. Golub, Zion Hilelly and Christopher Turner
A critical element of the AIMR Performance Presentation Stan- dards is the concept of the composite portfolio.
Rather than having to examine the results of a multitude of portfolios with overlapping strategies, clients may examine the performance of groupings of portfolios representing a particular investment strategy -- a much smaller number of portfolios.
The use of composite portfolio returns to describe the performance of a manager's strategies begs the question: how likely is it that any of the portfolios within the composite will achieve the average return of the composite?
This is more than a statistical question about the accuracy of a summary measure of performance. Rather, it is a fundamental characteristic of an investment manager, which addresses the very core of investment management: the consistency with which a manager delivers its average result to individual clients.
While in theory composites consist of portfolios with similar management strategies and objectives, in practice managing two portfolios to yield similar performance results can be very difficult. The difficulty arises largely from differing investment guidelines. Clients, while they all want to outperform their benchmark with minimum volatility, have a wide range of tolerances to different types of risk. For example, one portfolio might have a low tolerance for interest rate risk, while another might be sensitive to credit risk.
This difference in risk tolerance will affect investment decisions -- in this case, the first portfolio will require a tight duration band, while the second will not hold investments rated lower than A.
The ability to allocate trades equally among a composite's portfolios also presents a challenge to investment management. The problem is even greater when dealing with funds in which net asset values are not computed daily. In this case, an estimated value of the portfolio is used, making the actual allocation imprecise. Attempting to create two portfolios with the same proportional holdings in this circumstance is virtually impossible.
Ensuring similar holdings in two different portfolios is particularly difficult for fixed-income portfolios. An individual fixed-income deal, unlike most equity deals, cannot always be easily apportioned so each portfolio will receive identical performance.
Each pool of a mortgage pass-through, for example, will have subtle differences. Similarly, the range of investment guidelines in fixed-income portfolios can be quite wide.
A new AIMR standard seeks to allow investors to better evaluate an adviser's ability to address these issues. It requires advisers to report measures of the dispersion of portfolio returns within each composite along with the composite's performance history. The dispersion measures seek to describe numerically the consistency with which a manager delivers its average result.
UNDERSTANDING DISPERSION
Consistency as measured by dispersion is quite different from the concept of the volatility of a manager's investment style, as measured by tracking error, the standard deviation of active returns. Consistency seeks to describe the discipline of a manager's performance across the portfolios within a single investment strategy. The concept is measured by the variability of individual portfolio returns around the return of the composite.
To illustrate the difference between composite dispersion, which deals with performance volatility among portfolios, and standard deviation, which deals with performance volatility over time, let's compare two advisers. As shown in tables 1 and 2, (page 35) each adviser has two accounts and quite different management styles.
Adviser 1 has kept its composite return equal to 1.67% for three consecutive months; it appears to be doing an excellent job delivering zero volatility. Yet the returns of the adviser's portfolios differ substantially during each month; the adviser has not been consistent. This inconsistency is measured by the adviser's composite dispersion, which is equal to 47 basis points a month. It is clear the overall standard deviation of Adviser 1 is zero, but the risk faced by an investor in any one of the adviser's accounts is much greater than zero.
Perhaps the individual portfolios have very different guidelines, or different portfolio managers with differing skills. In this example, the volatility of composite returns does not reveal the actual risk of investing with this adviser.
The situation is reversed for Adviser 2. While the returns of this adviser's two accounts are very consistent, with zero composite dispersion, the composite returns for the three-month period are very volatile as measured by the standard deviation of 1.25%. The key here is that although the returns of the accounts are jumping around, they consistently move together. In this case, the portfolios all seem to be coming from the same, albeit risky, investment process. In this example the volatility of composite returns reflects the true risk of investing in any individual portfolio.
Clearly composite dispersion is a critical number. The consistency with which a manager can deliver its average return is as important as the variability of the average return itself to the risk faced by the client -- potential clients clearly have a bona fide interest in manager consistency.
COMPOSITE DISPERSION
The AIMR-PPS indicates standard deviation, or a slight reformulation of standard deviation for asset-weighted composites, should be the primary measure of composite dispersion. The standards further suggest the range of portfolio returns within the composite, high-low portfolio return statistics and other measures a firm deems valuable.
The high, low and range of returns are simple to calculate and easy to understand. Unfortunately, these statistics also may be misleading, as they are the result of the returns of only two portfolios. It will frequently be the case that as these are the absolute best and worst returns of the composite, they will not accurately describe the distribution of the returns of the remaining portfolios within the composite.
In addition to these simple statistics, the AIMR advocates a somewhat more complex measure, the quartile dollar dispersion. These statistics are calculated by sorting the returns of the composite's constituent portfolios from high to low, and then dividing the portfolios into four equal sized groups by market value. The asset-weighted average return of the top group, or first quartile, represents the average result for the best-performing quarter of the composite portfolio, as measured by market value of assets. The average return of the last group, or fourth quartile, represents the average result for the worst-performing quarter of the composite portfolio. The difference between these statistics provides a measure with an interpretation analogous to that of the sample range; however, it takes into account more of the returns observed on the subportfolios of the composite.
Although these statistics will be revealing, most investors will be primarily interested in the standard deviation of the returns of the subportfolios making up the composite. For equally weighted composites, this may be measured by the simple, sample standard deviation of the returns on the constituent portfolios. For asset-weighted portfolios, this is measured by the standard deviation calculated using asset weights. In either case, the AIMR suggests only portfolios that have been managed for the full year should be included in the standard deviation. For many managers with substantial entry and exit of subportfolios within composites, this restriction can lead to inaccurate dispersion statistics.
We have implemented an appropriate, easily calculated statistic that is suited to most managers' circumstances, regardless of the entry and exit experienced by their composites. This number is really just the square root of the sum of the monthly variances of portfolio returns around the composite returns (Fig. A).
In this formula, T is simply the number of months for which the composite dispersion is being computed. In addition to this value, we also report composite dispersion on an annualized basis. To do so, we simply multiply the average variance by 12 before taking the square root (Fig. B).
The monthly measure of variance in these formulas is given by the squared deviations of the individual portfolio returns from the composite return, squared and then all summed (Fig. C).
In this equation, N refers to the number of portfolios in the composite, while t indicates the month for which we are calculating the variance.
As the formula indicates, individual deviations of each portfolio's returns are multiplied by a weight, the proportion of the net asset value of the composite represented by each portfolio, before they are summed. This weight is given by the formula (Fig. D).
For any month, represented by t, the composite return is given by the equation (Fig. E).
To illustrate the actual calculation of the composite dispersion, we have included a hypothetical example, described in the table on page 37. This composite contains three portfolios:
Portfolio A, which is created after seven months; Portfolio B, which exists for 15 months; and, Portfolio C, which is discontinued after 11 months. For these portfolios, we invented total returns and net asset values. We then used the formulas described above to calculate the composite total return and the monthly standard deviations of the portfolio returns.
Suppose the annualized total return of index for this composite was 180 basis points: then the annualized active return is 30 basis points. The annualized dispersion since inception is 23 basis points. The theory of statistics tells us that the probability is 2/3 that a fund within this composite will have an active return more than one standard deviation away from the total return, i.e. between seven basis points and 53 basis points. Note this spread is approximately 150% of the active return.
This measure provides a convenient summary statistic to compare the active return/dispersion performance of funds.
CONCLUSION
The concept of the composite portfolio has been a critical element of the AIMR's effort to provide a transparent marketplace to investors seeking professional investment management. Rather than having to examine the results of a multitude of portfolios with overlapping strategies, clients may examine the performance of a much smaller number of portfolios, each with a distinctive strategy. The use of a summary measure of performance, like the return on composite, has at least the potential to mislead as well as inform. The inclusion of the composite dispersion in the statistics reported by investment companies helps ensure composite returns perform their function of informing investors.
