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Description of the Pages at this Web Site
| Page Title |
Page Purpose/Description |
Link
To Page |
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Home Page |
Provides the fair value and buy/sell levels for the index futures front months;
note that almost all index arbitrage activity involves the front month contracts. This page also
provides a basic description of index arbitrage. |
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IndexArb Terms Description |
Provides a more extensive description of index arbitrage, fair value,
and buy/sell programs and their trigger levels. |
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| Distant Months Contracts |
Provides the fair value and buy/sell levels for all listed index futures.
Although only the front months contracts are actively involved in index arbitrage, it is useful
to know the fair value and buy/sell values for other months' contracts to profit from contract
mis-pricing or to undertake contract-to-contract arbitrage. |
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IndexArb Values vs. Time |
Demonstrates how the fair value, buy, and sell premiums decay over time, from
now until the futures contract's expiration. These tables and graphs change daily because they
are based on data that change daily, namely, the closing value of the index, interest rates
applicable to the futures contract's time period, the time to expiration, and dividend forecasts,
which can change as a result of corporate announcements. |
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Stock Performance vs. Indexes |
Compares and ranks the absolute and relative performance of each stock in the
indexes covered. The relative performance compares the stock's performance to that of the index.
These rankings are useful for selecting subsets (or baskets) of stocks for partial hedging.
For example, stocks expected to outperform the index could be bought and the index future could be
sold; conversely, under-performing stocks could be sold and the index future could be bought.
Each stock's percentage weight in the index is shown to help in constructing hedge ratios. |
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Capitalization Analysis |
Provides the following:
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Summary capitalization statistics of the S&P 500. |
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A ranking of the top one hundred and bottom one hundred companies in the
S&P 500 according to their floating capitalization methodology. This ranking also
shows each stock's percent of total S&P 500 capitalization and the cum percent.
A stock that is eliminated from the index (which is not the result of
some corporate activity such as an acquisition or bankruptcy) can undergo a sharp drop.
Often, stocks that are eliminated have relatively low capitalizations and low stock prices.
Investors can easily identify these stocks by scanning the entries at the bottom of the
table. |
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Index Component Weights |
Provides the percentage weight of each stock in the S&P 500
and the Dow Jones Industrial Average. These weights can be used to construct hedge ratios. The
rankings can be sorted either alphabetically or by percentage weight in the index. The
latter ranking also shows the cum percentages.
The S&P 500 Index is a modified capitalization
weighted index. A pure capitalization index is constructed by dividing the cross-products of
the total, actual number of shares outstanding for each company and its respective stock price by the index divisor.
Originally, the S&P 500 Index was a pure capitalization index. A modified capitalization index is based on
something other than the total, actual number of shares outstanding. After September 16, 2005, S&P will use just
the floating number of shares, meaning that shares held by control groups will be excluded from the index's
calculation. A transition phase (from March 18, 2005 to September 16, 2005) will be based on half of the floating shares plus half of the total outstanding
shares. Further, any new additions to the index since March 18, 2005, have been added on the "full floating"
basis.
The Dow Jones Industrial Average is a price weighted index: this means that the sum of
the prices of stocks in the index are divided by the index's divisor to produce the index's
value. Each stock's weight in the Dow Jones Industrial Average index is its price divided
by the sum of the prices of all stocks in the index. |
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Dividend Analysis |
Provides estimates for dividends, in the following contexts:
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Aggregate dividend amounts and yields for the S&P 500, the NASDAQ 100,
and the Dow Jones Industrial Average indexes. |
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Aggregate dividend amounts and divisor adjusted dividends for each futures contract.
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Dividend amounts for each stock within each index futures contract. |
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Dividend amount (estimated for the next year)
and yield for each stock, by index. |
The relevance of dividends as a factor in index arbitrage is explained. Webpages
that cover individual stock dividends could be useful for identifying candidates for
partial hedging.
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Fair Value Decomposition |
Decomposes each index future into its two components: interest earned on the
index (or carrying cost) and dividends. This provides a comparison of the magnitude of these two
factors and insight into index arbitrage sensitivity to interest rate and/or dividend
forecast changes. |
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Yield Curve |
Provides the interest rates to be used for calculating the index arbitrage
values for all active index futures. The curve consists of linear line segments between zero
coupon yields constructed from actively quoted deposit rates and traded Eurodollar futures.
There is good price (i.e., yield) discovery for these instruments and, therefore, should provide
accurate rates for determining fair value and buy/sell program levels. [This method of yield curve
is widely used for analysis and valuations of swaps.] Different arbitrageurs have different cost
of capital; some will be lower and some will be higher than those provided by this yield curve
method. Nevertheless, it probably represents a good mid-point case. To use this curve (or
associated table), select the yield that corresponds to the applicable date (such as the
expiration date of a futures contract) or, equivalently, the number of days from now until
expiration. |
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IndexArb Calculator |
Provides a calculator that the investor can use to:
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Calculate new index arbitrage values between updates of this web site,
particularly during periods of extreme market volatility. |
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Perform "what-if" analyses, such as different interest rates,
dividend forecasts, or buy/sell program parameters. |
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Determine the fair value, fair value premium, and buy/sell program levels
for indexes not covered on our home page and for single stock futures. |
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Fair Value Background
First, let's clear up some syntax confusion. There is no authoritative or regulatory source
for these definitions but the following reflects the consensus usage.
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Fair value is the price of the futures contract when it is correctly priced relative to the
underlying index. At fair value, there is no positive or negative bias that the two
markets mutually exert on each other. For example, if the S&P 500 index were 1000,
a plausible fair value for the S&P 500 futures would be 1003.46. |
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Fair value premium is the difference between the fair value futures contract price and
the underlying index. Continuing the above example, fair value premium would be equal to
1003.46 - 1000 or 3.46. |
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So what's the problem? The problem is that colloquially the term "fair value premium"
is contracted to just "fair value". This can be observed in the financial press,
both printed and television. So, for the above example, fair value is often stated as just 3.46
(and not 1003.46). Since this contracted form is more commonly used, fair value premium
will hereafter be called just fair value and the equation will reflect this interpretation,
namely the difference between futures and index values and not just the futures value.
[Readers should expect to see equations for fair value elsewhere that calculate the full
futures value and not the difference.] |
Now, with the syntax completely clear, we proceed to the definition and equation. Fair value (FV) is equal to the
interest that could be earned on the index (i.e., the cost of carry) minus the relevant stock dividends
occurring during the futures' duration, which is the time from the given date (which is usually today) until the
futures' settlement (expiration) date. Thus, fair value consists of the two components of interest earned
and dividends, which, expressed as an equation, is as follows:
Fair Value Equation
FV = Interest on the index from now to the
future's expiration
- Dividends(Divisor Adjusted)
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| FV = |
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(Number Days / 365) |
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| Index Value * [(1 + interest rate) |
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-1] |
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| (Sum of Dividends) / Divisor |
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Notes regarding the above equation:
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The above equation is used in all fair value calculations at this web site. |
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The interest, or cost of carry, component is based on interest rates determined from
a zero coupon yield curve that is constructed from Deposit rates and Eurodollar futures.
[See the above description about the Yield Curve.] The interest rate that corresponds
to the exact number of days remaining in the futures contract is determined from the
yield curve using interpolation. This method is used to value swap instruments
and is a widely used method for determining rates to discount cash flows. |
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The Sum of Dividends term is based on actually declared or forecasted dividend amounts (not
yields) whose ex-dividend date will occur during the remaining life of the futures contract.
Since dividend amounts are used, they must be normalized by the index's divisor. The
shortcoming of this method is that companies can change their dividend policy, namely
per-share amount and ex-dividend dates, at any time such that the amount could be wholly
included or excluded or that a previously forecasted amount is altered. Despite this
shortcoming, this method provides a significantly better estimate of the dividend component
than the dividend yield method described below. We consider this approach to be the
most accurate method of accounting for dividends. We monitor dividend announcements daily,
adjust our perception of each company's dividend policy accordingly, and update our dividend
forecast database. Thus, viewers of this web site can expect this component to be refined daily. |
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Slippage and friction have intentionally been omitted from this equation. Major arbitrage
firms have sophisticated computer and communication systems in which to execute expeditiously
both the equity and futures sides of their program trades, so slippage is minimized.
(The exception might be the time needed to acquire stock for short sales.) Similarly,
friction, in terms of commissions and other costs, is usually quite small for these arbitrage
firms, given the frequency and size of their trades. |
Other, Less Desirable Fair Value Equations
The reader may encounter other equations for fair value and wonder how they compare
to the one recommended above. To address that issue, two equations that appear frequently,
and their shortcomings, are described below:
| 1. |
The Deposit/LIBOR Rate Model |
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Deposit rates are usually quoted for time periods of one and two days and one week;
LIBOR rates are usually quoted for one, three, six, and twelve months. Both rates quotes
are based on a calendar convention called ACT/360, meaning the actual number of days
for the instrument but 360 days in the year. Interest is calculated by multiplying the
principal, the Deposit or LIBOR interest rate, and the actual number of days divided
by 360. The problem with this model is which interest rate to use. When the number of
days (from now to the futures expiration) coincides with one of the quoted Deposit
or LIBOR rates, there is no ambiguity: simply use the rate that coincides with the desired
time period. Otherwise, one must choose the rate associated with the closest date; this
introduces a (slight) discrepancy and is the reason that this approach is not favored
here. The equation for this method follows: |
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FV = Index Value * interest rate * Number Days /
360 - (Sum of Dividends) / Divisor [Not recommended] |
| 2. |
The Deposit/LIBOR Rate and Dividend Yield Model |
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The second frequently seen equation couples the Deposit/LIBOR Rate model described above
with an estimate of the annual dividend yield of the index. This method reduces the interest rate used to
to calculate the cost of carry by the annual dividend yield of the index. This model can introduce a
significant discrepancy or worse a financially damaging error; further, this approach is mathematically
inconsistent because dividend yields are not quoted on an Actual/360 calendar. Further, dividends
are discrete entities, being either wholly included or excluded for a given program
trade; using a smoothed, annual rate is inappropriate for determining the impact of dividends on
a program trade, especially those that are short-dated. An arbitrageur would certainly
not execute an index arbitrage program trade without having a good estimate of the actual
dividend amounts that should be received/paid during that program, respectively. The
"Deposit/LIBOR Rate and Dividend Yield" equation follows: |
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FV = Index Value *
(interest rate - dividend yield)
* Number Days / 360 [Not
recommended] |
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