I recently changed several things regarding the Compact Model Portfolio (in particular the hedging strategy). This change went live, at a new brokerage, on the 9th. of April. To check that things are ok, we need to verify whether the returns series from the traded portfolio are not significantly distinguishable from the index — i.e. we need to investigate whether the traded portfolio is accurately tracking the desired index performance.

We have a small data set, so far, of only 12 days, so we need to be careful about our inferences. However, we have three tools to use:

• we can look at the time series of the total returns of both series and see if they appear similar (an eyeball or ballpark test);
• we can perform a linear regression of the traded portfolio daily returns onto the index portfolio daily returns, and apply statistical tests to investigate the null hypothesis (α,β) = (0,1) i.e. perfect tracking
• we can use the two-sided Kolmogorov-Smirnov test to investigate whether the empirical distributions of the respective daily return series are consistent with eachother.

Before presenting our results, let's discuss our expectations for the alternate hypothesis (that the traded portfolio does not track the index portfolio). The traded portfolio has frictions — brokerage fees, financing fees etc. — that are not represented in the ideal portfolio. In addition, the treatment of dividends is different. The ideal portfolio receives the dividend on the ex-dividend date, which is done to prevent spurious returns due to the expected ex-dividend drop; whereas, the traded portfolio will experience the ex-dividend drop and then receive the dividend income on the settlement date. The former effect should lead to a linear-regression α of less than zero. The latter effect should be a depression of the β below unity.

For the brief data sample we have, we cannot reject the null hypothesis. However, we have now established the toolset needed to investigate this issue, and will return to it after more time has elapsed.