Investment Performance Measurement Errors

This page explains different sources of performance measurement errors.

The key strategic issue to consider in regard to performance measurement errors is the difference between money-weighted and time-weighted returns.  Time-weighted returns, based on valuing the portfolio every time an external cashflow takes place, are clearly more accurate than the traditional approach of calculating monthly money-weighted returns.

The paper An Analysis of a Source of Errors in Performance Measurement, by Dr Peter Vann, analyzes the factors that cause money-weighted returns to contain inaccuracies that make them unsuitable for comparison with index returns (which are time-weighted).  In short, there are three factors that combine to determine the size of errors in money weighted returns.  These are:

1. The size of cashflows;
2. The timing of cashflows; and
3. The volatility of the fund.

If there are no cashflows, the measurement error will be nil.  However, as the size of cashflows increases, so does the size of the measurement error.  Measurement error also tends to increase if cashflows take place toward the middle of the month (rather than near the start of end of the month).  Finally, measurement errors increase with the volatility of the portfolio.  The paper provides formulas for estimating the likely size of the measurement error.  As a guide, for an equities portfolio experiencing a 5% cashflow mid-month, the likely size of the measurement error will be around 17 basis points.

The way to avoid this kind of error is by valuing the portfolio on every date where a cashflow takes place, and calculating the returns using these valuations.  In practice, the simplest solution is to do daily calculations and calculate daily returns.  This avoids any need to check for the presence of cashflows, or to compound returns over irregular periods.  A daily performance system simply takes daily valuations and calculates daily returns.  It is then possible to compound these daily returns to obtain the return over any period that one requires.

This brings us to one of the greatest fallacies about daily performance.  Daily performance means calculating daily returns.  However, this does not mean that daily performance implies a focus on short-term returns.  Rather, daily performance places the focus on accurate returns.  For example, suppose you want to know how one of your portfolios performed over the last six months.  A daily performance system can tell you that.  A monthly performance system can also give you an answer, but that answer will be full of errors (as described in the paper by Peter Vann).  To sum it up, if you use monthly return calculations, you will never know exactly what the return was — you will only know an approximate answer.  To make matters worse, in any particular case, you can't really know how big is the realized error in that case.

Another fallacy about daily performance is that it is too challenging to do portfolio accounting on a daily basis.  For some firms, it may be true that producing correct daily data is quite difficult.  But what is the best way to deal with this difficulty: by surrendering to it, or by taking the opportunity to improve the firm's business processes?  Certainly, any firm that can do daily unit pricing is much of the way toward producing the kind of data that will support daily performance measurement (and attribution).  In actual fact, one of the best ways to improve a firm's data quality is by introducing daily performance analysis.  This creates a feedback loop for discovering then fixing errors in the daily data.  If the data going into a daily performance system contains errors, these will usually become apparent fairly quickly during the process of creating and reviewing the performance reports.  One is then able to fix the business processes that lead to the errors.

A final fallacy about daily performance analysis is that it requires too much computing power.  The easiest way to counter this objection is that many of the world's largest asset managers (who have the most data to process) are already calculating daily performance.  Under Moore's law, the computing power that a given amount of money can buy doubles every 18 months.  The computer hardware industry has conformed with this law for the past 40 years.  After all that exponential growth, the amount of processing power that can be purchased for a few dollars is astounding.  Providing that one uses the right software, processing power poses no significant obstacle to implementing daily performance measurement and attribution.

References

It is well-understood that money-weighted returns are an inaccurate method for measuring portfolio performance.  Aside from the above information, you may wish to consult the following three sources:

Kritzman, Mark “What Practitioners Need To Know … About Return and Risk,” Financial Analysts Journal, May-June 1993 pp. 14-17.

Lerit, Steven J. “A Primer on Time-Weighted and Dollar-Weighted Returns”, The Journal of Performance Measurement, Fall 1996 pp. 40-44.

Lerit, Steven J. “Measuring the Impact of Cash Flows and Market Volatility on Investment Performance Results”, The Journal of Performance Measurement, Winter 1996 pp. 56-60.

Other Sources of Performance Measurement Errors

We will quickly mention other possible sources of error, such as:

• incorrect treatment of corporate actions;
• use of incorrect prices;
• application of incorrect exchange rates;
• spreadsheet errors.

How to Detect and Fix Performance Measurement Errors

We will discuss various reconciliation techniques that are available for quickly detecting and resolving these errors.  Examples are:

• Comparing index stock returns with portfolio stock returns;
• Comparing multiple valuation sources.

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Last modified: Friday, 20. June 2008