Exploiting leptokurtic distribution

A question on which many theorists focused is the question financial markets random nature. Is it possible to achieve, through an "active management", a gain relatively steady and well above the performance delivered by a "buy & hold" investment strategy ? The literature on the subject is vast and plentiful, and the clash of theoretical publications continues today between supporters of the overall efficiency of markets, vowing by the impossibility to beat a "buy & hold" strategy and opponents arguing that there are "trends" that justify an "active management".

More prosaically, for anyone who just wants to try to optimize its management without issuing yet another treatise on the subject, in the middle of both camps, it is possible to use a third way.

It is undeniable that any market operator has, at least once, noted the existence of trends or "suites of price changes in one direction" on his computer screen. From a purely statistical standpoint, studies of quotations in different units of time (intraday, daily or weekly) tend to prove that the departure of a "trend" is purely random, totally unpredictable. A point to the credit of the defenders of the theory of efficient markets. Nevertheless, the continuation of this "trend" does not always follow a "Normal law ". There might be the argument of defenders of the deterministic nature of financial markets. An illustration of this phenomenon can be represented by plotting the histogram of the amplitudes of quotations fluctuations during a given time.

An illustration of this phenomenon can be represented by plotting the histogram of the amplitudes of fluctuation during a given time. Shown centered around zero (see figure above) are shown two very different "snapshots" of a stock prices series characteristics. One representative of the randomness (the start and amplitude of trends) of a contract, and one representative of stochastic (random start of trends, important and very low magnitude trends over-represented). This distribution is called leptokurtic, and finding such a series of quotations prices offers hope to take advantage of a trend, and beyond justify active management.

Its presence is also the only empirical justification of the merits of the "trend following" or chartists conventional approaches. Note that this phenomenon is independent of the volatility of contract that is often considered essential to hope for a gain in "active" management. These distributions are more often found when the timeframe sampling unit is long (weekly), and in this case, they persist long enough to be traded profitably.

XS model

An empirical approach: XS is an empirical model, based primarily on price movement, using a combination of long-term statistical filter to take advantage of large price fluctuations and an algorithm in order to select different contracts that can generate the best performance by analyzing their distribution.

Systematic: The method does not leave room for human interpretation. The signals generated by a filter developed on data other than statistical stock market series (here the filter is among others used in guidance systems for aircraft and space craft) to avoid over-optimization. They are unambiguous, easy to follow (buy / sell) on contracts (futures / ETF) tracking the performance of major world indexes.

Low frequency and long-term:XS is a model generating orders whose performance is assessed relative to its benchmark over the long term. The time unit used is the weekly unit, for both the calculation of signals and the generation of buy and sell orders, for reasons of convenience, robustness regarding signals execution slippage.

A three steps "signals generation" process (yearly and weekly)

Process to calculate the Risk Index

On each market index identified annually by the selection algorithm, we record the signal generated by the filter. A buy signal does not move the Risk Index, a sell signal adds 20% to the Risk Index. Below is an example of calculating the "Risk Index"

The "Risk Index" thus calculated is an excellent indicator of market health. The fund manager or the investor should be very aggressive in buying the equity markets when the "Risk Index" is zero or low, and very cautious as the "Risk Index" is high. It can also be used as a signal to buy or sell on a world index "tracker" such as MSCI World indexes or a basket of futures contracts as it crosses the 50% barrier.

The XS model applied to the "World Index"

Uses of XSworld Risk Index : the XSworld Risk Index is the declination of the XS model to the world of global geographic indexes. It is a composite indicator used for the hedging of an existing portfolio or directly for the creation of an investment fund by systematic arbitration on the MSCI World (ex-USA) index, through futures contracts representing the composition of the index or through ETF (trackers).

XSworld Risk Index is based on a universe of potential market indexes: XSworld Risk Index is calculated from the signals generated from the filtering of the major geographical areas worldwide.

5 of which are chosen each year by the selection algorithm: for 2011, the algorithm has selected the following countries: Singapore, Russia, China, Malaysia, Austria XSworld Risk Index is then computed using the buy and sell signals generated for each index


How the XSWorld Risk Index can be used ?

To manage a "Long Only" fund: the manager buys or sells its positions according to the weekly Risk Index:

  • 0% to 50%, no exposure to equity markets,
  • 50% to 100% total exposure to equity markets.

To "hedge" an existing fund: the fund manager wants or is obliged to remain constantly invested, the risk indicator is used to hedge his existing fund. The manager sells off its fund a basket of futures contracts replicating the MSCI Barra World (Ex-USA) index or buys a "tracker" according to the value of the Risk Index.

  • 0% to 50%, no futures contract sold, no hedging
  • 50% to 100%, futures contract sold or reverse ETF bought for a total coverage of the fund.

To Create an investment fund:

  • When the Risk Index is between 0% and 50% the fund manager is a net buyer of a basket of futures contracts or an ETF (tracker) replicating the MSCI Barra World (Ex-USA) index.
  • When the Risk Index is between 50% and 100% the fund manager is a net seller of the basket of futures contracts on the index MSCI Barra World (Ex-USA) or buyer of a reverse ETF (tracker).