1. Index Futures
Professor Brooks
BA 444
02/12/08

2. 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

3. 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

4. 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( )(0.5) = 1350

5. 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

6. 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

7. 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

8. 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

9. 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?

10. 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 = $10,000,000
Futures Position lost $14,075,000
$250 x ( ) x 1126
If T-bills deposited, they earned $588,600
[ ] x $22,520,000
Net increase is $10,587,674

11. 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 = $10,000,000
Futures Position should have no gain or loss
$250 x ( ) x 1126
If T-bills deposited, they earned $588,600
[ ] x $22,520,000
Net increase is $10,588,600

12. 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 = $10,000,000
Futures Position made $19,705,000
$250 x ( ) x 1126
It T-bills deposited, they earned $588,600
[ ] x $22,520,000
Net increase is $10,591,192

13. 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