Problem 3 Suppose that the risk-free interest rate is 10% per annum with continuous compounding and that the dividend yield on a stock index is 4% per annum. The index is standing at 400, and the futures price for a contract deliverable in four months is 405. What arbitrage opportunities does this create?

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lukecoupland7061 lukecoupland7061

22-02-2020
Business

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Problem 3 Suppose that the risk-free interest rate is 10% per annum with continuous compounding and that the dividend yield on a stock index is 4% per annum. The index is standing at 400, and the futures price for a contract deliverable in four months is 405. What arbitrage opportunities does this create?

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ijaz4308 ijaz4308 · Answer 1 · 2020-02-22T10:51:15+01:00

Answer:

Please see explanation

Explanation:

To answer the given question, first we will calculate the theoretical future price which shall be determined using continuous compounding formula as follows:

Theoretical future price=400*e^(10%-4%)*4/12

=$408.08

The actual future price of a contract deliverable in 4 months is only $405 which means that the index future price is too low in relation to the index.

The suitable arbitrage strategy shall be:

1. to purchase the future contracts

2.Short sale the shares which are underlying the index