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Version 1.0
(4-28-2003)

This help section covers the following topics:
  Purpose of This Web Site
  How Knowledge of Index Arbitrage Can Assist Investment Timing
  How Index Arbitrage Program Trading Can Affect Various Types of Investments
  Description of the Pages at this Web Site
  Fair Value Equation

Purpose of this Web Site
The information at this site is intended to help arbitrageurs and investors who are not arbitrageurs but who can benefit from knowing likely arbitrageur activity. We intend to do this by presenting our estimates of the market conditions that could produce index arbitrage activity and a thorough tabulation of the underlying factors of those estimates.

The non-arbitrageur investor audience that could perhaps benefit the most from this site are those with a comparatively short term investment time horizon (say less than a year) and those who are actively trading stocks, index futures or ETFs, or options. Long term investors can essentially ignore index arbitrage conditions because long term market and economic factors will be the prevailing determinants of investment success or failure. Yet, long term investors that use hedging (and hedge funds) may find this site helpful. A relevant hedge example would be the purchase of a basket of stocks that are expect to outperform their associated index and the sale of the index future; the converse case is, of course, the short sale of underperforming stocks (or the sale of their single stock futures) and the purchase of the index futures.

The concepts covered at this site are not for the novice investor; further, even experienced investors should not be trading stocks, futures, ETFs, or options unless they thoroughly understand them and are prepared to incur losses, for which they will be solely responsible: see our page on Terms of Usage/Disclaimer. This web site is intended for informational purposes only and is not a solicitation, nor an offer, to buy or sell any security.

How Knowledge of Index Arbitrage Can Assist Investment Timing
Knowledge of the price of an index future and its associated spot index relative to each other can be indicative of future index arbitrage program trading activity, which can in turn can produce sudden and sharp market movements. It can be disconcerting to execute a trade and then, moments later, see a program trade that takes the market in the opposite direction. The types of instruments that can be affected by index arbitrage program trading include the following:
  Stocks
Exchange Traded Funds (ETFs),
such as SPDR (Spiders), QQQQ (Cubes), or DIA (Diamonds).
Index futures,
such as the S&P 500, NASDAQ 100, or Dow Jones Ind. Avg.
or the e-mini or mini versions of these.
Options on stocks or indexes.

Hence, before placing an order to trade the above instruments, it might be prudent to know if a buy or sell program is currently possible for the relevant future-spot index pair. Even if the future-spot index difference indicates a program trade would be profitable for arbitrageurs, there is no certainty that it would be executed; nevertheless, it would be indicative of the current market bias. If you are a long term investor whose investment horizon exceeds one year, you can ignore index arbitrage conditions because the attendant long term market and economic factors will be greater determinants of your investment success or failure.

To learn about index arbitrage buy and sell program trades, specifically when they occur and how they are constructed, click here.

 
How Index Arbitrage Program Trading and Any Induced Continuing Momentum Can Affect Various Types of Investments
An index arbitrage buy program is the simultaneous buy of the stocks in the index and the sale of the index futures. Thus, a buy program exerts an upward influence on stock prices and a downward influence on futures prices. Conversely, a sell program is the simultaneous short sell of the stocks in the index and the buy of the index futures, producing a downward influence on stock prices and an upward influence on futures prices. This influence on equity and futures price that is directly attributable to index arbitrage program trades is summarized in the table below under the column labeled "Program Trade Effect".

A large index arbitrage program or several programs executed in quick succession can frequently induce a continuing market momentum of conventional trading. This effect of program trading to be the catalyst that perpetuates equity buying or selling can result from the occurrence of meaningful technical events, such as the penetration of resistance or support levels, trend lines, moving averages, Bollinger Bands, etc. The audience of market technicians who are alert to these market movements has been swelled in recent years by day traders and boutique hedge funds. This induced influence is summarized in the table below under the column labeled "Continuation Effect".

These two factors explain why the index futures price can increase after a buy program: initially the buy program will depress the futures price but the continuing market rise can be of sufficient magnitude to cause the futures price to increase.

Table of Index Arbitrage Program Trading Effects
  Sell Programs Buy Programs
Trade Type Program Trade Effect Continuation Effect Combined Effect Program Trade Effect Continuation Effect Combined Effect
Buy stock, ETF, or call option
Write naked put option
Sell short stock or ETF
Write naked call option
Buy put option
Buy index future
(full or mini)
Sell index future
(full or mini)

Key: + The "+" sign indicates a positive (desirable) influence for trade profitability, with prices increasing for long trades and decreasing for short trades.
- The "-" sign indicates a negative (undesirable) influence for trade profitability, with prices decreasing for long trades and increasing for short trades.
? The "?" mark indicates uncertainty because the magnitude of the two opposing effects of initial program trade and continuation cannot be known.


  Description of the Pages at this Web Site
Page Title Page Purpose/Description Link
To Page
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.
IndexArb Terms Description Provides a more extensive description of index arbitrage, fair value, and buy/sell programs and their trigger levels.
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.
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.
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.
Capitalization Analysis Provides the following:
Summary capitalization statistics of the S&P 500.
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.
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.
Dividend Analysis Provides estimates for dividends, in the following contexts:
Aggregate dividend amounts and yields for the S&P 500, the NASDAQ 100, and the Dow Jones Industrial Average indexes.
Aggregate dividend amounts and divisor adjusted dividends for each futures contract.
Dividend amounts for each stock within each index futures contract.
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.
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.
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.
IndexArb Calculator Provides a calculator that the investor can use to:
Calculate new index arbitrage values between updates of this web site, particularly during periods of extreme market volatility.
Perform "what-if" analyses, such as different interest rates, dividend forecasts, or buy/sell program parameters.
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.




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.
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.
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.
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)
 
FV  =
  (Number Days / 365)
Index Value   *   [(1 + interest rate)     -1]
 
  -  
 
(Sum of Dividends) / Divisor


Notes regarding the above equation:
  The above equation is used in all fair value calculations at this web site.
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.
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.
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
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:
FV  =  Index Value  *  interest rate  *  Number Days / 360  - (Sum of Dividends) / Divisor     [Not recommended]

2. The Deposit/LIBOR Rate and Dividend Yield Model
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:
FV  =  Index Value  *  (interest rate  -  dividend yield)  *  Number Days / 360     [Not recommended]

 

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