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).

Actual Volatility and Forward Implied Volatility Continue To Diverge

Actual historical volatility for the S&P 500 over the past 3 months (HV63) fell to 9.24 today, putting current 30-day forward volatility (VIX) at a 50% premium. From the VIX Futures Data page:

This is getting to be a pretty large gap and it looks like it could be a good time for new long positions in XIV in the next day or two. However the risk of a position in XIV right now is that the premium between VIX and front month futures (the yellow and blue lines above) is only 2%. This means that if we do see a VIX spike there is very little "buffer" in M1 to absorb the spike so it will be more likely to see gains as well, especially if VIX stays above M1 for a few days.

We can see this risk reflected in the VXX Daily Forecast gauges. A short VXX (or long XIV) position is still in favor (just barely), but the risk of a spike has been increasing over the past several days. In fact, if you look at the daily chart of VIX you'll see that it's been on a choppy rise over the past 2 weeks -- a pattern that sometimes leads to a large VIX spike. I still think that a smaller position or no position is justified until we see some real relief in the VIX..

Some other interesting action today can be observed by using the intraday SPY arbitrage model, which seemed to be all over the map.

Short term futures were up over 2% (as seen in the decline of XIV), pricing in a downward move in the SPY. The term structure for the first two months flattened to under 1 point until about mid-day when XIV decided to reverse to catch up to SPY and close up 1.5%. VIX futures closed lower and with a wider contango spread (-1.3).

Treasury yields decoupled from SPY, falling all day and closing substantially lower (see TBF). 

High Yield Credit (HYG) sold off pretty hard toward the end of the day and finished negative.

So a bit of disagreement between assets and reason for continued caution. 

Weekly Wrap and the Week Ahead

A slow and steady week in VIX futures brought down all points along the curve with some additional emphasis on the front two months. Overall the term structure remains somewhat compressed, with just 4.7 points separating 1st and 7th month. 

There was a slight divergence in correlation between XIV and SPY today as we closed at new SPX highs - a signal for some caution in both XIV and SPX longs. From the intraday SPY arbitrage model:

Treasuries and high yield corporate bonds diverged  from SPY during the week as well, widening the gap on the daily SPY arbitrage model, with SPY trading at a $5.00 premium to the model:

And yet there's no reason VIX can't head lower given that actual volatility over the past 3 months (HV63) is just 10.8.

The Week Ahead In VIX Futures

Very little changed on the week for VIX futures, with most months only gaining 1-2%. Spot VIX however came off its low of 11.05 last week and gained 22%. Week-over-week term structure (does not include March VIX futures which expired this week):

The term structure may look normal but if you consider the steepness of the curve you'll see it flattened a bit this week, down to just 4.5 points separating 1st and 7th month (from 5.8 points last week).  Month 1 to month 2 flattened as well, down to 1.25 points from 2.1 last week. This results in a relatively small positive roll yield in XIV, which by itself, isn't likely to get you very far.

Forward implied volatility remains reasonably priced relative to 1- and 3-month historical volatility, with a ~25% premium. From the VIX Futures Data page:

Of course most of next week's action will likely be influenced by the outcome of the Cyprus bailout negotiations. If they can reach a favorable outcome, VIX is likely to fall back toward 1- and 3- month historical volatility, currently near 11. There are many opinions on what will happen but I found this piece from the former Vice Chairman of Moody's to be particularly interesting.

Lastly, a chart of the intraday SPY arbitrage model from today. Model components broke from tracking the S&P's +0.8% move today, with treasuries and volatility remaining flat and high yield credit being sold.

Looking at the New VIX Futures Months After March Expiration

Today is the last day of trading for March 2013 VIX futures.  As discussed would happen in my week ahead post, March futures closed within about 3% of VIX.

Closing term structure:

Looking forward to tomorrow April currently sits at 15.4 and May at 16.25 resulting in a smaller contango spread of -0.85, which applies to XIV, VXX, and UVXY. With VIX at 14.39, April VIX futures are just 7% higher.

For those looking at trading ZIV, the contango spread between month 4 and month 7 will start narrower at -1.5 tomorrow.

Implied volatility has popped up a bit off of realized volatility, but with a volatility risk premium of 26% VIX pretty well priced once more. Here is the current chart from the VIX Futures Data page:

There was not much room to play in the intraday SPY arbitrage model today as the model stuck closely to the SPY.

And in case you missed it I posted about a new tool today to measure Twitter sentiment on VXX which was positive earlier in the day but is unsurprisingly heading toward 50/50 as VXX ended the day flat.

Market Wrap - 3/13

In what was otherwise a rather unremarkable sideways day in the markets, I found the movement in the underlying components of the SPY arbitrage model to be quite interesting.

Looking at the model compared to the S&P 500 (SPY) there were two arbitrage opportunities during the day and another rapid convergence of the two into the close.

Taking a look at the components level you can see the Treasury bond component (TBF) dive after strong demand for the 1:00pm 10-year auction drove up prices. As a result the model became deeply discounted relative to the SPY for most of the afternoon until a last minute rally in high yield corporate bonds (HYG) to very neatly close the gap between the S&P 500 and the model.

While the volatility component (XIV) closely tracked the S&P 500 all day, yesterday was a different story as it dragged heavily.

All in all this seems to represents some tension in the market as investors start to take increased caution and diversify a bit after what has essentially been 9 weeks of going nowhere but up for stocks.

I'd also like to point out the movement over the past 6 weeks of stocks vs the dollar index (UUP), which typically move inversely to each other. Another reason for caution in my opinion.

New SPY Arbitrage Tool Available

I'm happy to announce the availability of a new trading tool on the Trading Volatility site, the SPY Arbitrage Model. 

The model is updated in real-time throughout the day, plotting the S&P 500 (SPY) against a model of the implied value for the S&P 500 as derived from a collection of related assets (volatility (XIV), interest rates (TBF), and credit (HYG)). With this model a trader can place relatively low risk arbitrage trades to take advantage of prices as they diverge and recouple during the day.


Let's take a look at Friday's data: 

To get the most our of this trade you want to look for points at which the difference between SPY and model are large -- generally +/-$0.20 is a good rule of thumb depending on your trade sizes and transaction costs.  On the areas I highlighted above, the second area I highlighted (towards the end of the day) provides a better opportunity than the first, as the difference between SPY and model is $0.30. The trade approach is then to sell the SPY while simultaneously buying the components in the model. Once the SPY and model converge, positions should then be closed.

To maintain near market-neutral on the trade the weighting of each component needs to be balanced according to the beta for each component, at least as a starting point (this is a topic I'll cover in another post). Some adjustments can be made based on where each component is trading. Again, consider data from Friday:

When the arbitrage opportunity opened up in the last hour of trading, two components of the model were lagging (XIV and HYG) the SPY, while TBF was essentially in line.  In this case an alternate trade would have been a short position in the SPY, but only take longs in XIV and HYG since it is less likely that TBF would make an upward move while SPY moves lower. This helps to maximize gains and reduce transaction costs.

Important note: If your positions are small relative to your transaction costs or if you are subject to wash sales rules, this may not be a good strategy to employ. I recommend crunching the numbers for your specific situation to determine if this strategy is right for you.