Index Futures Professor Brooks BA 444 02/12/08

The Underlying Asset Index Futures Like Other Futures Portfolio of stocks Index of stocks S&P 500 Wilshire 5000 Dow Jones Industrial Average (DJIA) Like Other Futures Delivery Date Futures Price and Spot Price

Index Futures Value of the underlying asset Price-weighted (DJIA) Value-weighted Most indexes are value weighted Σ (stock price x outstanding shares) Standard and Poor’s 500 Cash Settlement Do not delivery stocks Deliver price difference between the underlying and the futures price at maturity

Index Futures Price Futures – Spot Parity… Spot is at 1344 Adjusted for dividends as the index does not pay dividends FT = S0 x e(risk free rate – dividend yield)(Time) Example with current prices Spot is at 1344 Dividend yield at 2.5% Risk-free rate at 3.5% F0.5= 1344 x e(0.035-0.025)(0.5) = 1350

Convergence Much like the call or put option converges to its intrinsic value at expiration, the index futures price converges to the spot price at expiration of the futures contract See graph on Page 203, Figure 9-3

Uses of the Index Futures Speculation Betting on the general movement of the market Hedging – offsetting some risk of the market moving against your portfolio Common for pension funds, foundations, etc. Eliminating some of the systematic risk If market falls against a long portfolio…you incur a loss Hedging with a short position in an index futures contract minimizes the loss

Hedge Ratio How many index future contracts should you sell? Need current value of your portfolio Need dollar value of index future Need beta of your portfolio Note, contracts sold only as whole contracts

Hedge Example OSU Foundation has $400 million with a beta of 0.95 S&P 500 December Futures Price at 1350 CFO wants to protect downside of portfolio through year end because of Capital Campaign Sell December Index Futures on S&P 500 Number of contracts: [$400,000,000 / (1350) x $250] x 0.95 ≈ 1,126

Hedge Example Continued Margin Required $20,000 x 1126 = $22,520,000 Or T-Bills worth $22,520,000 In December, what happens? S&P rises to 1400 S&P stays flat at 1345 S&P falls to 1280 What is the overall gain or loss of the OSU Foundation?

Hedge Example Continued Price at 1400 Portfolio should have gained about 3.512% or $14,074,074 [((1400 /1350) -1) x 0.95] x $400,000,000 Plus dividends of $400,000,000 x 0.025 = $10,000,000 Futures Position lost $14,075,000 $250 x (1350-1400) x 1126 If T-bills deposited, they earned $588,600 [1.0350.75 -1] x $22,520,000 Net increase is $10,587,674

Hedge Example Continued Price at 1350 (finishes at Futures) Portfolio should have no gain or loss [((1350 /1350) – 1) x 0.95] x $400,000,000 Plus dividends of $400,000,000 x 0.025 = $10,000,000 Futures Position should have no gain or loss $250 x (1350-1350) x 1126 If T-bills deposited, they earned $588,600 [1.0350.75 -1] x $22,520,000 Net increase is $10,588,600

Hedge Example Continued Price at 1280 Portfolio should have lost about 4.925% or $19,703,703 [((1280 /1350) – 1) x 0.95] x $400,000,000 Plus dividends of $400,000,000 x 0.025 = $10,000,000 Futures Position made $19,705,000 $250 x (1350-1280) x 1126 It T-bills deposited, they earned $588,600 [1.0350.75 -1] x $22,520,000 Net increase is $10,591,192

Hedging in Retrospect Hedge is not perfect Can’t buy partial futures contracts Portfolio may not perform exactly as predicted by its beta Dividends are not guaranteed in size and timing Can use “hedge” to increase or decrease beta of the portfolio