From the April 01, 2006 issue of Futures Magazine • Subscribe!

Trading with fair value

Terms such as “premium,” “discount,” “fair value” and “the cash spread” are often used in the markets. Most often they refer to the relationship between the cash equities market and their relevant near-month equity futures contract.

Most brokers and quote vendors provide some sort of symbol that yields a continuous calculation of the near month S&P 500 futures contract (such as /SPZ5*) minus the cash S&P 500 index ($SPX). Depending upon your broker or quote vendor, some common symbols used for this value are $PREM, $PREM.X, SP-PREM, PREM or $SPS, which is the format used at CyberTrader.

This value is so important because it can tell you whether the “proper” relationship between the two benchmarks is being maintained or not. As long as the markets are in balance, this value generally will oscillate around a central line known as the fair value. However, when the market gets volatile and buy and sell thresholds are crossed, it can sometimes result in quick market swings above or below fair value.

The near-month futures usually trade at a value that is slightly higher than the current value of the cash index. The difference between the two (the spread or premium) is caused by the cost of carry. The cost of carry is composed primarily of interest, dividends and time value. The rate on the most recently issued 90-day Treasury bill is often used to represent the risk-free interest rate. The dividends are the combined dividend payments from the stock represented in the S&P 500 index and the time value relates to the expiration date of the futures contract. This premium will decrease a small amount each day as expiration approaches until the cash and futures prices are nearly the same.

With this information you can calculate the “proper” spread between the futures and the cash index using the following formula:

Theoretical Futures Fair Value = $SPX * [1 + (r - d) * x/365]


r = risk-free interest rate

d = aggregate dividend rate of the stocks in the $SPX

x = number of days until expiration of the futures contract.

For example, for an $SPX value of 1230.96, let’s calculate the theoretical fair value of the December futures contract and see how close we come to the actual quoted price of 1233.69.

The current values for our formula are: r = 3.87%, d = 1.60%, x = 36 days. Therefore, we have:

TFV = 1230.96 * [1 + (0.0387 - 0.0160) * 36/365]

= 1230.96 * [1+ (0.0227) * 0.0986]

= 1230.96 * [1.0022]

= 1233.67

As is clear, this gets us pretty close to the actual value of the futures contract.

With these two numbers, we can then determine the fair value premium. This is simply the theoretical futures price minus the cash price: 1233.67 - 1230.96 = 2.71. This figure will match what you’ll see commonly quoted around the industry as the cash/futures premium or basis. This means the futures at 1233.69 are trading just slightly (0.02) above the theoretical fair value price.

Because we know the price of the futures contract, the price of the cash index and what the difference should be between the two of them, we can potentially uncover some extreme short-term trading opportunities as the two get out of whack. The reason this happens is they trade on completely different exchanges. Most of the stocks in the S&P 500 cash index ($SPX) trade on the New York Stock Exchange and a few are on the Nasdaq. S&P 500 futures contracts trade on the Chicago Mercantile Exchange (CME). As a result, news or large order activity that may occur on one exchange and not the other can cause the difference between the two contracts (the basis or premium) to fluctuate throughout the day.


When those fluctuations are large enough (meaning the premium of the futures contract over the cash contract gets too large or too small), arbitragers stand ready to bet that moves will take place to realign the contracts and move them back toward the fair value premium. In fact, their actions actually cause these moves to take place.

A certain amount of small fluctuation is normal and occurs almost every second, but when those fluctuations get too large, interesting things happen. What levels are considered too large or too small will differ among arbitrage firms, but they are what dictate what are known in the industry as the “program buy” and “program sell” thresholds. These two thresholds can also be found on the Web sites of many arbitrage

trading firms.

To see these actions happening, you’ll want to use a one-minute chart and watch the spread indicator, such as the $SPS in the example, closely. Generally, a reliable confirmed trigger is one or two candles on a candlestick chart breaking through the buy or sell lines. Typically, you will see the cash market move up sharply on buy triggers, and sharply lower on sell triggers.

As these buy and sell signals are reached, the arbitragers will execute program trades on either the futures markets (by buying or selling S&P 500 full size or E-mini contracts) or on the cash markets (by buying or selling SPYDR ETFs, for example). Quite simply, when program buys trigger, the cash market is bought and the futures market is sold off. When program sells trigger, the cash market is sold and the futures market is bought. These program trades cause the markets to make sharp moves that can last from a few seconds to a few minutes. This, in turn, can create short-term trading opportunities for /ESZ5 E-mini traders and even $SPX and $OEX option traders. You have to be quick on the draw and cautious, however, because while these signals are often accurate, they are also short-lived.

For example, when buy program triggers are reached (meaning the futures are trading at too great a premium over the cash market), buy orders will be placed on SPYDRs and sell orders on /SPZ5 or /ESZ5. This type of activity would drive the price of the cash market up and the futures market down causing them to move back toward the fair value number. Likewise, when sell program triggers are reached (meaning the futures are trading at too small of a premium or even at a discount to the cash market), buy orders will be placed on the /ESZ5 or /SPZ5 and sell orders will be placed on SPYDRs. This type of activity would drive the price of the futures market up and the cash market down causing them to move back toward the fair value number.

To get a visual representation of what is happening see “Beyond the bounds” (below). The red line indicates program sell levels (1.63) and the green line indicates program buy levels (3.60). The blue line indicates the fair value (2.71). Because these values are set in the morning, and don’t change until the next day, you can add these lines to your trading charts in the morning and simply leave them there until the next trading session.

However, don’t assume that sharp market moves can’t happen without these signals; that is certainly not the case. In the chart, a quick market rally of about two points on the $SPX occurred between 2:20 p.m. and 2:30 p.m., with little warning from the spread oscillator. There are many other factors that can cause market swings, and if the futures and cash market both move higher at the same time, the spread will remain in the middle of the channel.

By contrast, if we zoom in on an area earlier in the same day around lunch time, as shown in “No free lunch” (below), we see a sell program that preceded a sharp drop of about 1.5 to 2.0 points in the cash market. We can see that the futures dropped to a premium of less than 1.63 above the cash market and that triggered a sell program. That sell program caused arbitrage sells in the cash market which you can see by the sharp drop off in the purple line ($SPX) above. This particular drop lasted less than two minutes.

An $OEX or $SPX option trader may have been able to take advantage of this sell-off by establishing bearish positions, such as long puts or short calls. An at-the-money put option on the $OEX would have gained about 0.60 during this drop, for a gain of $60 per contract before commissions. An E-mini trader could have gone long E-mini contracts, which would have gone up as the futures market was bought.

Often, the reversal from these programs is almost as quick as the moves caused by the programs, so you would generally only want to hold these positions for one to two minutes. Occasionally, if the signal is a little unclear, you may be able to take a reverse position after the move, and profit on the rebound. “On borrowed time” (below) shows a buy example. The move of about 2.00 to 2.25 points would have created an opportunity for buying calls, selling puts or selling E-minis. The sharp sell-off after the spike indicates these positions had to be closed within a few minutes to capture the profit.

These are just a few examples of the kind of moves you may see when you watch the arbitrage activity that goes on between the two markets. On quiet days it is not uncommon for there to be no triggers at all, while days with several economic reports, unexpected news events or just high volatility might have several.


Because the E-mini futures trade virtually 24 hours a day, they often will create huge gaps before the cash market opens at 9:30 a.m. in New York. Once the cash market opens, the two will get in line quickly but it will generally take about two minutes. As a result, the $SPS values are completely inaccurate from about 9:30 a.m. to 9:32 a.m. each morning. After that, you should see accurate spread calculations until the cash market closes again at 4:00 p.m.

Like any trading system, the buy/sell triggers can generate false signals, and acting on those signals could result in significant losses quickly, so you must be ready to close your positions immediately if they move against you. This is not a strategy that allows room for the market to come back your way. This type of trading is high risk. Don’t attempt it if you can’t already follow your current trading system in strict fashion. However, if your broker provides a streaming trading platform with real-time quote data and you are looking for intraday scalping opportunities, this strategy may give you some ideas you haven’t seen before.

Randy Frederick is director of derivatives, senior registered options principal and one of the chief architects of CyberTrader’s options trading platforms and analytical tools.

About the Author

Randy Frederick is Managing Director of Active Trading and Derivatives for Charles Schwab

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