Attribution Analysis

Summary: 
To what do we attribute a manager's performance? Is it stock picking, investing in the right style, or market timing? Were certain sectors over or underweighted? These are the questions that attribution analysis attempts to answer.

To what do we attribute a manager’s performance? Is it stock picking, investing in the right style, or market timing? Were certain sectors over or underweighted?

These are the questions that attribution analysis attempts to answer. To answer these questions for short time periods, such as a day, a week, a month or a quarter, requires a sophisticated process that must identify and price each security in the portfolio at least daily (some even argue that this should be done intra-day at the time of any transaction). This kind of attribution analysis is costly and time consuming and is only practical for separately managed institutional portfolios. It is possible to do a more general attribution analysis using returns-based style analysis on any portfolio, like mutual funds, for which monthly or quarterly returns are available.

Most of a manager’s returns are attributed to asset class returns. A U.S. equity manager’s returns depend mostly on how well the U.S. stock market does. The second most important factor for an equity manager is investment style. Most growth stock managers perform “well” when growth stocks are in favor. Conversely they perform “badly” when growth stocks are out of favor. Our first goal is to find out how much of the manager’s return comes from the general market and investment style. We accomplish this using a technique called style analysis (for a more complete discussion of style analysis see Style Analysis).

Attribution Analysis Example

Let’s work through an example of attribution analysis. Using only the monthly returns for The Needham Growth Fund and the monthly returns from the four Russell style indices and T-Bills, we find the combination of indices that best describes Needham’s behavior/style. This combination is shown in Figure 1. In Figure 2 the red portion of the pie chart shows that these indices account for 78.2% of the variance in Needham’s return. The variance of Needham’s return that can’t be explained by the market and style is represented by the green portion of the pie. This residual variance or behavior is likely due to the manager’s stock selection or sector bets.

Figure 1: Indices
Indices


Figure 2: Performance Attribution
Performance Attribution

The portion of the manager’s returns that are explained by exposures to the style indices could be passively replicated by buying the appropriate percentages of index funds or ETFs that represent the style indices. The manager’s alpha is generated by the portion of the fund that we cannot passively replicate. This represents the manager’s active bets. They could be stock bets, sector bets, or even market timing bets. In an attempt to identify these sources of returns, we start by constructing a custom benchmark called a style benchmark that is based on the index weights in Figure 1. The performance graph and table (Figure 3) show that Needham beat its custom style benchmark by an annualized 11.05%. This is the excess return Needham achieved over what we could passively construct to represent Needham’s investment style. This is the result of either manager skill or luck (how we differentiate between the two is explained in Mutual Fund Analysis). For now we assume manager skill.

Figure 3: Manager Performance
Manager Performance

Should Needham’s excess return be attributed to stock selection, sector weightings, and/or market timing? To see the impact of sector bets we perform another style analysis using sector indices rather than style indices. Because we are using returns and a rolling window we don’t expect to precisely identify the sector weights at any specific time but rather get an idea of what the sector exposures have been over the life of the fund and how they have changed over time.1

Figure 4: Sector Analysis
Sector Analysis

Figure 4 above contains the results of the sector analysis, which shows that Needham is heavily weighted in technology, health care, and T-Bills. T-Bills represent cash or anything that makes the portfolio behave like cash. Based on the Needham Fund's prospectus the fund is run somewhat like a hedge fund. It shorts stocks and uses derivatives to reduce risk. Once again, using the exposure to the indices used in the style analysis, we construct a custom style benchmark. Figure 5 below shows that Needham outperforms this benchmark by 9.04% annualized. So of the 11.05% outperformance, about 2% is from their sector bets. The balance, 9.04%, is the result of either stock selection or market timing.

Figure 5: Manager Performance with Custom Benchmark
Manager Performance with Custom Benchmark

Market timing doesn’t necessarily mean moving from 100% stocks to 100% cash. It can be as subtle as buying low beta stocks when one perceives the market is over valued. It could also be a value manager building cash because he can’t find good valuations.

Figure 6: Upside, Downside I
Upside/Downside I

One way to evaluate the results of market timing is to see how managers do in both up and down markets. To do this Zephyr developed an Upside/Downside Market Capture Analysis. If a manager goes up more than the benchmark when the benchmark goes up, the manager plots above the horizontal line in Figure 6 above. If a manager goes down more than the benchmark when the benchmark goes down, he plots to the right of the vertical line. If the manager goes down less he plots to the left of the vertical line.

Aggressive managers who go up more and down more plot in the northeast quadrant. Defensive managers who go up less and down less plot in the southwest corner. Managers that go up more and down less, as is the case with Needham, plot in the northwest quadrant. We believe that this is the result of good market timing particularly if there is a consistent pattern of such behavior, as seen in Figure 7 below. Managers with bad market timing that go up less and down more fall into the southeast quadrant. Needham went up 10% more than the benchmark when the benchmark had a positive return. When the benchmark went down the fund declined about 22% less.

Figure 7: Upside, Downside II
Upside/Downside II


Using returns-based style analysis with a tool like StyleADVISOR, one can get a very good idea of whether a manager’s alpha is from stock selection, sector bets or market timing.

End Notes:

1The whole concept of sector exposure is imprecise even when done daily with a securities based system. Broad economic sectors are made up of industry groups that can often be as disparate as the sectors themselves. Every index provider creates different sectors. S&P Citigroup’s are different from Russell’s, which are different from Morningstar’s etc. Then you have the problem of how stocks get assigned to an industry and sector. Is General Electric an industrial, health care, aerospace, or finance company? How many other companies have businesses in multiple sectors?

 
 

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