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Arbitrage, quantitative investing, strategy-based indices, systematic strategies
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Summary

  • Structural Arbitrage can be implemented without shorting.
  • The strategy eliminates open-ended tail risk.
  • Investors should shrewdly choose lower returns to sleep soundly.

The idea behind Structural Arbitrage is that profits are possible by acting as a synthetic insurance company which sells expensive insurance in the volatility market, and then synthetically reinsures that market risk with long duration government bonds.

And happily, Structural Arbitrage can be implemented without shorting and the attendant open-ended tail risk. I insist upon having my risk defined to the capital I have invested in a strategy, even in a worst-case-scenario discontinuous market shock where positions can gap to heretofore unimagined levels. Therefore, my personal choice is to use strategies which do not have open-ended shorting risks at all, even if there are alternatives with almost twice the performance. I enjoy making money with math in a manner which allows me to sleep soundly (even if I actually am suffering some of the convexity performance drag that I could capture if I did not abhor tail risk).

In the past few years, Exchange Traded Products (ETPs) based upon the short term VIX futures indices (VIX ETPs) have become tremendously popular. In theory, these instruments increase in value when markets become more volatile, and decrease in value when markets become less volatile. In practice, these funds act almost as if they are synthetic continuously traded Put options on the S&P 500, with the associated time decay.

The effect of contango in these markets synthetically resembles time decay, so that VIX ETPs tend to lose value over long time periods. Moreover, it is very well chronicled that these funds may represent effective hedges during very short, discrete time periods, but are very poor hedges over longer time periods.

Interestingly enough, 20+ year U.S. Government Bonds (Long Bonds) tend to also behave like hedges for the S&P 500, often moving inversely to the market, especially in times of severe equity market stress.

Synthetically, or in substance, we can view Long Bonds as Put options on the S&P 500 as well. However, unlike VIX ETPs, not only do Long Bonds hedge equities well in discrete time periods of market stress, but they also tend to retain more of their value over time than VIX ETPs. And this is quite logical, since a Long Bond is an asset which pays interest over time, whereas VIX ETPs, like Put options, are almost like ice cubes with values that melt away in one's hand if significant downside volatility does not materialize.

Both Long Bonds and VIX ETPs effectively (on average) behave as Put options in relation to the S&P 500. So let's think of them as such in their function, if not their form.

Most humans are interested in trading things on their own merits. They have predictions about Long Bonds, and they trade Long Bonds accordingly. Or they have predictions about future volatility, and trade VIX ETPs accordingly.

But we must think about instruments and markets in inter-relation to each other.

The potential benefit of studying inter-relationships between markets is that we might find an inefficiency that lasts for years. It may be logical for individual markets to behave a certain way when traded upon their own merits, but this behavior may be inter-market inefficient when the meta-behavior of such trading creates pricing discrepancies in how risk is priced between totally different markets.

Therefore, we might syllogistically make the proposition that if VIX ETPs are related to the S&P 500 and if Long Bonds are also related to the S&P 500, that then Long Bonds and VIX ETPs must also be inter-related to each other.

Simply put, VIX ETPs lose much of their value over time. This makes them a very expensive form of insurance, or equity hedge. Long Bonds retain more of their value over time than VIX ETPs do. This makes Long Bonds a cheaper form of insurance, or equity hedge.

An economist might say that we can treat Long Bonds and VIX ETFs as close substitutes for equity hedging. And close substitutes should sell for similar prices. But in this case, they most definitely do not. They sell for wildly divergent prices. Illogically, the worse hedge is more expensive, and the better hedge is cheaper!

Why not, like a shrewd insurance company, sell the more expensive form of insurance, and buy the cheaper form of insurance as reinsurance against catastrophe? Maybe we could pocket the difference in how these two markets price equity risk as a profit.

Literally, if the idea works, we will be running a virtual insurance company for S&P 500 market risk. But we will not have the overhead (or competition) of a conventional insurance company. Imagine an insurer that sells insurance, then reinsures against catastrophe. Similarly, we are selling expensive insurance by synthetically shorting VIX ETPs through their inverse analogues, then reinsuring more cheaply by purchasing ETPs which hold Long Bonds. But unlike most insurers, our theory is that we can fully reinsure the risk we have written by selling insurance which is usually too expensive, and by buying reinsurance which is usually too cheap.

This arbitrage has persisted thus far, because while market participants recognize that volatility and long bonds are both linked to equity prices, they have not made the logical/syllogistic leap that, therefore, volatility and long bond markets should also be linked to each other.

Now like a proper experiment, let's move beyond a cool idea, or hypothesis, and explore some objective, explicit, systematic rules that are testable.

Let us test the performance of buying inverse VIX ETPs and buying Long Bonds ETFs. After brute force testing of every two instrument combination and dollar weighting, I believe the most interesting performance is obtained by the following rules:

I. Buy XIV (NASDAQ:XIV) with 40% of the dollar value of the portfolio.
II. Buy TMF (NYSEARCA:TMF) with 60% of the dollar value of the portfolio.
III. Rebalance weekly to maintain the 40%/ 60% dollar value split between the positions.

Here are the strategy's results in a linear scale:

(click to enlarge)

The strategy far exceeds the Sharpe and MAR of the S&P 500 (NYSEARCA:SPY), but with only a 0.12 correlation. Structural Arbitrage is a very interesting portfolio diversifier.

I have named this strategy Structural Arbitrage, because it arbitrages structural differences in pricing equity risk between two different markets, and reframes market structures in novel synthetic terms. However, since Structural Arbitrage relies upon a structural mispricing between how two different markets price equity risk, it is important to remember that like any other strategy, that it could stop working if the inefficiency it exploits ceases to exist. However, the persistent difference between how these two markets synthetically price equity risk is exceedingly glaring. We ascribe this Structural Arbitrage's persistence to the industry-wide focus on incrementally improving tired, commoditized arbitrage strategies which have existed for decades, rather than a focus on innovation.

Massive market inefficiencies have the status of the Loch Ness Monster in the Economic world. Everyone claims a sighting, but few have any proof that it exists. Beyond a shadow of a doubt, I have proven that a massive market inefficiency exists, having published a book on the phenomenon long before the strategy's outperformance this year. And the inefficiency may continue, because it takes advantage of structural inter-market relationships that persist because these markets are being traded rationally on their own terms. Arbitraging away this particular inefficiency might require VIX and Long Bond markets to not trade rationally on their own terms, which may be a disequilibrium position for markets. Hence there is a chance that this arbitrage could persist.

We are in essence synthetically arbitraging asset class inter-market structures the way that other firms might arbitrage multiple currency pairs or stock pairs and their relationships intra-market. In the Structural Arbitrage frame, we are in essence synthetically pairs trading markets themselves. Since the volatility futures market prices systematic equity risk more expensively and the long bond market prices systematic equity risk more cheaply, the difference in synthetically pricing equity risk in these two markets represents a robust return stream with potentially excellent risk/reward characteristics. The ongoing mispricings between these two synthetic premiums represents this Structural Arbitrage strategy's profits. Therefore, any entity putting on this arbitrage trade implicitly becomes an insurer which insures systematic equity risk dearly and then reinsures, or lays off, that risk more cheaply.

A less precise way of viewing a 40/60 XIV/TMF portfolio is as alpha generation by a short gamma position, whose drawdown and tail risk can be cheaply insured or hedged in the long duration U.S. government bond market at a price which creates substantial profits and risk control.

Indeed, when a XIV position is combined with a TMF position in a 40/60 ratio, the resultant portfolio is not short gamma at all, but represents a non-correlated return stream with excellent investment characteristics as a systematic investment strategy.

However, the bigger picture is that massive and easy profits tend to never last, especially in financial markets. Hence, I estimate unscientifically that Structural Arbitrage will make outsized returns for four more years, at best. And for me? On to the next strategy. My clients demand that we stay a thousand steps ahead. Innovation is the product.

Disclosure: I have no positions in any stocks mentioned, but may initiate a long position in XIV, TMF over the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.

Source: Make 40% A Year With Math And Without Shorting