Trading Sciences provides a truly sophisticated picture of the negative sentiment one wishes to defend against in a well crafted risk management system.

Conventional risk measurement systems assume a normalized density distribution and use standard deviations to estimate tail probabilities. More elegant methods consist of fat-tail measurement techniques, those that account for the reality of semi-rare tail events that occur far more frequently than the normal assumption would imply. One such method uses a Student’s t density, which can approximate such fat tails and thus offer a better picture of risk. Another uses a Monte-Carlo approach.

We differentiate ourselves in risk measurement technology on several fronts. First, we offer two unimodal (single peak) estimation methods that model fat tails, one using a direct algorithm that is especially functional with small sample counts, and another that uses a proprietary non-linear modeling that is especially effective at fat-tail estimation. Both methods separately address upside and downside tail differences. These methods do not represent huge departures from the typical Gaussian density measurement system; they are just far more accurate.

Second, we offer “touching” densities. Whenever there is a chance an automated trading system, stop mechanism, or a human trader may intervene intra-day, it is more appropriate to look at the density of excursions from the prior period’s close. Note, a period could represent any time horizon, whether it is a day, an hour or even a tick (eg. bar). When looking at a day, for example, touching densities are typically bimodal. This is because most days will have two excursions from the prior day’s close, but there will be some days where there is only one: the market opens up or down and never looks back. This is the real world, and when represented as a density, two peaks are almost always evident. We fit bimodal densities using a non-linear fit of a proprietary model that manages the bimodal as well as the different fat tails upside and downside.

Finally, we offer component densities – revolutionary way to evaluate risk. Densities that use touching or excursions are especially effective at mapping the semi-rare fat tail events that represent a special kind of sentiment. That may be a mood where the investors are punishing the overall market in a harsh sentiment, or one where only a specific security is facing this particular sentiment. It may also be on the other side, a sentiment that represents a semi-rare opportunity to profit from a large upside move. Magnitudes of these various sentiments are reflected in a density by “component” peaks that occur at various levels of wins and losses. A component density is like a contour map of the sentiments that have been in play on a given entity. A component density is realized from a multimodal nonlinear peak fit where the hidden peaks (those that don’t have a local maximum) are mathematically “deconvolved,” or extracted, from the overall density.

**Easily View Changes in Density Over Time**

Changes in densities across time represent how sentiments shift in overall market moods. DM’s 3-D mapping features shows exactly how density distributions change over any specified time horizon. The following plot contains a 3D surface where a 250 bar (1min/bar) analysis with a 1-min time horizon is plotted across a 250 bar time horizon. In this plot, we see the density compacting and the fat downside tails diminishing across the 4 hrs of trading.

Densities also change across time on longer time horizons. The following non-parametric density contour plot covers a 250-day analysis. Here we see the tails first expanding and then contracting. Even with a full year sample from which the density is derived, there are decided upside-downside differences at various points in time: