DerivativesLecture 6

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

Example – Commodity Speculation: No MarginYou think you know everything there is to know about pork bellies (bacon) because your butler fixes it for you every morning. Because you have decided to go on a diet, you think the price will drop over the next few months. On the CME, each PB K is 38,000 lbs. Today, you decide to short three May Ks @ 44.00 cents per lbs. In Feb, the price rises to 48.5 cents and you decide to close your position. What is your gain/loss?

Futures Strategies

Nov: Short 3 May K (.4400 x 38,000 x 3 ) = + 50,160

Feb: Long 3 May K (.4850 x 38,000 x 3 ) = - 55,290

Loss of 10.23 % = - 5,130

Example –Commodity Speculation: With MarginYou think you know everything there is to know about pork bellies (bacon) because your butler fixes it for you every morning. Because you have decided to go on a diet, you think the price will drop over the next few months. On the CME, each PB K is 38,000 lbs. Today, you decide to short three May Ks @ 44.00 cents per lbs. In Feb, the price rises to 48.5 cents and you decide to close your position. What is your gain/loss?

Futures Strategies

Nov: Short 3 May K (.4400 x 38,000 x 3 ) = + 50,160

Feb: Long 3 May K (.4850 x 38,000 x 3 ) = - 55,290

Loss = - 5,130

Loss 5130 5130

Margin 50160 x.15 7524 ------------ = -------------------- = ------------ = 68% loss

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