Question

Demonstrate an arbitrage strategy and calculate the arbitrage strategy using Spot-Futures Theorem.

Answer 1

Futures Price = Spot Price × (1 + Risk-Free Interest Rate – Income Yield)

the deviation from parity would present a risk-free arbitrage opportunity. Entering a futures position does not require a payment of cash, so the risk-free rate that can be earned from the cash is added. (Although margin must be posted, it is much less than the value of the contract, and margin can be in the form of Treasuries, which earn interest.) The income yield is subtracted because no income is earned without owning the underlying asset. Applying this formula to a stock:

Futures Market Arbitrage Opportunity If Spot-Futures Theorem Violated

Suppose that you pay $2,600 for 1 share of a stock index exchange-traded fund (ETF) that tracks the Nasdaq 100 at the beginning of the year and that it pays $52 in dividends during the year. At the same time, you sell a futures contract short for the Nasdaq 100 that is cash-settled, requiring you to pay $2,700 at the end of the year. (Note this futures contract is hypothetical since there is no contract for just 1 share of an ETF or stock, but it simplifies the math while still illustrating the principle.) Suppose further that:

• Risk-free rate = 5%
• Dividend yield = 2%

Therefore, the futures settlement price should be:

= ETF Price × (1 + .05 – .02) = $2,600 × 1.03 = $2,678, but if it is $2,700 instead, here is what you can do:

That $22 Risk Free Profit is Called the Arbitrage.

I hope my efforts will be fruitful to you