Since their introduction, stock index futures contracts have become very popular
ID: 2766217 • Letter: S
Question
Since their introduction, stock index futures contracts have become very popular and are now widely traded by finance professionals. Many factors, including (1) the current price of the underlying stock index, (2) the time to contract maturity, and (3) the dividends paid to the stocks in the underlying index, will affect the settlement price of a stock index futures contract. What is the fourth primary factor involved in stock index futures contract pricing, and how does this factor affect settlement prices?
Explanation / Answer
Interest Rates:
While interest rates are not the only factors that affect the futures prices (other factors are underlying price, interest (dividend) income, storage costs and convenience yield), in a no-arbitrage environment, risk-free interest rates should explain futures prices.
If a trader buys a non-interest earning asset and immediately sells futures on it, because the futures cash flow is certain, the trader will have to discount it at a risk-free rate to find the present value of the asset. No-arbitrage conditions dictate that the result must be equal to the spot price of the asset.
A trader can borrow and lend at the risk-free rate, and with no-arbitrage conditions the price of futures with time to maturity of T will be equal to:
F0,T=S0*er*T
where S0 is the spot price of the underlying at time 0; F0,T is the futures price of the underlying for time horizon of T at time 0; and r is the risk-free rate.
Example 1:
If the underlying price of a non-dividend (interest) paying and non-storable asset is S0 = $100, and the annual risk-free rate, r, is 5%, assuming that the one-year futures price is $107, we can show that this situation creates an arbitrage opportunity and the trader can use this to earn risk-free profit. The trader can implement following actions simultaneously:
Borrow $100 at a risk-free rate of 5%.
Buy the asset at spot market price by paying borrowed funds and hold.
Sell one-year futures at $107.
After one year, at maturity the trader will deliver the underlying earning of $107, will repay the debt and interest of $105 and will net risk free of $2.
Example 2:
Suppose that everything else is the same as in the previous example, but the one-year futures price is $102. This situation again gives a rise in arbitrage opportunity, where traders can earn profit without risking their capital, by implementing the following simultaneous actions:
Short sell the asset at $100.
Invest the proceeds of the short sell in the risk-free asset to earn 5%, which continues to be compounded annually.
Buy one-year futures on the asset at $102.
After one year the trader will receive $105.13 from his risk-free investment, pay $102 to accept the delivery through the futures contracts, and return the asset to the owner from which he borrowed for short sell. The trader realizes risk-free profit of $3.13 from these simultaneous positions.