Chapter 9 Stock Index Futures © 2004 South-Western Publishing

Outline Introduction Stock indexes and their futures contracts Uses of stock index futures Hedging with stock index futures

Introduction The fastest growing segment of the futures market is in financial futures In 1972, physical commodities comprised over 95 percent of all futures volume Today, physical commodities amount to only one-third of total futures volume

Stock Indexes and Their Futures Contracts Stock index futures contracts The S&P 500 stock index futures contract Pricing of stock index futures Basis convergence

Stock Indexes Introduction Capitalization-weighted indexes

Introduction The S&P 500 index represents about 90% of all U.S. stock index futures trading First published in 1917 Currently one of the Commerce Department’s leading indicators

Capitalization-Weighted Indexes The S&P 500 index is capitalization-weighted Each of the 500 share prices in the index is multiplied by the number of outstanding shares in that particular firm Standard and Poor’s calculates the index by adding these figures and dividing by the index divisor

Capitalization-Weighted Indexes (cont’d) Assume only three firms are in an index Assume the initial divisor is arbitrarily set at 2,700,000

Capitalization-Weighted Indexes (cont’d) Day 1 Index = 270,000,000/2,700,000 = 100.00 Stock Shares Out Closing Price Shares x Price A 1,000,000 $10 10,000,000 B 5,000,000 $22 110,000,000 C $15 150,000,000 Total 270,000,000

Capitalization-Weighted Indexes (cont’d) Day 2 Index = 271,000,000/2,700,000 = 100.37 Stock Shares Out Closing Price Shares x Price A 1,000,000 $11 11,000,000 B 5,000,000 $20 100,000,000 C 10,000,000 $16 160,000,000 Total 271,000,000

Capitalization-Weighted Indexes (cont’d) Day 3 – B splits two for one Index = 262,000,000/2,700,000 = 97.04 Stock Shares Out Closing Price Shares x Price A 1,000,000 $12 12,000,000 B 10,000,000 $11 110,000,000 C $14 140,000,000 Total 262,000,000

Stock Index Futures Contracts As with other futures, a stock index future is a promise to: Buy or sell Standardized units Of a specific index At a fixed price At a predetermined future date

Stock Index Futures Contracts (cont’d) Stock index futures are similar in every respect to a traditional agricultural contract except for the matter of delivery Index futures settle in cash rather than by delivery of the underlying asset

The S&P 500 Stock Index Futures Contract There is no actual delivery mechanism at expiration of an S&P 500 futures contract You actually deliver the dollar difference between the original trade price and the final price of the index at contract termination

Pricing of Stock Index Futures Elements affecting the price of a futures contract Determining the fair value of a futures contract Synthetic index portfolios

Elements Affecting the Price of A Futures Contract The S&P 500 futures value depends on four elements: The level of the spot index The dividend yield on the 500 stock in the index The current level of interest rates The time until final contract cash settlement

Elements Affecting the Price of A Futures Contract (cont’d) SPX Dividend Yield SPX Index S&P 500 Stock Index Futures Time until Settlement T-bill Rate

Elements Affecting the Price of A Futures Contract (cont’d) Stocks pay dividends, while futures do not pay dividends Shows up as a price differential in the futures price/underlying asset relationship

Elements Affecting the Price of A Futures Contract (cont’d) Stocks do not accrue interest Posting margin for futures results in interest Shows up as a price differential in the futures price/underlying asset relationship

Determining the Fair Value of A Futures Contract The futures price should equal the index plus a differential based on the short-term interest rate minus the dividend yield:

Determining the Fair Value of A Futures Contract (cont’d) Calculating the Fair Value of A Futures Contract Example Assume the following information for an S&P 500 futures contract: Current level of the cash index (S) = 1,484.43 T-bill yield ® = 6.07% S&P 500 dividend yield (D) = 1.10% Days until December settlement (T) = 121 = 0.33 years

Determining the Fair Value of A Futures Contract (cont’d) Calculating the Fair Value of A Futures Contract Example The fair value of the S&P 500 futures contract is:

Synthetic Index Portfolios Large institutional investors can replicate a well-diversified portfolio of common stock by holding A long position in the stock index futures contract and Satisfying the margin requirement with T-bills The resulting portfolio is a synthetic index portfolio

Synthetic Index Portfolios (cont’d) The futures approach has the following advantages over the purchase of individual stocks: Transaction costs will be much lower on the futures contracts The portfolio will be much easier to follow and manage

Basic Convergence As time passes, the difference between the cash index and the futures price will narrow At the end of the futures contract, the futures price will equal the index (basic convergence)

Uses of Stock Index Futures Speculation Spreading Arbitrage Anticipation of stock purchase or sale Hedging

Speculation Each one-point movement in the S&P 500 index translates to $250 A person who is bullish could obtain substantial leverage by buying S&P contracts

Spreading Spreads using index futures can be used to speculate with reduced risk E.g., a speculator believing the Nasdaq will outperform the Dow Jones could employ an intermarket spread by buying Nasdaq 100 futures and selling DJIA futures

Arbitrage Sometimes the market price of a futures contract temporarily deviates from the price predicted by pricing theory An arbitrageur could short the futures contracts and buy stock if the price deviates upward An arbitrageur could short the stock and buy futures contracts if the price deviates downward

Anticipation of Stock Purchase or Sale Futures contracts can be used to lock in a price in anticipation of a stock purchase or sale E.g., a portfolio manager might want to get out of the market, but for tax reasons does not want to sell securities until the new year

Hedging The primary purpose of S&P futures is to facilitate risk transfer from one who bears undesired risk to someone else willing to bear the risk S&P futures are used by most large commercial banks and by many pension funds and foundations to hedge

Hedging With Stock Index Futures Systematic and unsystematic risk The need to hedge The hedge ratio Hedging in retrospect Adjusting market risk

Systematic and Unsystematic Risk Systematic factors are those that influence the stock market as a whole E.g., interest rates, economic indicators, political climate, etc. Systematic risk or market risk

Systematic and Unsystematic Risk (cont’d) Unsystematic factors are unique to a specific company or industry E.g., earnings reports, technological developments, labor negotiations, etc. Unsystematic risk

Systematic and Unsystematic Risk (cont’d) Proper portfolio diversification can virtually eliminate unsystematic risk The market assumes that you have been smart enough to reduce risk through diversification Beta measures the relative riskiness of a portfolio compared to a benchmark portfolio like the S&P 500

Systematic and Unsystematic Risk (cont’d) Portfolio Variance Number of Securities

Using Futures Contracts to Hedge Portfolios The Need to Hedge Using Futures Contracts to Hedge Portfolios You are the manager of a $100 million equity portfolio. You are bullish in the long term, but anticipate a temporary market decline. How can you use futures contracts to hedge your stock portfolio?

The Need to Hedge (cont’d) Using Futures Contracts to Hedge Portfolios (cont’d) If you are long stock, you should be short futures. You need to calculate the number of contracts necessary to counteract likely changes in the portfolio value.

The Hedge Ratio Introduction The market falls The market rises The market is unchanged

Introduction To construct a proper hedge, you must realize that portfolios are of Different sizes Different risk levels The hedge ratio incorporates the relative value of the stock and futures, and accounts for the relative riskiness of the two portfolios

Introduction (cont’d) To determine the hedge ratio, you need: The value of the chosen futures contract The dollar value of the portfolio to be hedged The beta of the portfolio

Introduction (cont’d) Determining the Factors for A Hedge Suppose the manager of a $75 million stock portfolio (with a beta of 0.9 and a dividend yield of 1.0%) wants to hedge using the December S&P 500 futures. On the previous day, the S&P 500 closed at 1,484.43, and the DEC 00 S&P 500 futures closed at 1,517.20.

Introduction (cont’d) Determining the Factors for A Hedge (cont’d) The value of the futures contract is: $250 x 1,517.20 = $379,300

Introduction (cont’d) Determining the Factors for A Hedge (cont’d) The hedge ratio is:

Using the Hedge in A Falling Market The Market Falls Using the Hedge in A Falling Market Assume the S&P 500 index falls 5%, from 1,484.43 to 1,410.20 after three months. Given beta, the portfolio should have fallen by 5.0% x 0.9 = 4.5%, which translates to $3,375,000. However, you receive dividends of 1% x .333 x $75,000,000 = $250,000. If you sold 178 contracts short at 1,517.20, your account will benefit by (1,517.20 – 1,410.20) x $250 x 178 = $4,761,500.

The Market Falls (cont’d) Using the Hedge in A Falling Market (cont’d) The combined positions (stock, dividends, and futures contracts) result in a gain of $1,636,500.

Using the Hedge in A Rising Market The Market Rises Using the Hedge in A Rising Market Assume the S&P 500 index rises from 1,484.43 to 1,558.70 after three months. Given beta, the portfolio should have advanced by 5.0% x 0.9 = 4.5%, which translates to $3,375,000. You still receive dividends of 1% x .333 x $75,000,000 = $250,000. If you sold 178 contracts short at 1,517.20, your account will lose (1,517.20 – 1,558.70) x $250 x 178 = $1,846,750.

The Market Rises (cont’d) Using the Hedge in A Rising Market (cont’d) The combined positions (stock, dividends, and futures contracts) result in a gain of $1,778,250.

The Market is Unchanged Using the Hedge in An Unchanged Market Assume the S&P 500 index remains at 1,484.43 after three months. There is no gain on the stock portfolio. However, you still receive dividends of 1% x .333 x $75,000,000 = $250,000. If you sold 178 contracts short at 1,517.20, your account will benefit by (1,517.20 – 1,484.50) x $250 x 178 = $1,455,150.

The Market is Unchanged (cont’d) Using the Hedge in An Unchanged Market (cont’d) The combined positions (stock, dividends, and futures contracts) result in a gain of $1,705,150.

Hedging in Retrospect A hedge will usually not be perfect because: It is not possible to hedge exactly Stock portfolios seldom behave exactly as their beta suggests The futures price does not move in lockstep with the underlying index (basis risk) The dividends on the S&P 500 index do not occur uniformly over time

Adjusting Market Risk Futures can be used to adjust the level of market risk in a portfolio:

Adjusting Market Risk (cont’d) Determining the Number of Contracts Needed to Increase Market Exposure Suppose the manager of a $75 million stock portfolio with a beta of 0.9 would like to increase market exposure by increasing beta to 1.5. Yesterday, DEC 00 S&P 500 futures closed at 1517.20 How can the manager use futures to accomplish this goal, assuming the composition of the stock portfolio remains unchanged?

Adjusting Market Risk (cont’d) Determining the Number of Contracts Needed to Increase Market Exposure (cont’d) The manager should go long futures and hold them with the stock portfolio. Specifically, he should purchase 119 S&P 500 futures contracts: