The Cambridge Opera Association has come up with a unique door prize for its December 2019 fund-raising ball: Twenty door prizes will be distributed, each one a ticket entitling the bearer to receive a cash award from the association on December 31, 2020.
The cash award is to be determined by calculating the ratio of the level of the Standard and Poor’s Composite Index of stock prices on December 31, 2020, to its level on June 30, 2020, and multiplying by $100. Thus, if the index turns out to be 1,000 on June 30, 2020, and 1,200 on December 31, 2020, the payoff will be 100 × (1,200/1,000) = $120.
After the ball, a black market springs up in which the tickets are traded. What will the tickets sell for on January 1, 2020? On June 30, 2020? Assume the risk-free interest rate is 10% per year. Also assume the Cambridge Opera Association will be solvent at year-end 2020 and will, in fact, pay off on the tickets. Make other assumptions as necessary.
Would ticket values be different if the tickets’ payoffs depended on the Dow Jones Industrial Index rather than the Standard and Poor’s Composite?
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