What Is Attribution Analysis?

Attribution analysis is a sophisticated method for evaluating the performance of a portfolio or fund manager. Also known as “return attribution” or “performance attribution,” it attempts to quantitatively analyze aspects of an active fund manager’s investment selections and decisions—and to identify sources of excess returns, especially as compared to an index or other benchmark.

For portfolio managers and investment firms, attribution analysis can be an effective tool to assess strategies. For investors, attribution analysis works as a way to assess the performance of fund or money managers.

How Attribution Analysis Works

Attribution analysis focuses on three factors: the manager’s investment picks and asset allocation, their investment style, and the market timing of their decisions and trades.

The method begins by identifying the asset class in which a fund manager chooses to invest. An asset class generally describes the type of investments that a manager chooses; within that, it can also get more specific, describing a geographical marketplace in which they originate and/or an industry sector. European fixed income debt or U.S. technology equities could both be examples.

Then, there is the allocation of the different assets—that is, what percentage of the portfolio is weighted to specific segments, sectors, or industries. 

Specifying the type of assets will help identify a general benchmark for the comparison of performance. Often, this benchmark will take the form of a market index, a basket of comparable assets.

Analyzing Investment Style

The next step in attribution analysis is to determine the manager’s investment style. Like the class identification discussed above, a style will provide a benchmark against which to gauge the manager’s performance.

The first method of style analysis concentrates on the nature of the manager’s holdings. If they are equities, for example, are they the stocks of large-cap or small-cap companies? Value- or growth-oriented?

American economist Bill Sharpe introduced the second type of style analysis in 1988. Returns-based style analysis (RBSA) charts a fund’s returns and seeks an index with comparable performance history. Sharpe refined this method with a technique that he called quadratic optimization, which allowed him to assign a blend of indices that correlated most closely to a manager’s returns.

Explaining Alpha

Once an attribution analyst identifies that blend, they can formulate a customized benchmark of returns against which they can evaluate the manager’s performance. Such an analysis should shine a light on the excess returns, or alpha, that the manager enjoys over those benchmarks.

The next step in attribution analysis attempts to explain that alpha. Is it due to the manager’s stock picks, selection of sectors, or market timing? To determine the alpha generated by their stock picks, an analyst must identify and subtract the portion of the alpha attributable to sector and timing. Again, this can be done by developing customize benchmarks based on the manager’s selected blend of sectors and the timing of their trades. If the alpha of the fund is 13%, it is possible to assign a certain slice of that 13% to sector selection and timing of entry and exit from those sectors. The remainder will be stock selection alpha.

Market Timing and Attribution Analysis

Though some managers employ a buy-and-hold strategy, most are constantly trading, making buy and sell decisions throughout a given period. Segmenting returns by activity can be useful, telling you if a manager’s decisions to add or subtract positions from the portfolio helped or hurt the final return—vis-à-vis a more passive buy-and-hold approach.

Enter market timing, the third big factor that goes into attribution analysis. A fair amount of debate exists on its importance, though.

Certainly, this is the most difficult part of attribute analysis to put into quantitative terms. To the extent that market timing can be measured, scholars point out the importance of gauging a manager’s returns against benchmarks reflective of upturns and downturns. Ideally, the fund will go up in bullish times and will decline less than the market in bearish periods.

Even so, some scholars note that a significant portion of a manager’s performance with respect to timing is random, or luck. As a result, in general, most analysts attribute less significance to market timing than asset selection and investment style.

What Is Analysis of Variance (ANOVA)?

Analysis of variance (ANOVA) is an analysis tool used in statistics that splits an observed aggregate variability found inside a data set into two parts: systematic factors and random factors. The systematic factors have a statistical influence on the given data set, while the random factors do not. Analysts use the ANOVA test to determine the influence that independent variables have on the dependent variable in a regression study.

The t- and z-test methods developed in the 20th century were used for statistical analysis until 1918, when Ronald Fisher created the analysis of variance method. ANOVA is also called the Fisher analysis of variance, and it is the extension of the t- and z-tests. The term became well-known in 1925, after appearing in Fisher’s book, “Statistical Methods for Research Workers.” It was employed in experimental psychology and later expanded to subjects that were more complex.

The Formula for ANOVA is:


$\begin{aligned} &\text{F} = \frac{ \text{MST} }{ \text{MSE} } \\ &\textbf{where:} \\ &\text{F} = \text{ANOVA coefficient} \\ &\text{MST} = \text{Mean sum of squares due to treatment} \\ &\text{MSE} = \text{Mean sum of squares due to error} \\ \end{aligned}$​F=MSEMST​where:F=ANOVA coefficientMST=Mean sum of squares due to treatmentMSE=Mean sum of squares due to error​

What Does the Analysis of Variance Reveal?

The ANOVA test is the initial step in analyzing factors that affect a given data set. Once the test is finished, an analyst performs additional testing on the methodical factors that measurably contribute to the data set’s inconsistency. The analyst utilizes the ANOVA test results in an f-test to generate additional data that aligns with the proposed regression models.

The ANOVA test allows a comparison of more than two groups at the same time to determine whether a relationship exists between them. The result of the ANOVA formula, the F statistic (also called the F-ratio), allows for the analysis of multiple groups of data to determine the variability between samples and within samples.

If no real difference exists between the tested groups, which is called the null hypothesis, the result of the ANOVA’s F-ratio statistic will be close to 1. The distribution of all possible values of the F statistic is the F-distribution. This is actually a group of distribution functions, with two characteristic numbers, called the numerator degrees of freedom and the denominator degrees of freedom.

Example of How to Use ANOVA

A researcher might, for example, test students from multiple colleges to see if students from one of the colleges consistently outperform students from the other colleges. In a business application, an R&D researcher might test two different processes of creating a product to see if one process is better than the other in terms of cost efficiency.

The type of ANOVA test used depends on a number of factors. It is applied when data needs to be experimental. Analysis of variance is employed if there is no access to statistical software resulting in computing ANOVA by hand. It is simple to use and best suited for small samples. With many experimental designs, the sample sizes have to be the same for the various factor level combinations.

ANOVA is helpful for testing three or more variables. It is similar to multiple two-sample t-tests. However, it results in fewer type I errors and is appropriate for a range of issues. ANOVA groups differences by comparing the means of each group and includes spreading out the variance into diverse sources. It is employed with subjects, test groups, between groups and within groups.

One-Way ANOVA Versus Two-Way ANOVA

There are two main types of ANOVA: one-way (or unidirectional) and two-way. There also variations of ANOVA. For example, MANOVA (multivariate ANOVA) differs from ANOVA as the former tests for multiple dependent variables simultaneously while the latter assesses only one dependent variable at a time. One-way or two-way refers to the number of independent variables in your analysis of variance test. A one-way ANOVA evaluates the impact of a sole factor on a sole response variable. It determines whether all the samples are the same. The one-way ANOVA is used to determine whether there are any statistically significant differences between the means of three or more independent (unrelated) groups.

A two-way ANOVA is an extension of the one-way ANOVA. With a one-way, you have one independent variable affecting a dependent variable. With a two-way ANOVA, there are two independents. For example, a two-way ANOVA allows a company to compare worker productivity based on two independent variables, such as salary and skill set. It is utilized to observe the interaction between the two factors and tests the effect of two factors at the same time.

What Is Autocorrelation?

Autocorrelation is a mathematical representation of the degree of similarity between a given time series and a lagged version of itself over successive time intervals. It’s conceptually similar to the correlation between two different time series, but autocorrelation uses the same time series twice: once in its original form and once lagged one or more time periods. 

For example, if it’s rainy today, the data suggests that it’s more likely to rain tomorrow than if it’s clear today. When it comes to investing, a stock might have a strong positive autocorrelation of returns, suggesting that if it’s “up” today, it’s more likely to be up tomorrow, too.

Naturally, autocorrelation can be a useful tool for traders to utilize; particularly for technical analysts.

Understanding Autocorrelation

Autocorrelation can also be referred to as lagged correlation or serial correlation, as it measures the relationship between a variable’s current value and its past values.

As a very simple example, take a look at the five percentage values in the chart below. We are comparing them to the column on the right, which contains the same set of values, just moved up one row.