1. Lecture 8

2.  Underlying Assets (sample) S&P 500 NYSE Composite Index Major Market Index (MMI) (CBOE) Value Line Index Why Are They Traded? 1. Arbitrage 2. Change position quickly 3. Create synthetic fund 4. Hedge equity position

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

6. 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

7. 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

8. 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.  Cash Substitute Strategy - example Price 0 30 60 90 Time (days) --- 95% stocks 5% cash --- 100% Stocks

10. 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. Substitution Strategies 1. Temporary position 2. 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

12. 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. 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 11.2 contracts = ------------------------ X 1.3 3,000,000 347,500

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

16. 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

17. 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. 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. 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? 21.8 contracts = ------------------------ X 0.8 10,000,000 367,500

20. Underwriter Hedging – EXAMPLE - continued Asset PositionFutures Position StartLong 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 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. 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. 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. 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