The evaluation of active portfolio management relative to a benchmark is one of two common approaches to portfolio performance analysis. The blog Active Management Evaluation with Partial Moments shows how to merge the well known measures of active return and asymmetric measures of reward and risk to gain additional points of view on manager performance
Many organizations that offer performance evaluation services on traditional investment funds also offer peer group comparison. Carl Bacon, in his book Practical Portfolio Performance Measurement and Attribution, offers his views on the pros and cons of peer groups which he defines as collections of competitor portfolios of similar strategies grouped together to present comparable statistics. A benefit of peer groups is that the evaluation of nominal returns as opposed to active returns is more appropriate because it is more appropriate than benchmark comparison. In our example we show that it is also valuable for comparing the active rewards of investment managers with similar strategies. On the negative side, peer groups can suffer from “survivorship bias” in which poor performing portfolios are either closed or removed from the universe. In our example, we consider the current universe of managers only to derive the universe statistics.
The percentile rank of a performance measure for the managers in a universe is a consistent way of comparing a manager’s result with the universe. For example, the universe of Multi-Cap Core Fund managers consists of over 700 funds as of March 2011. Let us say we are interested in the percentile rank of a manager’s average active return over a three year period ending March 2011. We begin by computing this performance measure for all of the managers provided they have three years of reported performance. Those that do not have the required return history are excluded from the analysis. The remaining results are reordered in ascending order so that the first observation is the smallest three year average active return and the last is the largest average active return. The 25th percentile value which is called a quantile by statisticians is that number such that 25% of the results are less than this value. The median quantile is that number such that half of the results are less than this value. The 75th percentile quantile is that number such that 75% of the results are less than this value. Typically the minimum and maximum values for a performance measure are also reported. These quantiles define the league table against which individual managers are assessed.
The result for a particular manager can be ranked against the values computed for the universe to obtain a percent rank for the manager. The performance measurement industry has adopted a different view of ranking from the one used in other fields. The percentile rank is a number between 0% and 100% with 0% being the top-ranked portfolio and 100% being the bottom-ranked portfolio. In the following example, we will stick with the statistician’s way and you can make the translation.
The universe comparison of average return and upper partial moment of order 1 constructs ranks of rewards in which higher rewards earn a higher rank. The universe comparison of lower partial moment of order 1 defines what actuaries in the insurance industry call loss distributions. A smaller loss deserves a higher rank than a greater loss.
We use the same Multi-Cap Core Fund manager from the previous blog with reported returns starting in January 1972. Specifically, we examine the realized returns for the 10 year period ending March 2011. Table 1 shows the universe quantiles for the 10 time periods, the corresponding fund values and percentile ranks for the nominal return average. Notice that our illustrative fund had above median performance for the one through four year holding periods. The longer the holding period, the less attractive the fund is. A similar situation occurs when you look at the average active returns found in Table 2. You want to be in the highest percentile in the league table.
Table 3 presents the peer group analysis of the active return downside loss. Remember that these are loss rankings. As such you want to be in the lowest percentiles of the league table and our illustrative fund seems to fare well in this performance measure. Table 4 completes the illustration with the peer group analysis of active return upside reward and except for the three year holding period the manager’s relative performance in peer group is disappointing.
Once again, there is more to be learned about a manager’s return history by making use of partial moments. The investor should ask the provider of portfolio performance analysis if they can offer partial moments in their service. This is not a fashion but rather it is a perspective that should always be considered by investors.
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