Gavin is planning on investing $1 million in a rock concert to be held one year

Question

Gavin is planning on investing $1 million in a rock concert to be held one year from today. He 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. Tere is a 50% chance it will rain the day of the concert. Someone suggests that Gavin buy rain insurance. He can buy one unit of insurance for 50 cents, and the unit pays $1 if it rains and nothing if it does not. He can purchase as many units as he wants, up to $3 million.

What number of units will minimize the variance of his return? What is this minimum value? What is the corresponding rate of return?

(What we know: expected rate of return=(1.5E6+0.50u)/(1E6+0.50u) u is units of insurance).

Explanation / Answer

Solution-

Minimum variance is 0

How to achieve minimum variance?

Payoff if it rains = payoff if it does not rain

u = 3.0 milion

E(r) = (1.5 mil + 0.5 * 3 mil) / (1.0 mil + 0.5 * 3 mil) - 1

E(r) = 0.2 = 20%

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