3 million revenue from his $1 million investment -- unless it rains. If it rains, he will lose his entire investment. There is a 50% chance that it will rain the day of the concert. Gavin suggests that he will buy rain insurance. He can buy one unit of insurance for $0.50 and this unit pays $1 if it rains and nothing if it does not. He may purchase as many units as he wishes, up to $3 million. (a) What is the expected rate of return on his investment if he buys x units of insurance? (The cost of insurance is in addition to his $1 million investment.) (b) What number of units will minimize the variance of his return? What is this minimum value? And what is the corresponding expected rate of return? [Hint: Before calculating a general expression for variance, thing about a simple answer.]
Explanation / Answer
a) Expected rate of return = 0.5*2+0.5*(-1) = 0.05 = 5% = $50000
It is important to note, however, that the expected return is usually based on historical data and is not guaranteed.
b)
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