FORWARD-LOOKING VS. BACKWARD-LOOKING TRACKING ERROR

In Exhibit 10.1 the tracking error of the hypothetical portfolio is shown based on the active returns reported. However, the performance shown is the result of the portfolio manager's decisions during those 30 weeks with respect to portfolio positioning issues such as beta, sector allocations, style tilt (that is, value versus growth), stock selections, and the like. Hence, we can call the tracking error calculated from these trailing active returns a backward-looking tracking error. It is also called the ex post tracking error.

One problem with a backward-looking tracking error is that it does not reflect the effect of current decisions by the portfolio manager on the future active returns and hence the future tracking error that may be realized. If, for example, the manager significantly changes the portfolio beta or sector allocations today, then the backward-looking tracking error that is calculated using data from prior periods would not accurately reflect the current portfolio risks going forward. That is, the backward-looking tracking error will have little predictive value and can be misleading regarding portfolio risks going forward.

The portfolio manager needs a forward-looking estimate of tracking error to accurately reflect the portfolio risk going forward. The way this is done in practice is by using the services of a commercial vendor that has a model, called a multifactor risk model, that has defined the risks associated with a benchmark index. Statistical analysis of the historical return data of the stocks in the benchmark index are used to obtain the factors and quantify their risks. (This involves the use of variances and correlations.) Using the manager's current portfolio holdings, the portfolio's current exposure to the various factors can be calculated and compared to the benchmark's exposures to the factors. Using the differential factor exposures and the risks of the factors, a forward-looking tracking error for the portfolio can be computed. This tracking error is also referred to as the predicted tracking error or ex ante tracking error.

There is no guarantee that the forward-looking tracking error at the start of, say, a year would exactly match the backward-looking tracking error calculated at the end of the year. There are two reasons for this. The first is that as the year progresses and changes are made to the portfolio, the forward-looking tracking error estimate would change to reflect the new exposures. The second is that the accuracy of the forward-looking tracking error depends on the extent of the stability in the variances and correlations that were used in the analysis. These problems notwithstanding, the average of forward-looking tracking error estimates obtained at different times during the year will be reasonably close to the backward-looking tracking error estimate obtained at the end of the year.

Each of these estimates has its use. The forward-looking tracking error is useful in risk control and portfolio construction. The manager can immediately see the likely effect on tracking error of any intended change in the portfolio. Thus, she can do a what-if analysis of various portfolio strategies and eliminate those that would result in tracking errors beyond her tolerance for risk. The backward-looking tracking error can be useful for assessing actual performance analysis, such as the information ratio discussed next. Evaluating the factors that caused past portfolio performance, called attribution analysis, is an important use.