Lyxor shows, by which mechanisms, certain management strategies apparently innocuous, such as "averaging down" or how the systematic search for an "entry point" can lead to situations of failure if their risk is not previously identified and controlled. More generally, it has been shown that contrarian strategies require greater risk control than the trend-following strategies which are naturally less exposed to extreme risks.

In order to achieve these results, this White Paper offers a systematic analysis of management strategies, running on a single underlying asset. It establishes essentially a classification of strategies of dynamic management as a function of their investment (contrarian or trend-following) philosophy. Indeed, It shows how distant are the risk profiles of these these familles of strategies. The contrarian strategies (aiming to buy asset when price declines) exhibit high returns probabilities but, on the other hand, are exposed to devastating consequences in the event of adverse market scenario. To avoid such event, it is necessary to set up a priori risk management rules consistant with reducing one’s positions when a loss threshold is reached. Conversely, it is shown that trend-following strategies can exhibit lower probabilities of gains, but do not involve exposure to extreme risks.

A large number of popular management strategies can be split into an option profile and some trading impact

Nicolas Gaussel

For example, a contrarian strategy - "Averaging Down", which is systematically increasing the amount of one’s investments after a each drop in price of an asset, - will lead to gains as soon as the price goes up (without necessarily waiting for the initial level). A backtest of this strategy, on the Eurostoxx 50, shows as such that such a strategy, could generate almost consistent 10% returns per year between 1994 and 2000. However, this implies taking a growing risk in the event of market downturns. Entire investments were lost during the 2001 crisis.

On the other hand, it has been shown that strategies following the markets are, by construction, covered against exreme risks. In practice, the trend-following strategies, such as those used by the CTA have in effect responded remarkably well during the recent crisis.

This study finally allows us to reply to numerous questions such as: Which strategies will profit more out of the volatility of the markets? What are the worst and the best possible scenarios for a given strategy? What are the risks in a strategy playing the return to averaging? In replying to these questions, we can indicate when and why certain strategies get good results as well as the risks to which each one is exposed.

Breakdown of management strategies into an option profile and some trading impact.

The results mentioned in the introduction are based on the breakdown of the strategies in management between an optional profile and trading impact. As a pre-requisite to the analysis of the breakdown, investment strategies must be described as a function of the underlying price only. This explains those situations in which a manager may decide on the amount he has to invest by considering only the price and certain fixed parameters. We show, in this paper that a certain number of popular strategies fit into this framework. The exposure can therefore be viewed as a trader’s delta and its is possible to show that the intergral of this delta corresponds exactly to the option profile implicitly associated with this strategy. This change in perspective can perhaps be illustrated by he schema below.

Two large set of strategies: trend-following and contrarian

Following the reasoning outlined above, we see that trend-following strategies will gererate convex profiles, whilst contrarian ones generate concave profiles. The concave profiles have as a feature to lose gradually as the market goes down, which explains their high potential risk. However, if the probability that the underlying rises or falls is 50%, the concavity of the profile implies that the probability of positive gain will be greater than 50%, as we can get an idea on the diagram below.

One can also see that trend-following strategies will lose even more than the market volatility is high. These strategies leading to buy systematically after a drop and to sell systematically after a drop will more penalised than the size of the buy-sell options will be great. Its this same effect which is forms the basis for the positive time value of options with a convex profile. These differents aspects are matched in the table below

The White Paper of Lyxor provides a strict analysis of these differents aspects and, studies in detail, a cetain number of popular strategies like, for instance, those that average down for mean reversion, the stop-loss strategies, strategies for systematic trend following, etc