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Short Histories

When working with multiple funds, it is often the case that one or more of them do not have the same length of history as the rest. This creates a problem because the standard method of covariance matrix estimation requires equal histories for all variables in the set. In addition, the number of available returns for each variable should be at least equal to the number of variables being analyzed. There are a several ways to deal with these problems.

The most straightforward approach is to truncate all samples to the size of the shortest one. In this case, the issue is resolved at the cost of removing observations. This means that information available in the samples is disregarded.  

The second option is to rely on purely statistical approaches and take advantage of an unequal histories method which takes into account all observations in computing the covariance matrix. This is the method traditionally used in risk management systems and it is also available in Cognity. The disadvantage of this method is that it is completely non-transparent to the user and that it relies on the assumption that returns are jointly normally distributed.

The third approach is to back-fill the short histories taking advantage of a back-filling method. In contrast to the unequal history method, backfilling creates an artificial time series which can then be analyzed. This approach is based on statistical techniques as well as economic reasoning. The basic idea is to discover the factor drivers of risk and return for each fund and use them to generate artificial data for the fund. The advantage of this method is that the backfill process is completely transparent, can incorporate fat tails, and makes economic sense.

There are different backfill methods available for backfill. Choosing a particular backfill method is determined by a combination of user preferences and the amount of available data. These are the most frequently used methods:

  • Proxy Method - this is the simplest backfill method which can be used regardless of the amount of available data. It is a crude method and we recommend its usage only when there is very little data available.

 

  • One-Factor Method - this is a regression based approach and is similar to the CAPM. The recommended usage of this method is when you have a very limited number of available returns in the sample. The disadvantage of this method is that it does not make use of all available information when generating the backfill data. Another drawback is that it may alter the dependency structure within the data and the distributional properties of the backfilled variables.

 

  • One-Factor Bootstrapped Method - this is a regression based approach specific to Cognity which makes full use of all the available information and preserves the dependency structure within the dataset. It also preserves the distributional properties of the variables and can be used for data infilling. Data infilling allows you to generate higher frequency data, e.g. you can generate monthly data for a variable that only has quarterly returns or generate weekly data for variables that have monthly returns.

 

  • Stepwise Bootstraped Method - this is a multivariate regression based approach specific to Cognity. It shares all the desirable properties of the one factor bootstrapped method. In addition, it allows for the usage of a broad set of backfill instruments and employs a statistical technique to discover the most significant drivers of risk and return for each backfilled variable from that set. The set of backfill instruments is fully user configurable and there can be different sets for each variable that will be backfilled. This method generally results in a higher quality backfill compared to the one factor bootstrapped model but it also requires more data to work properly.