Using Futures Contract to Hedge Risk 218202 1

Using Futures Contract to Hedge Risk • 2/18/202 1 Fin 355 -Using Futures Contract to Hedge Risk | Dr. Menahem Rosenberg 1

Forward Contract • Forward Contract – An agreement between two parties to exchange some item in a future date at a prearranged price. – Forward price - price specified in the forward contract for the delivery of the specified item – Spot price - the price for immediate delivery of the item. – Usually no money changes hand at the contract initiation. – Long position – buyer of the item – Short position - seller of the item . 2/18/202 1 Fin 355 -Using Futures Contract to Hedge Risk | Dr. Menahem Rosenberg 2

Future Contract • Future contract – A standardized forward contract, that is traded on an organized exchange. • Standardization – item definition, quality, quantity and delivery date and place. • Type of future contracts: – Agricultural – Industrial – Financial 2/18/202 1 Fin 355 -Using Futures Contract to Hedge Risk | Dr. Menahem Rosenberg 3

Future Contracts Mechanics • All trades are recorded as trades with the exchange clearing house. • Initial margin – Minimal Cash position required to initiate a future contract. • Marking to Market – At the end of the trading day, cash is added (subtracted) to the margin to reflect that day’s gain(loss). • Maintenance Margin – The lowest cash position after negative marking to market that will require cash addition. • Margin Call – The formal request for additional cash. 2/18/202 1 Fin 355 -Using Futures Contract to Hedge Risk | Dr. Menahem Rosenberg 4

S&P 500 Contract • November 13 spot 882. 53 2/18/202 1 Fin 355 -Using Futures Contract to Hedge Risk | Dr. Menahem Rosenberg 5

Futures Pricing • T-bill Future contract – Call for the delivery of 89 -91 days to maturity of $1 million par treasury bonds. • Assume contract matures at T 1 the delivered bonds mature at T 2. Assume f 1, 2 is the pure discount forward rate between T 1 and T 2. • The the forward contract price F is 2/18/202 1 Fin 355 -Using Futures Contract to Hedge Risk | Dr. Menahem Rosenberg 6

Pricing Stock Index Futures • Let: – P - current value of the index – Dividend stream paid by the firm in the index. – PV(D) – Present Value of the dividend stream. – risk free rate – F - current Forward price • Arbitrage argument : 2/18/202 1 Fin 355 -Using Futures Contract to Hedge Risk | Dr. Menahem Rosenberg 7

Pricing Stock Index Futures • Let d be the dividend yield 2/18/202 1 Fin 355 -Using Futures Contract to Hedge Risk | Dr. Menahem Rosenberg 8

Portfolio Hedging • Number of contract needed to hedge a portfolio: – Portfolio size relative to future contract size – The relative volatility of the portfolio to the future contract price volatility. • sp portfolio return standard deviation • sp future contract return standard deviation • rp, m coefficient of correlation between the portfolio return and the future contract return • h - hedge ratio 2/18/202 1 Fin 355 -Using Futures Contract to Hedge Risk | Dr. Menahem Rosenberg 9

Portfolio Hedging • Using the correlation coefficient definition: • In addition the hedger should consider the portfolio size relative the future contract size. Define index unit as one future contract value 2/18/202 1 Fin 355 -Using Futures Contract to Hedge Risk | Dr. Menahem Rosenberg 10

Portfolio Hedging • Optimal portfolio hedge 2/18/202 1 h* Fin 355 -Using Futures Contract to Hedge Risk | Dr. Menahem Rosenberg 11