How The SPY Arbitrage Model Can Be Used In Trading

In March I announced the availability of the Intraday SPY Arbitrage Model.  This tool provides traders with information about how the S&P 500 is tracking against other asset classes during the day and can be helpful in various ways. Today I'll discuss two ways of using the arbitrage model to place market-neutral arbitrage trades.

For reference (and perhaps for those with short attention spans), I'll provide the weights up front. For the curious skeptics I'll explain below.

SPY:  +$12
XIV:     -$1
TBT:     -$2
HYG:  -$13.2

The first way is to trade using the intraday SPY arbitrage model. Below is a graph from March 8, 2013 showing the difference between the price of SPY and the model:

In order to take advantage of the arbitrage opportunities such as the $0.40 spread in the last hour of trading, one must know the correct weighting of securities. With the weights applied correctly the result would be to capture any difference between the SPY and model from the time you enter to the time you close out the trades.

In what is seemingly a ridiculous chart, below is a comparison of the the above chart (difference between the SPY and the model) and a trade consisting of the components and weight ratios as specified above. The point here is that they are identical, thus proving that by using the weights specified you get the exact same result as the difference between the SPY and the model.

In this particular instance, since SPY is higher than the model a trader would short the SPY and be long the model components in the weights given. Specifically, short $155 of SPY and long $12.92 XIV, $25.83 TBT, and $170.5 HYG (these numbers come from the -12 : 1 : 2 : 13.2 dollar ratio).

Side note: If you can not find shares to short for a given security, you can substitute in the inverse ETF (e.g. long VXX in place of short XIV, or long SH in place of short SPY) using the same dollar amount. You can also reduce the amount of capital required by substituting in a leveraged ETF (e.g. long UVXY in place of long VXX, or long SSO/UPRO in place of SPY), but be sure to reduce the amount of dollars for that component by half (or by a third if you are using a +/-3x ETF in place of SPY).  The net result will be the same with these substitutions.

Assuming the standard securities, the example above requires a total short position of $155 and total long of $209.25. Your gain on this low-risk trade, should the spread collapse from $0.40 to $0.00, would be $0.40.  If the spread increases further the trade would lose money for each penny it widens. Note that the spread does not always approach zero at the end of the day, and intraday spreads as large as $0.80 or higher can occur.

For a more practical trading scenario, multiply the standard dollar amounts by 100 for a short position of $15,500 and total long of $20,925.  The net gain on a spread collapse from $0.40 to $0.00 would be $40. As mentioned above you can reduce your capital requirements by substituting in leveraged ETFs, but this trade clearly requires a large amount of capital and low commissions to be of much use. (**For potential issues using this trade please see the end of this post.)

Daily SPY Arbitrage Model
For traders looking for a longer term play, the same weights can be applied to the Daily SPY Arbitrage Model which updates prices only at the end of each day.  In this model a trader can place trades spanning weeks or months and take advantage of larger arbitrage spreads. For example, the current spread is nearly $10 as shown in the graphs below. Using the practical trading example (discussed above) of $15,500 short and $20,925 short, a collapse of a $10 spread to $0 represents a gain of $1,000.

Knowing at what size spread to open a trade can be difficult in this model and requires some analysis of the bond market in addition to stocks. Given that central banks around the world are doing all sorts of things to influence bond prices, prices in different markets can be disconnected for an extended period of time. These factors make this trade suitable for advanced investors only.

One big difference in the daily model vs the intraday model is that if you take long positions in leveraged ETFs for a trade and hold for any duration of time longer than a day you will open yourself up to negative compounding errors. I won't go into the details on that concept but you should do a Google search on it and know what it is. To turn the compounding errors around in your favor, you can take short positions in the inverse leveraged ETF for the position that you want to take. For example, go short SPXU with a 1/3 dollar amount instead of being long SPY.

One last point of clarification for both models is that all the arbitrage models charts currently reference TBF as the treasury component. The intraday model actually uses TBT for calculations because it has a higher trade volume than TBF. The daily model obtains data using TLT in order to avoid distortion of the model caused by compounding errors. Regardless, the model weights use TBT as a reference because I find it to be easiest to communicate the weights with consistency. Feel free to use your favorite 20+ yr treasury ETF but be sure to make adjustments off of the TBT weight.

**Some issues with using the model:
- You may run into problem finding shares available to short through your broker, especially on lower volume securities. This can be a problem specifically with HYG which does not have an inverse ETF.
- If you currently have an open short position, your broker could request that you close your position (or force close it ) if they get low on available shares.
- If you are subject to wash sale rules your losses may not properly offset your gains.
- The model is based on several indexes and will only be accurate to the extent that they are tracking their intrinsic value.  This can be checked on your trading platform.  For example to check XIV you would look up the symbol "XIV-XIV.IV".
- When there are gaps up/down in the morning there is the possibility that the intraday data doesn't line up correctly and needs to be adjusted.  If the arbitrage opportunity looks too good to be true (especially early in the morning), it probably is (check the SPY vs Model Components graph to make sure they are all starting together).

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