Financial Engineering Lecture 8

Stock Index Futures Underlying Assets (sample)• S&P 500• NYSE Composite Index• Major Market Index (MMI) (CBOE)• Value Line Index

Why Are They Traded?1. Arbitrage2. Change position quickly3. Create synthetic fund4. Hedge equity position

Index Mutual Fund Management• Index mutual funds attempt to track the market index• It is difficult to track the Market index because the market

index…• …pays no taxes• …incurs no transaction costs• …does not experience reinvestment risk

Methods used to enhance index mutual fund returns• Index arbitrage

• Index futures are often mispriced (1-3% annually)

• Create low cost surrogate funds with futures• Long index position allows for low cost arbitrage

Index Futures Strategies

Index Arbitrage A profit opportunity from change in the

traditional basis spread between index prices and index futures prices

The basis spread between the index and index futures contract should be constant.

Spreads which are larger or smaller than normal will result in arbitrage opportunities.

Index Arbitrage

Price

0 30 60 90 Time (days)

--- S&P 500 Index

--- S&P 500 Futures Contract

Index Arbitrage

Price

0 30 60 90 Time (days)

--- S&P 500 Index

--- S&P 500 Futures Contract

To return to the proper basis spread, the contract will have to drop RELATIVE TO the index.

Strategy:

• Short the contract

• Long the index

Index Arbitrage (another example)

Price

0 30 60 90 Time (days)

--- S&P 500 Index

--- S&P 500 Futures Contract

To return to the proper basis spread, the contract will have to rise RELATIVE TO the index.

Strategy:

• Long the contract

• Short the index

Cash Substitute Strategy If you hold cash equivalents, holding futures

instead, allows upside potential Example: If you hold 95% equity & 5% cash, you

will underperform the market because cash earns less

Also called “Full Investment Strategy”

Futures Strategies

Cash Substitute Strategy - example

Futures Strategies

Price

0 30 60 90 Time (days)

--- 95% stocks 5% cash

--- 100% Stocks

Cash Substitute Strategy – example (continued) Annual returns

◦ Stocks return = 12% ◦ Cash equivalent return = 4%

100% Stock 95% Stock 5% Cash1.00 x .12 = .12 .95 x .12 = .114

.05 x .04 = .002.116

12% vs. 11.6%

Futures Strategies

Substitution Strategies1. Temporary position2. Simulate an equity investment with futures (i.e.

Hedge Fund)3. Accelerate investment process

◦ Similar to “Full Investment Strategy”

Example• You manage a mutual fund• End of year causes influx of cash• Goal - keep cash position at minimum• New year is anticipated to produce large outflows

Futures Strategies

Example – Accelerate Investment Process You manage a $25 million mutual fund Investors send you $3 million in cash, for

which you do not yet have investments selected.

Assume the S&P Index contract is currently valued at 1390.

If your mutual fund has a beta of 1.3 and you wish to immediately be fully invested, what will you do?

Futures Strategies

Example – Accelerate Investment Processcontinued We need to simulate a $3,000,000 investment in our

mutual fund (i.e. a long position)

1 S&P contract = 1390 x 250 = $347,500

Futures Strategies

11.2 contracts = ------------------------ X 1.3 3,000,000

347,500

Example – Accelerate Investment ProcessContinued

11 x 347,500 x .15 = $573,375

ANSWER: To be fully invested you need to simulate a $3,000,000 investment. A deposit of $573,375 into a margin account and going long 11 S&P 500 Index contracts will accomplish this goal.

This strategy will simulate full investment for your mutual fund.

Futures Strategies

Temporary position

The same approach used to “accelerate the investment process” can be used to create a temporary position.

Futures Strategies

Simulate an Investment (Hedge Fund)

The same approach used to “accelerate the investment process” can be used to create a hedge fund.

The difference between a simulated investment and an actual investment is◦ Leverage◦ Length of investment◦ Money required

Futures Strategies

Underwriter Hedging Equity underwriters: commission,

guarantee or purchase. A guarantee or purchase an equity issue

creates price risk Risk exists from date of purchase to sale

date Index contracts can be used to hedge

risk Beta is used as the hedge ratio

Futures Strategies

Underwriter Hedging – EXAMPLE• On September 1 Merrill Lynch (ML) agrees to buy

$10mil of HSE Corporate stock & resell it on Sept 4

• ML estimates a $100/share price• The S&P 500 Index contract is priced @ 1470• 1470 x 250 = $367,500• How can ML hedge its risk if HSE has a beta of

0.8?• What is their profit or loss if on Sept 4, they sell

HSE @ $90 & close their contract on the S&P contract @ 1290?

Futures Strategies

Underwriter Hedging – EXAMPLE - continued• On September 1 Merrill Lynch (ML) agrees to buy $10mil of HSE Corporate stock &

resell it on Sept 4• ML estimates a $100/share price• The S&P 500 Index contract is priced @ 1470• 1470 x 250 = $367,500• How can ML hedge its risk if HSE has a beta of 0.8?• What is their profit or loss if on Sept 4, they sell HSE @ $90 & close their contract on

the S&P contract @ 1290?

Futures Strategies

21.8 contracts = ------------------------ X 0.8 10,000,000

367,500

22 contracts

Underwriter Hedging – EXAMPLE - continued

Futures Strategies

Asset Position Futures PositionStart Long stock Short 22 contracts

100,000 x $100= 1470 x 250 x 22 = $10,000,000 $8,085,000

Price drops to $90 Long 22 contracts @ 1350 100,000 x $90= 1290 x 250 x 22 =

Finish $9,000,000 $7,095,000 . loss $1,000,000 gain $ 990,000

Net position Gain / Loss = - $ 10,000

Futures contracts allow cheap entry & exit from markets

Index contracts can be used to alter portfolio allocation for short periods of time

Use index contracts when large outflows are expected

Futures Strategies

Currency FuturesIdentical to commodity futures in short termStrategy is naive hedge

ExampleOn May 23, a US firm agrees to buy 100,000

motorcycles from Japan on Dec 20 at Y202,350 each. The firm fears a decline in $ value

Spot price = 142.45 (Y/$) or .00720 $/YDec Futures = 139.18 (Y/$) or .00719 $/YEach K is Y12,5000,000

How can we hedge this position

Currency Futuresexample continued100,000 x Y202,350 = Y 20235 mil

20235 mil = 1,619 ks 12.5 mil

You should buy 1619 yen futures to hedge the risk

Currency Futuresexample continued

if $/Y drops to .00650 ($/Y) or 153.846Y/$Cost = $ cost - futures profitcost = 20235 (.0065) - (1619)(12.50)(.00065- .007190)

cost = 131.53 - (-13.96) = $ 145.49 mil

if $/Y rises to .008 ($/Y) or 125 Y/$Cost = $ cost - futures profitcost = 20235 (.008) - (1619)(12.50)(.0080- .007190)

cost = 161.88 - 16.39 = $ 145.49 mil