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Financial Engineering

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? Arbitrage Change position quickly Create synthetic fund Hedge equity position.

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Financial Engineering

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  1. Financial Engineering Lecture 8

  2. Stock Index Futures • Underlying Assets (sample) • S&P 500 • NYSE Composite Index • Major Market Index (MMI) (CBOE) • Value Line Index Why Are They Traded? • Arbitrage • Change position quickly • Create synthetic fund • Hedge equity position

  3. Index Futures Strategies • 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

  4. 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.

  5. Index Arbitrage --- S&P 500 Index ---S&P 500 Futures Contract Price 0 30 60 90 Time (days)

  6. Index Arbitrage • --- 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 Price 0 30 60 90 Time (days)

  7. Index Arbitrage (another example) • --- 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 Price 0 30 60 90 Time (days)

  8. Futures Strategies 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”

  9. Futures Strategies • Cash Substitute Strategy - example --- 95% stocks 5% cash ---100% Stocks Price 0 30 60 90 Time (days)

  10. Futures Strategies Cash Substitute Strategy – example (continued) • Annual returns • Stocks return = 12% • Cash equivalent return = 4% 100% Stock 95% Stock 5% Cash 1.00 x .12 = .12 .95 x .12 = .114 .05 x .04 = .002 .116 12% vs. 11.6%

  11. Futures Strategies Substitution Strategies • Temporary position • Simulate an equity investment with futures (i.e. Hedge Fund) • 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

  12. 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?

  13. Futures Strategies Example – Accelerate Investment Process continued • 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 3,000,000 347,500 11.2 contracts = ------------------------ X 1.3

  14. Futures Strategies Example – Accelerate Investment Process Continued 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.

  15. Futures Strategies Temporary position • The same approach used to “accelerate the investment process” can be used to create a temporary position.

  16. 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

  17. 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

  18. 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?

  19. 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? 10,000,000 367,500 21.8 contracts = ------------------------ X 0.8 22 contracts

  20. Futures Strategies Underwriter Hedging – EXAMPLE - continued Asset Position Futures Position Start 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

  21. Futures Strategies • 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

  22. Currency Futures Identical to commodity futures in short term Strategy is naive hedge Example On 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 $/Y Dec Futures = 139.18 (Y/$) or .00719 $/Y Each K is Y12,5000,000 How can we hedge this position

  23. Currency Futures example continued 100,000 x Y202,350 = Y 20235 mil 20235 mil = 1,619 ks 12.5 mil You should buy 1619 yen futures to hedge the risk

  24. Currency Futures example continued if $/Y drops to .00650 ($/Y) or 153.846Y/$ Cost = $ cost - futures profit cost = 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 profit cost = 20235 (.008) - (1619)(12.50)(.0080- .007190) cost = 161.88 - 16.39 = $ 145.49 mil

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