In prior posts we have demonstrated relative skill of 18% in making out-of-sample forecasts of the Dynamic Trading Risk Factor, a factor series that we hypothesize is a driving factor for the returns of companies that make money by dynamically trading securities and earning a premium from by selling the synthetic options created by such trading activity to their investors. We have also shown that the returns of well known public  financial companies, such as Goldman Sachs and Berkshire Hathaway are well explained by this factor. By well explained we mean that a linear regression of the monthly returns to investors, including dividends if any, onto the factor has a significant β and a large R². Exhibited below is our up-to-date chart comparing the monthly returns of Goldman Sachs, on which the rest of this analysis will concentrate, with those of the Dynamic Trading Risk Factor.

We originally performed this analysis in February, 2009; so in the following I will treat the period 2001:01–2009:01 as in-sample and 2009:02–2010:03 as out-of-sample. Using the Jackknife procedure discussed earlier, we find a bias corrected skill of 4% ±14% relative to the forecasts computed from the in-sample average monthly returns. The Dynamic Trading Risk Factor based forecasts are obtained by using the α and β, as established by linear regression within the in-sample period, as the model coefficients and the out-of-sample conditional mean factor forecasts from the AR(1) model for the driving factor series.

Using the metrics established in Grinold & Kahn's Active Portfolio Management, this forecast has an Information Coefficient, or IC of 23% which would lead to a Sharpe Ratio of 0.8 if traded on a monthly basis (I used G&K's  “rule of thumb” SR≈IC√N to estimate the Sharpe Ratio).

Standing alone, this skill estimate is not statistically signficant, but we know we have skill in forecasting the factor series and we know that the out-of-sample α and β for Goldman Sachs are consistent with their in-sample estimates, so my best guess is that the skill is weak but real.