# Performance Measurement: The What, Why, and How of the Investment Management Process

The rationale underlying the performance measurement process can best be summarized by the following anonymous quote: “You can’t know where you’re going until you know where you’ve been.”

Speaking at the 65th CFA Institute Annual Conference, Carl Bacon, CIPM, chairman of StatPro, said that active investment managers must understand the “what, why, and how” of their past performance in order to effectively manage their current clients’ portfolios. Performance measure is a four-step process that entails: (1) benchmark selection; (2) calculation of the portfolio’s excess return; (3) performance attribution; and (4) risk analysis. Because of the feedback that the performance measurement process provides, Bacon believes that it should be an integral part of the investment decision-making process, instead of external to it.

**Selecting the Benchmark
**

The performance measurement process begins with the selection of an appropriate benchmark (ex ante) that will be subsequently used (ex post) to assess the performance of a portfolio. The benchmark must be investable, accessible, independent, and relevant. Benchmarks can be based on indexes (e.g., FTSE 100, the S&P 500, the Barclays Capital Aggregate Bond Index), peer groups (a portfolio that contains the same types of securities as the designated portfolio), or based on target returns (e.g., the risk-free rate, inflation plus, funding requirements).

**Calculating the Excess Return
**

Excess return is the difference between a portfolio’s return and its benchmark’s return. Excess return can be calculated arithmetically or geometrically:

*Please note that this assumes the initial value of the portfolio is the same as the benchmark.**

Arithmetic excess return is more widely used because it is easier to understand and provides large and absolute values in rising markets. However, the geometric return is more appropriate to use when measuring excess returns over multiple periods (compoundable) or in different currencies (convertible), or when comparing returns (proportionate).

**Applying a Performance Attribution Analysis
**

Performance attribution quantifies the relationship between a portfolio’s excess returns and the active decisions of the portfolio manager. In other words, it relates the excess returns of the portfolio (both positive and negative) to the active investment decisions of its manager. It provides feedback to portfolio managers, senior management, and external consultants on why the portfolio either outperformed or underperformed its benchmark. It is especially useful when the manager has underperformed his benchmark. One of the most widely used attribution models is the Brinson model, which examines performance in terms of allocation decisions (returns based on sector or asset weighting) and individual security selection decisions.

According to Bacon, there are three main types of attribution:

**Returns-based attribution**, which uses factor analysis.**Holdings-based attribution**, which is calculated on a periodic basis and uses holdings data. The key advantage of using holdings-based attribution is that it is easy to implement because a variety of pricing sources can be used. Two disadvantages are that: it will not reconcile to performance return, and it can’t be used as an operational tool.**Transactions-based attribution**, which is calculated from holdings and transactions data. Unlike holdings-based attribution, transactions-based attribution reconciles to the return of the portfolio and therefore can be used as operational tool. In addition, it identifies all sources of excess return. However, this type of attribution is more difficult to implement and requires accurate and complete data.

**Performing a Risk Analysis**

Risk analysis is important for those who are responsible for both managing and controlling the portfolio’s risk. Risk managers view risk positively. They are in the “front office”and are paid to take risk. Risk controllers, on the other hand, view risk negatively. They are in the “middle office”and are paid to monitor and/or reduce risk. Basic risk measures can be divided into three categories:

**Absolute risk measures**, such as standard deviation, the Sharpe ratio, and M^{2}.**Relative risk measures**, such as tracking error and the information ratio.**Regression**, which measures the alpha, beta, and standard error of the portfolio’s return.

In summary, performance measurement is an important tool in the investment management process, because it answers the what, why, and how of past active portfolio management decisions. To quote the astronomer Carl Sagan, “You have to know the past to understand the present.”

***Correction:** An early version of this article offered incorrect methods for calculating the arithmetic and geometric excess return. These formulas were updated on 2 August 2012.

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*All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute or the author’s employer.*

Michael,

I thought that Arithmetic excess return is the (Portfolio return) – (Benchmark return).

But the equations given divide this term by ‘Initial portfolio value.’ Why?

Similarly, I thought that Geometric excess return is the

[(Portfolio return) – (Benchmark return)] / (Benchmark return).

But the equations given divide this term by ‘Final portfolio value’ instead of by ‘Benchmark return.’ Why?

Andre

Andre, first, you have to recall that we’re dealing with Carl, who is a huge fan (the crusader, as I’ve called him at times) for geometric. Second, I have never quite seen his version of arithmetic before; I agree with you that it’s simply Portfolio Return minus Benchmark Return (Carl’s either introduced a twist or someone interjected a typo; this happens). As for geometric, this version, too, is new to me, as I’m used to (Portfolio Return / Benchmark Return) minus one. The industry (world view) preferance for arithmetic dwarfs those who support geometric. This is really an academic subject, as the clients even in the UK overwhelmingly (as per our surveys) prefer arithmetic. Still lots of fun for discussion, preferably over a pint.

Someone once said to me (I forgot the person and this wasn’t his exact words), “why use three variables to calculate a geometric excess return when the initial index value generally is not printed in a presentation?”

David, I’m sure you worked with Carl before (I saw one of your many debates with Carol during CIPM conference in the past). Why not invite him to this link and ask him to clarify the return calculations.

I believe the statement for arithmetic total excess return is correct but the equation examples stated above are incorrect. The reason is because returns are in ratio form but value is in money form.

In addition, my understanding of geometric excess return is different comparing to Andre Mirabelli’s statement. Geometric excess return should be calculated, first converting the returns to decimal numbers and then add 1 to both the portfolio and index decimal numbers. Take the portfolio results, divided by index results, subtract 1 and finally multiple by 100.

( [ (1+{Portfolio return/100}) / (1+{Index return/100}) ] – 1 ) * 100

Finally, there are two different Brinson models (Brinson Fachler and Brinson Hood Beebower). Although the excess returns are broken down identically (between allocation and sector returns), and the computation are completely different.

tyc

Michael,

You are correct, I left out a 1 in the denominator of geometric return.

I should have written:

[(Portfolio return) – (Benchmark return)] / (1 + Benchmark return).

But I still do not think your equations are correct.

Even just on dimensional terms, a return cannot equal a return divided by a dollar value.

I would like to add, tyc and Andre methods could have small return differences over a very longer time period.

The best way to answer the question from Andre is to test the method by using an example. Portfolio beginning value 200 ending value 210. Index beginning value 200 ending value 205.

The author’s excess geometric return is:1.2195%.

Using either Andre or tyc excess geometric return method: 2.439%

Michael,

Recall that the unit “$” needs to be treated just like any other algebraic quantity and that 100% = 1,

As I understand things, your formulas’ suggestions applied to your example give:

Arithmetic excess return = [Portfolio return – Benchmark return]*100%/(Initial portfolio value)

= [($210/$200 – 1) – ($205/$200 – 1)]*100%/($200)

= [ (0.05) – (0.025) ]*100%/$200 = 0.0125%/$.

Geometric excess return = [Portfolio return – Benchmark return]*100%/(Ending portfolio value)

= [($210/$200 – 1) – ($205/$200 – 1)]*100%/($205)

= [ (0.05) – (0.025) ]*100%/$250 = 0.012195%/$.

As I previously noted, these values have problematic units. If we did the calculation in pennies instead of dollars, the results would change. But a return calculation should not depend on the units used for the values.

Whereas my formulas’ suggestions applied to your example give:

Arithmetic excess return = [Portfolio return – Benchmark return]*100%

= [($210/$200 – 1) – ($205/$200 – 1)]*100%

= [ (0.05) – (0.025) ]*100% = 2.5%.

Geometric excess return = [Portfolio return – Benchmark return]*100%/(1 + Benchmark return)

= [($210/$200 – 1) – ($205/$200 – 1)]*100%/[ 1 + ($210/$200 – 1) ]

= [ (0.05) – (0.025) ]*100%/[1.025] = 2.439%.

These values of (approximately) 2.5% make more sense to me then your answers which come in (ignoring your units) at around half that.

Andre

Andre,

I agree with the things you wrote except the following: “But a return calculation should not depend on the units used for the values.”

In my opinion, a return calculation is heavily dependent on the units used for the values. For a result to be measurable and comparable, the data or unit needs to be similar.

Unless we only focus on measurability and not comparability, then the equation Michael wrote could be use (although I won’t recommend others to use it).

tyc

Thanks for your feedback everyone. The formula has now been corrected.

I believe I may have seen the revised formula used in an attribution presentation (I believe it was IRR attribution by Dr. Stefan Illmer).

However, portfolio values generally do not match the index values. Unless the underline values (or data) that go into the revised formula is adjusted to start off with identical numbers, it’ll probably double (or more) the effort just to calculate excess return.

It might be better to use what Andre or David had stated. A more interesting topic is on attribution analysis. I’m surprised no one wrote about my error.

Hi, I am trying to calculate a performance against a benchmark using five allocations as such:

Money Market & Equivalents (Lipper Money Market Index) = 2.4% allocation

Municipal Bonds (Lipper General & Insured Muni Debt) = 25.8% allocation

Taxable Bonds (Baclays Treasury index) = 21.4% allocation

US Equities (S&P 500 Index) = 48.3% allocation

Int’l Equities (MSCI Eafe Index) = 2.1% allocation

Benchmark is 50% S&P Index, 40% Barclay Aggregate Bond Index and 10% Lipper Money Market Index.

I know the portfolio return is 3.2% and that the benchmark return is 3.8% but I can’t figure how to get to these percentages. Can you provide any help?

Thank you so much!

Mike

Hi, I want to know what career path and growth opportunities does performance analysis profession provide in terms of various roles and compensation

This article discusses the types of career paths and career ladders that an employer can use to assist employees in their career progression within the organization. Traditional career paths and ladders are discussed, as well as nontraditional methods of career progression developed in response to changes within society, organizations and the workforce. This article does not address other aspects and methods of developing employees, managers and leaders.