THE TIME ARBITRAGE

I remember meeting Ajay Shah, Professor and Columnist in 2000, during my early days as a derivatives analyst in Mumbai. He talked about how speculators-arbitrageurs and hedgers together create the magic in derivatives market. It was indeed magical as from its humble beginnings when nobody believed in the potential of markets and badla was still considered the real thing, we came a long way. Little did then we realize that in less than 10 years we would be illustrating the gaps in the hedge ratio and our understanding of hedging and arbitrage activity. Hedge was the basic premise for establishing the derivatives markets in India. The L C Gupta committee report delved on this in detail illustrating it in the evolution and economic purpose of derivatives.
Readers who would have read our half yearly outlook on India (28 July) would have seen how illusionary the hedging process is. If between 24 sector pair trades one could create 32% annualized returns with the maximum ruling at 173% (Sensex – Real) and only six out of 24 pairs delivering less than 5% annualized returns, there was something about hedging or pair returns we do not know. One might also say, “what about BETA?” (the sensitivity quotient between assets). We are comparing sector indices here and if you think beta argument can really disprove these results, it is a tough task. We can demonstrate not only returns between highly correlated and similar beta assets but also between an asset and its own stock future (Long Nifty – Short Nifty Futures). The best part is that it’s all very simple.
So what happened? Did the hedge ratio fail? How could a conventional risk management idea make money or for that matter lose it? If you were long Sensex and short BSE Real, you would have lost 173% annualized. The idea is not just about lack of trading instruments. India doesn’t have well traded sector futures and options, as market participants focus more on stock futures than understanding or trading sectoral exposures.
Are we correct in saying that Hedge funds did everything but hedging that’s why they went under? Did we ever think that there could be gaps in the hedging theory and that’s why what was not supposed to sink, drowned? The idea that in the long term it works could also be an illusion, as there are costs involved and hedging as an activity is more about minimizing losses rather than eliminating them. The very reason there are not very many companies offering hedging solution. Did Hedging outfits suffered because the cost of hedging was exorbitant?
The arbitrage philosophy
Understanding hedging has a lot to do with how we comprehend the hedge process. Arbitrage pricing theory (APT) is a general theory of asset pricing that has become influential in the pricing of stocks. APT holds that the expected return of a financial asset can be modeled using the sensitivity factor aka beta coefficient. The derived rate of return will then be used to price the asset. If the price diverges, arbitrage should bring it back into line. Arbitrage is the practice of taking advantage of a state of imbalance between two or more markets and thereby making a risk-free profit. The theory was initiated by the economist Stephen Ross in 1976.
This back into line philosophy is at the heart of the hedge failure. This could also be the reason why we as a society are running farther from understanding risk than getting closer to comprehending it.
History of statistical arbitrage
How far we are from understanding cyclicality, time and fractals and how poorly we implement them in our strategies can also be understood by studying the history of statistical arbitrage. Statistical arbitrage aka stat. arb was started in 1985, a decade after the APT.  Reversion to mean was born. In his recent book Statistic Arbitrage, Andrew Pole comprehensively delves into stat arb. Pair trading was a simple idea of trading similar historical prices. The strategy was based on reversion, which occurs everywhere and anywhere. This was a sign of fractalled nature, but the author barely mentions the term (three times) in his 257 page work.
Despite the lack of fractal details, the normal distribution in prices needed for reversion in prices is dismissed as an erroneous claim. Fractal watchers do the same as heavy tails and power law are the mathematical explanation for fractals.  The author spends a few chapters of the book explaining why stat. arb. was beset with problems starting from 2000 and how the strategy exhibited a diminished economic potential. He cites ideas like more advanced algorithms, volatility, vagueness of practitioners, and lack of knowledge on part of the investors.
The author asks a lot of relevant questions like how does one identify when a price is away from the mean and how much? How long will the return to mean take? Are heavy tails the reason for frequent miscalculation and underestimation of risk? Why simple probability theorems cannot guarantee reversion which is challenged by heavy tails? Why we must always learn from the predictable occurrences, however odd they may look at first sight? Why we should be buying in weakness and sell in strength?  Why patterns of stock prices are occurring at least two higher frequencies above in time scales? Why LTCM failure could have been linked to higher time frequency patterns? Why Gauss is not the God of reversion?
But the book fails to admit time cyclicality and builds its case mostly through reversion. Somewhere simplistic thinking takes over simple thinking. Like how to judge whether a spread tomorrow will be greater or smaller. If it’s greater than the mean today it will be smaller tomorrow. Pole also looks at reversion to mean as more magical than the fractalled nature of markets. Though he mentions that mean reversion involves temporal dynamics and time frequency analysis, temporal aspects are the source of profits, trades at a point of time are the means with which the opportunity is exploited, but there is not even one mention of time cyclicality in the book. It’s not the first time that we have missed the idea.
Missing the idea
The idea dismissed by Pole that simple probability theorems cannot guarantee reversion are strangely the same ideas explored by other reversionists. Larry Connors of Trading markets searches for statistical probabilities that help traders profit when stocks revert to the mean. “The further prices stretch away from the mean on a short term basis, the sharper they snapback”, Connors was quoted in Bloomberg Markets. Connors and Ceaser Alvarez, are ex Microsoft engineers who worked on the development team of excel program. They seek to identify tradable price patterns based on statistical probabilities. The duo works with a large database of 8.5 million trades.
Robert Shiller’s MacroMarkets’ is also not free of mean reversion. In his 1993 book, MacroMarkets: Creating Institutions for managing society’s Largest Economic Risks, the author talks about unmanaged risk and the need for a risk management solution. To hedge Oil risk MacroMarkets introduced a new way to include Oil in a portfolio. Dubbed Macroshare $ 100 Oil UP and Macroshare $ 100 Oil DOWN exchange traded securities issued by paired trusts. According to a Bloomberg market report, “the trusts have an income distribution agreement under which assets flow from one to another in proportion to the level of the benchmark”.
As OIL moves above or below 100, the funds flow from one bucket to the other. This is supposed to be a hedging mechanism to help people. Whether we call it an innovative solution, this is still a pair attempt at managing risk. Pair trading based on reversions are far from perfect and prone to failure. The idea about comprehending markets is tougher than the idea of comprehending market cyclicality. This is why teaching market participant’s cyclicality by creating more pair offers is just adding to the already oversaturated market. The market is already trying to take a detoxifying pause from structured products.
The behavioral finance idea of losers vs. winner’s index has more merit because it illustrates cyclicality. The only unfortunate part is that behaviorologists don’t admit that the idea of selling winners and buying losers is the central idea of performance cycles.
Conclusion
A hedge is not only imperfect but inefficient and costly. Statistical arbitrage is a euphemism for Time arbitrage, performance cycles and till the time we don’t focus attention on TIME our attempt to understand risk will fail. We will have someone or something to blame then. According to Paul Samuelson, “Financial engineering is like science that can help mankind or create atomic bombs”. We will worship Beta and then pronounce it dead, rechristen it later as Jenson Beta, but there is one thing we will intuitively avoid, cycles of time.