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 $2.8 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 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 $2.8 million. (a) What is the expected rate of return on his investment if he buys u 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 them? [Hint: Before calculating a general expression for variance, think about a simple answer.]
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 $2.8 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 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 $2.8 million.
(a) What is the expected rate of
(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 them? [Hint: Before calculating a general expression for variance, think about a simple answer.]
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