What is style analysis?

Before we discuss style analysis we should first answer the question “What is style as it pertains to investment portfolios?” We will focus on US equity managers, but “style” can just as easily apply to other kinds of managers, like fixed income managers and non-US equity managers. Most managers have an investment philosophy that leads to a process for building portfolios. That process causes the portfolio’s returns to behave in a certain way. This behavior is what we call style. A manager’s philosophy might be, for example, to look for stocks that have been beaten down by bad news or are currently selling below what might be deemed their intrinsic value. This philosophy leads to a process of buying stocks with low price to book ratios and low price to earnings ratios. The return pattern (or price behavior) of such a portfolio is very different from that of a portfolio made up of stocks with high price to book ratios and high PE ratios. The behavior reflects the manager’s style, which in this case would be called “value”. Similarly some managers specialize in small company stocks while others focus on the stocks of large companies. The US equity market is commonly differentiated along two dimensions – size (large capitalization stocks vs. small capitalization stocks) and valuation (value stocks vs. growth stocks). The four primary styles are Large Value, Large Growth, Small Value, and Small growth. As we will see later, there can be many variations when defining a particular manager’s style.

Why do we care about Manager Style?

There are two key reasons to identify a manager’s style. To determine whether a manager has skill, and is therefore worth paying an active management fee, we must find the proper benchmark for the manager (for a discussion on benchmarking see Benchmarks). If a manager specializes in small cap tech stocks and other small growth stocks is it appropriate to measures this manager’s performance against a large cap core index such as the S&P 500? No. It would be much more appropriate to use something like the Russell 2000 Growth Index. Better yet, we believe a custom, blended style benchmark is the premier benchmark for performance analysis.

Manager style is also an important part of creating a diversified portfolio. Few investors give all their money to one manager with instructions to do whatever they want. Instead we realize that most managers are specialized and that our job is to build a portfolio of managers. We must determine how much growth, value, small, and large cap we want our total portfolio to include. Without any strong views regarding the future performance of one style over another, the prudent path is to build a portfolio whose style would be close to the style of our broad market benchmark, such as the Russell 3000 for US Equities. At first blush this might sound like we are just building a big index fund. But this is not the case. If each of our managers beats their respective style benchmark then our total fund will beat the broader market benchmark. This is another reason that it’s important that managers’ styles are consistent and predictable. Taken in this context each manager is a member of a team and it’s important that every manager maintains her position on the team.

How do we determine a manager’s style?

One way to determine a manager’s style is to analyze the stocks the manager has in her portfolio. If they are predominately growth stocks then it is reasonable to say that the manager is a growth manager. Before Bill Sharpe developed style analysis (also called returns-based style analysis) this was the primary way to determine style. Holdings-based analysis is time consuming, expensive, and becomes increasingly difficult when trying to determine a manager’s style over multiple time periods. It is necessary to have a long history of all the stock holdings to perform holdings-based analysis. The analysis of holdings would have to be sophisticated enough to detect the variations within the same style category and how those variations effect the behavior of the portfolio. For a more technical discussion of why returns-based is superior to holdings based see “Evaluating Style Analysis,” an academic article by Jenke R. ter Horst, Theo E. Nijman, and Frans A. de Roon and published in the January 2004, Volume 11, Issue 1 of the Journal of Empirical Finance.

Figure 1

In 1988 William F. Sharpe developed returns-based style analysis. The idea behind this is simple; managers with different styles behave differently and this behavior can be determined by looking at their return pattern. Figure 1 shows the difference in returns between the Russell Large (1000) Growth index and the Russell Large (1000) Value index over rolling three year periods. Sharpe referred to a manager’s return pattern as “tracks in the sand.” If a manager’s “tracks” looked similar to the “tracks,” of a Large Cap growth Index then it is probably safe to say that the manager is a large cap growth manager. This is accomplished by calculating the correlations of the manager’s returns versus the returns of various style indices. A simple way to do style analysis is to calculate the correlation of a manager’s returns to the returns of a series of style indices (large value, large growth, small value and small growth). The index with the highest correlation to the manager’s returns would define the manager’s style. The problem with this simplistic approach is that it doesn’t recognize variations in a manager’s styles. For instance, some growth managers are growthier than others. Because of this, a single index does not accurately reflect a managers’ style.

To better approximate a manager’s style, Sharpe decided to use multiple indices and a statistical process called quadratic optimization (for a technical discussion of style analysis math see Becker [2003a, 2003b, 2003c]). As an example, let’s look at the style of the Fidelity Low Price Stock Fund. The only information we have from this fund are the monthly total returns. We also have the monthly returns for the four Russell style indices and T Bills for the same period. Using a software program like Zephyr’s StyleADVISOR, which incorporates a quadratic programming package, we find the combination of the Russell indices that best describes this fund’s style. That combination is seen in Figure 2. We have added T Bills to our indices to reflect cash in the portfolio or anything that makes the portfolio behave like cash. The best way to describe the style of the Fidelity Low Priced stock fund is 17.3% cash, 16.7% Large Value, 55.1% Small Value and 10.9% Small Growth. Figure 3 shows this fund on a style map. Although it is a small value fund it is larger than the Russell Small (2000) Value index and a little growthier. In fact, very few funds or managers have the exact same style. This methodology allows you to capture this difference in style. The combination of indices not only defines the manager’s style, but it is the best benchmark for performance analysis (see Benchmarks).

Figure 2

Figure 3

Earlier, we mentioned our desire for style consistent managers. By making a slight modification to the analysis and allowing a “rolling window” we can see a manager’s style history. Figure 4 shows a number of style points starting with the first 36 months and progressing to the most recent 36-month period. The smaller dots represent the earlier periods. Figure 5 also shows the evolution of the fund’s style. Here the style indices are color coded and the horizontal axis displays time. We can see in this example that the fund started as a core fund made up of both small value and small growth and has gradually become more of a small value fund. This analysis measured 134 time periods but took less than a second to calculate. Compare this to the time it would take to examine, quantify and characterize 134 portfolios (assuming you could get portfolio holdings each month for over ten years).

Figure 4

Figure 5

Thanks to the brilliance of William F. Sharpe, we can easily determine a manager’s style and style history using only returns. With this we can build better benchmarks and create more diversified portfolios of managers.