Gavin Jones’s friend is planning to invest $1 million in a rock concert to be he

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, my goodness, 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 $3 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 return? [Hint: Before calculating a general expression for variance, think about a simple answer.]

Explanation / Answer

a.

b.3 milion of insurance will minimize the variance.

using equation,

.125u^2.75u+1.125=0

u=3 million

corresponding rate of return=20%

initial investment= 1 million Investment in insurance= u x.5 Expected rate of return= (1.5+u)/(1+.5u) .5x3+u

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