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What are Fair Value, Sell Active, Sell Threshold, Buy Threshold, and Buy Active?
When do sell programs and buy programs occur?
Index arbitrage is a form of program trading activity that can produce sudden and possibly sharp market movements. Foreknowledge of the likelihood of an impending program trade can help investors with the timing of initiating either long or short positions in stocks, index futures, Exchange Traded Funds (ETFs), and options. Specifically, investors could benefit from knowing the conditions under which program trades might occur by either avoiding trades in the opposite direction or taking trades in the same direction. For example, if conditions indicate that a sell program is imminent, an investor might wish to defer a stock or call option purchase until the futures and equities markets have returned to equilibrium and the sell program conditions no longer exist. Conversely, if buy program conditions exist, an investor could proceed to execute a stock or call option purchase and possibly benefit from a rising market caused by the buy program.

There are two types of index arbitrage programs: sell and buy. Buy programs occur when the futures market is over-valued relative to the stock market and consists of the index futures being sold and the stocks in the index being bought. Sell programs, the opposite case, occur when the futures market is under-valued relative to the stock market and consists of the index futures being bought and the stocks in the index being sold. Over-valued and under-valued conditions arise because trading in the futures and equities markets occurs independently.

Index arbitrage program trades are triggered when the arithmetic difference between an index's futures contract price and the index's spot (or current) price reaches an over or under-valued extreme. This arithmetic difference is known by the various names of premium, basis or spread; this website uses the term premium because it is used by CNBC and many quote services. An example of the calculation of premium follows: if the S&P 500 futures contract price is 1409 and the S&P 500 spot index is 1400, the premium is 9. Whether this particular premium has bearish or bullish implications depends on whether it falls in the range of sell programs, no programs, or buy programs.

These program ranges are delineated by the five premium values of sell active, sell threshold, fair value, buy threshold, and buy active, which are described below. These five significant values are mathematically determined; an equation for "fair value" is presented in the Help Pages. Additional information about sell and buy programs and the associated five significant values of the futures-spot premium are given below:
Sell Programs
A sell program is the simultaneous (short) sell of all (or almost all) the stocks in the index (in weighted proportions) and the purchase of the index's futures contract. If the sell program is of sufficient magnitude, the stocks comprising the index will decline and, correspondingly, the index's futures contract will rise, producing the effect of a stock market decline and a futures market rise.

A sell program condition arises when the "futures - spot" premium shrinks significantly below fair value. This can happen because the futures and equity markets move independently and, in this case, either the futures contract has moved sufficiently lower and/or the spot index has moved sufficiently higher, relative to each other. [The spot index moves higher when one or more stocks in the index increases.] If the resulting, shrunken premium reaches the sell threshold, an index arbitrageur can capture a riskfree profit by executing a sell program. The short stock position and long futures position can be held either to the futures' settlement (expiration) date (at which time the premium imbalance is contractually guaranteed to have disappeared) or to an earlier date when the premium imbalance has disappeared due to market action.

In a typical sell program, the stock sales are short sales. The resulting proceeds are invested in fixed income instruments whose interest belongs wholly or partially to the arbitrageur, according to a pre-arranged short interest rebate agreement with the stock lender.

Two significant values in the sell program range are the sell active and the sell threshold values, described below:
No Programs
Buy Programs
A buy program is the simultaneous purchase of all (or almost all) the stocks in the index (in weighted proportions) and the sale of the index's futures contract. If the buy program is of sufficient magnitude, the stocks comprising the index will rise and, correspondingly, the index's futures contract will decline, producing the effect of a stock market rise and a futures market decline.

A buy program condition arises when the "futures - spot" premium expands significantly above fair value. This can happen because the futures and equity markets move independently and, in this case, either the futures contract has moved sufficiently higher and/or the spot index has moved sufficiently lower, relative to each other. [The spot index moves lower when one or more stocks in the index decreases.] If the resulting, excessive premium reaches the buy threshold, an index arbitrageur can capture a riskfree profit by executing a buy program. The long stock position and short futures position can be held either to the futures' settlement (expiration) date (at which time the premium imbalance is contractually guaranteed to have disappeared) or to an earlier date when the premium imbalance has disappeared due to market action.

Two significant values in the buy program range are the buy threshold and the buy active values, described below:
Sell
Active (SA)
Sell
Threshold (ST)
Fair Value
(Premium) (FV)
Buy
Threshold (BT)
Buy
Active (BA)
This is the "futures - spot" index premium value at which sell programs should be prevalent, thereby producing a meaningful decline in the stock market.

Sell program arbitrageurs will realize different rates of return on the investment of the proceeds of their stock short sales. Nevertheless, at this extreme premium level, one can expect numerous arbitrageurs to execute sell programs, causing the premium between the futures and equity markets to increase and, thereby, correcting the prior imbalance.

Yet, just because compelling premium values exist, it does not automatically mean that arbitrageurs will execute sell programs. Sell program activity might not occur for a variety of reasons such as arbitrageurs being fully committed or awaiting even more favorable conditions.
This is the minimal "futures - spot" index premium value at which sell programs might be initiated. So, some sell programs are possible and this could cause a stock market decline.

The sell threshold will vary among arbitrageurs due to several reasons, four of which are covered here. First, it may not be possible to execute simultaneously the two legs of the arbitrage, so some allowance must be made for slippage and this will vary among arbitrageurs. Second, trading commissions will vary. Third, sell program arbitrageurs face different rates of returns on the investment of the proceeds of their stock short sales. Specifically, the interest rates and the percentage amount of rebated interest vary among arbitrageurs and their stock lenders. Fourth, arbitrageurs will make different estimates of the dividends that must be paid to the stock lender during the program's duration

Therefore, the magnitude of the premium needed to meet individual arbitrageur's profit requirements and to trigger sell programs will vary.
This is the "futures - spot" index premium value at which the futures and the equity markets are in equilibrium.

No (profitable) index arbitrage type programs will occur at fair value nor when the "futures - spot" premium level falls within the range extending from the sell threshold to the buy threshold.

This absence of program activity is the usual state of the relationship of the futures and equity markets: even though they operate independently, their general movements are correlated and, hence, program trading opportunities are usually not present.

Definition
In words, the fair value premium is equal to the interest that could be earned on the index minus the relevant stock dividends occurring during the program's duration, which is the time from a given date until the futures' settlement (expiration) date.

An equation for fair value is presented in the Help Pages.
This is the minimal "futures - spot" index premium value at which buy programs might be initiated. Thus, a limited number of buy programs could occur, possibly causing a stock market rise.

The buy threshold will vary among arbitrageurs due to several reasons, four of which are covered here. First, it may not be possible to execute simultaneously the two legs of the arbitrage, so some allowance must be made for slippage and this will vary among arbitrageurs. Second, trading commissions will vary. Third, buy program arbitrageurs have different costs of capital in which to finance their stock purchases. Fourth, arbitrageurs will make different estimates of the dividends that will be captured during the program's duration.

Therefore, the magnitude of the premium needed to meet individual arbitrageur's profit requirements and to trigger buy programs will vary.
This is the "futures - spot" index premium value at which buy programs should be prevalent, thereby producing a meaningful rise in the stock market.

Although arbitrageurs incur different costs of capital in financing the purchase of the stocks that comprise the index, numerous buy programs should be launched at this extreme premium level. The impact of these buy programs would be to reduce the premium between the futures and equity markets, thereby providing a self-correcting influence.

Yet, just because compelling premium values exist, it does not automatically mean that arbitrageurs will execute buy programs. Buy program activity might not occur for a variety of reasons such as arbitrageurs being fully committed or awaiting even more favorable conditions.

 

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