Vlad (co-founder) and I were discussing this week our approach to research, and Vlad summed it up pretty neatly – he said, “we are allergic to superficial research” I want to take his statement a step further and add, “we are allergic to superficial research and research that cannot be easily applied“.
With the above in mind we have set ourself a rigorous benchmark before we put an alert into production. Let me digress for a moment to provide you some context. When Vlad and I worked on a previous project (we have been collaborating daily for more than 5yrs now) we picked up on a bias that existed beyond the vendors assertions of bias free data. The subtle distortion was a self-reporting bias present within the data. For those familiar with quantitative modelling, there is a pretty universal formulae: garbage in = garbage out. Below my brilliant partner contributes to the solution of an enormous problem.
Likelihood of Survival [Example of our Philosophy]
As we saw from the Long Term Capital Management fiasco, even traders with excellent risk-adjusted performance can fail if they take on substantial risk. Thus, it makes sense for us to consider the likelihood of survival when evaluating trader performance. To further control for inherent survivorship bias with a self-reporting database, we defined “death” as occurring when a trader has a drawdown of greater than 15% (this number can be adjusted to your risk profile). We built a multivariate model to predict the likelihood of a trader’s survival given the trader’s performance attributes, enabling us to project the likelihood of traders failing, given their past performance.
Assume that a random variable
where the brackets denote the scalar product, X is a vector of parameters, ? are the coefficients, and ? is an error term. If we know a particular realization of X we can find the probability:
where F is a distribution function. Since we do not know the true value of X we should correct the probability above by an extra term corresponding to the variance of the estimate of X. In our situation, X is a (asymptotically) multivariate Gaussian and this correction is easily made.
To use the above model, we have to find a relation between the realized maximal drawdown and the input parameters including the expected maximal drawdown, expectancy, volatility, value of the Kelly fraction, parameters of the alpha-stable MLE fit, etc.
The model obtained was pruned using a stepwise regression. For each fund we define its survival as not to achieve the maximal drawdown of more than 15% in a year and the survival probability is the estimate of the probability P (max drawdow < 15%) from the input data. In this way we can associate with each fund its “survival probability”.
Do not fear if you have no idea what we just said, the point is that we intend doing all the heavy lifting and providing you with a simple but deep actionable take away. As we get closer to launch and then post launch we will provide illustrative examples and tutorials how you will get the most from your PsyQuation experience.