Lecture 8
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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
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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
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Methods used to enhance index mutual fund returns
Index arbitrage
• Index futures are often mispriced (1-3% annually)
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Create low cost surrogate funds with futures
Long index position allows for low cost arbitrage
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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.
--- S&P 500 Index
Price
--- S&P 500 Futures Contract
0
30
60
Time (days)
90
--- S&P 500 Index
--- S&P 500 Futures Contract
Price
To return to the proper basis
spread, the contract will have
to drop RELATIVE TO the
index.
Strategy:
•Short the contract
•Long the index
0
30
60
Time (days)
90
--- S&P 500 Index
--- S&P 500 Futures Contract
Price
To return to the proper basis
spread, the contract will have
to rise RELATIVE TO the
index.
Strategy:
•Long the contract
•Short the index
0
30
60
Time (days)
90
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
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Also called “Full Investment Strategy”
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Cash Substitute Strategy - example
--- 95% stocks 5% cash
Price
--- 100% Stocks
0
30
60
Time (days)
90
Cash Substitute Strategy – example (continued)
 Annual returns
◦ Stocks return = 12%
◦ Cash equivalent return = 4%
100% Stock
1.00 x .12 = .12
12%
95% Stock 5% Cash
.95 x .12 = .114
.05 x .04 = .002
.116
vs.
11.6%
Substitution Strategies
1.
Temporary position
2.
Simulate an equity investment with futures (i.e.
Hedge Fund)
3.
Accelerate investment process
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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
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?
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
11.2 contracts = ------------------------ X 1.3
347,500
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.
Temporary position
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The same approach used to “accelerate the
investment process” can be used to create a
temporary position.
Simulate an Investment (Hedge Fund)
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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
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
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?
Underwriter Hedging – EXAMPLE - continued
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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
21.8 contracts = ------------------------ X 0.8
367,500
Underwriter Hedging – EXAMPLE - continued
Start
Finish
Asset Position
Long stock
100,000 x $100=
$10,000,000
Futures Position
Short 22 contracts
1470 x 250 x 22 =
$8,085,000
Price drops to $90
100,000 x $90=
$9,000,000
loss $1,000,000
Long 22 contracts @ 1350
1290 x 250 x 22 =
$7,095,000
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gain $ 990,000
Net position Gain / Loss = - $ 10,000
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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
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
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
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