How Useful is the Information Ratio to Evaluate the Performance of Portfolio Managers?

MA-Thesis / Master von Christoph Schneider

Abstract:

„I do not want a good General, I want a lucky one.” (Napoleon Bonaparte).

In contrast to Napoleon, investors typically do not want to pick a lucky person to administer their funds, but both Napoleon and the investor face a similar problem: how to separate the lucky from the skilled. Historic data shows that five out of one hundred portfolio managers achieve an outstanding performance just by luck, and statistics also reveal that luck – in most cases – does not persist over time. The lucky managers will, however, always cite their superior skills as a reason for their success, while the unsuccessful ones will place the blame on bad luck. By assessing all active managers on the two dimensions luck and skill, four groups are created. The separation of the skilled and lucky from the unskilled but lucky managers and the separation of the skilled but unlucky from the unskilled and unlucky managers is of special interest to all stakeholders in the investment industry. It is, therefore, the investor’s task to apply understandable guidelines, preferably on a quantitative basis, when it comes to evaluating a portfolio manager. On the other hand, it is the fund administration’s task to judge the performance of its managers objectively and to transfer the results into a variable remuneration scheme or to decide about the replacement of a certain manager.

The idea of comparing the performance of different risky investments, for example investment funds, on a quantitative basis dates back to the beginnings of the asset management industry and has been an important field of research in finance since then. Performance measures serve as valuable quantitative evidence for the portfolio manager’s performance as well as for the evaluation of investment decisions ex post. Based on the idea of the capital asset pricing model (CAPM) proposed by Treynor, Sharpe, and Lintner, Treynor developed the first quantitative performance measure intended to rate mutual funds, the Treynor Ratio. Since then, a large number of performance measures with very different characteristics have been developed. Besides academia, the driving force behind the development of more sophisticated performance measures has always been the investors. This is understandable, as „the truly poor managers are afraid, the unlucky managers will be unjustly condemned, and the new managers have no track record. Only the skilled (or lucky) managers are enthusiastic”.

By combining and applying the results of previous research to a new sample of nearly 10,000 mutual funds that invest in different countries and asset classes, this thesis clarifies its central research question: Is the Information Ratio a useful and reliable performance measure? In order to answer this central question, it has been split up into the following sub-parts: What are the characteristics of a useful and reliable performance measure? What actually is „good” performance? Is the „good” performance a result of luck or of skilled decisions and does it persist over time? How does the Information Ratio compare to other performance measures, and what are its strengths and weaknesses? This empirical study aims at answering all of these questions and provides a framework for performance evaluation by use of the Information Ratio.

The Information Ratio, developed in 1973 by Treynor & Black, is one of the most important performance measures in the investment management industry. It is a ratio for the excess return of a portfolio relative to a specified benchmark divided by the volatility of the excess returns. The measure, therefore, is able to show how much additional return has been generated per unit of additional risk, which is important information in the field of active management. Besides the interesting characteristics of the Information Ratio, it is of special interest because it is founded on two different theoretical frameworks. While the first framework goes back to the founders of the Information Ratio, the second framework closely connects it to the fundamental law of active management, which was developed by Grinold. The fundamental law of active management is a central framework for active managers and provides insight on how to use the rationale behind the Information Ratio to construct active portfolios for predefined risk budgets. Additionally, the Information Ratio has not yet been analyzed in an extensive empirical study across different asset classes and countries, which is therefore a supplementary motivation for this paper.

The empirical study is based on return data of nearly 10,000 funds in the timeframe from January 1, 1998 until December 31, 2008 and yields some important results, which are summarized very briefly in this paragraph. Generally, funds have been categorized according to their investment universe in 13 distinct classes, for example „Equity US” or „Money Market EUR”. In order to judge the value of a certain performance measure, a quartile-based grading system with the four categories „very good”, „good”, „below average”, and „poor” has been developed. Threshold values have been calculated that separate the „very good” quartile from the „good” quartile, and so on. Using this method, the threshold values of the Information Ratio are found to vary over time and also across different asset classes, so that it becomes necessary to re-calibrate the framework annually. The quality and reliability of the Information Ratio is dependent on certain factors of the data selection process. Firstly, only one benchmark should be used for all funds in a fund category in order to allow for better comparability and the selection of this benchmark can heavily influence the threshold values. The benchmark should optimally cover a large proportion of the market that is within the investment universe of the respective fund. Secondly, data frequency should be as high as possible, for example, daily or weekly. Monthly data does not accurately represent the true volatility of returns within a calendar year. Thirdly, non-normally distributed fund returns can affect the usability of the Information Ratio. For example, money market funds show strong non-normal returns, and, therefore, cannot be reliably evaluated with the Information Ratio. There are, however, other measures available that take higher moments of return distributions into account. In order to separate lucky managers from skilled ones, the track record plays an important role, as luck generally is not persistent over time. The final framework evaluates the performance of the active manager based on the quartile-based grade of the Information Ratio, penalizes low active weights using an additional measure and incentivizes persistent (skilled) performance by looking at the manager’s track record.

Course of the Investigation:

Following the introduction and the motivation for the topic, Section 2 lays out the theoretical foundations of this paper. Firstly, Sub-section 2.1 explains different methods of fund performance management by describing the characteristics of reliable performance measures in part 2.1.1, and continues by presenting six widely-used ratios to evaluate fund performance in the mutual fund industry in parts 2.1.2 to 2.1.7. Each performance measure is explained briefly and its advantages and disadvantages are outlined in order to get a good overview of the rationale behind these measures. As the Information Ratio is at the center of interest of this study, it is explained in detail in Sub-section 2.2. In order to better understand the motivation behind active management, Sub-section 2.3 describes the fundamental law of active management. This leads to a better understanding of the relevant parameters that influence the level of excess returns and clarifies the theoretical framework of the Information Ratio from a different perspective. Sub-section 2.4 presents agency problems in the fund management industry in general and special issues that are related to the Information Ratio.

Section 3 elaborates on the composition and characteristics of the dataset that is used in the empirical study by explaining the selection of mutual funds (3.1) and benchmark indices (3.2), as well as by showing descriptive statistics of the different fund categories (3.3).

The empirical study, which is the central part of this thesis, is presented in Section 4. It starts in Sub-section 4.1 by testing the Information Ratio for stability over time and across different fund categories and continues in Sub-section 4.2 by comparing the ranking order of the Information Ratio against several other performance measures. Sub-sections 4.3 and 4.4 provide information about the robustness of the Information Ratio against the selection of different benchmarks and data frequencies. Other influences that could possibly affect the quality of the Information Ratio, such as non-normality of returns or survivorship bias inherent in the dataset, are described and analyzed in Sub-section 4.5. In order to separate lucky from skilled managers, the persistency of good Information Ratios over time has been researched in Sub-section 4.6. The empirical part concludes with a summary and the development of a specific performance evaluation framework detailed in Sub-section 4.7.

Section 5 sheds light on the experiences and opinions of several practitioners with respect to performance measurement in general and the use of the Information Ratio in particular. This view will complement the results of the empirical analysis.

The thesis concludes with Section 6, where all findings are summarized and starting points for future research are presented.

Table of Contents:

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Chapter 4.3, The Art of Selecting the Benchmark:

The selection and allocation of benchmarks for this study (cf. Table 2), which are used to calculate the Information Ratios, has mostly been done based on popularity of the indices and their ability to cover the price development of a certain market. In fund management companies, the selection of a benchmark usually is the result of intense negotiations between the fund manager and the investors, as the benchmark has a major impact on the alpha of the fund and on the influences of specific investment restrictions. Depending on style and country focus, one benchmark might be more favorable to the fund manager than another.

Therefore, it is necessary and important to analyze the sensitivity of the Information Ratio toward the selected benchmark within this paper. Lehmann & Modest have shown that benchmark selection does have a very strong influence on the resulting alphas as well as their volatility. While the Standard & Poor’s 500 Index has been used throughout this paper in connection with Equity US funds, two additional indices, the equally-weighted Dow Jones Industrial Average and the market-weighted Russell 1000 Index, will be introduced to compare the resulting Information Ratios. The Dow Jones Industrial Average is based on a basket of 30 large cap, industrial companies in the US. It has been quoted since 1896 and has a strong focus on manufacturers of industrial and consumer goods. The Russell 1000 Index is a proxy for the large cap segment of the US equity market and is based on the 1,000 largest companies in terms of market value. The Russell 1000 covers about 92% of the US equity market, has been calculated since 1984, and is in direct competition with the S&P 500. Figure 8 illustrates the development of the three indices over the 11-year observation period. It can be seen that the indices move very similarly. However, all of them emphasize different market segments and show a different behavior in certain periods.

After having calculated three different Information Ratios (based on the S&P 500, the Dow Jones Industrial Average, and the Russell 1000) for all Equity US funds from 1998 to 2008, the threshold values between the first 25% of the funds and the second 25% of the funds have been calculated again. This threshold value separates the first quartile and the second quartile, that is „very good” funds from „good” to „poor” funds. The result is charted in Figure 9.

It can be recognized that the Information Ratios based on the S&P 500 and the Russell 1000 are closely related, while the Information Ratios based on the Dow Jones Industrial Average behave differently and are far more volatile. It seems that the Dow Jones Industrial Average does not cover the investment universe of the Equity US funds very well. This can be due to the fact that this index is only based on 30 companies. Differences that seemed to be little at first glance in Figure 8 had a major impact on the threshold values of the Information Ratios as presented in Figure 9.

The difference of the threshold values has been tested for significance using the Wilcoxon signed-rank test. This test has been used, because all three sets of Information Ratios are not normally distributed according to the Lilliefors test and are assumed to be dependent on each other. The z-values of the Wilcoxon test are presented in Table 8, and significantly different values are flagged with an asterisk. Firstly, the Information Ratios based on the Dow Jones Industrial Average index were tested against those based on the S&P 500 index. Secondly, the Information Ratios based on the Russell 1000 index were also tested against those based on the S&P 500 index. To conclude, while some threshold values are quite close, all are significantly different from those based on the S&P 500 using a 5% level of significance. These results are in line with Goodwin, who also found that the selection of the benchmark has a strong influence on the resulting Information Ratios.

The results are confirmed when looking at the rankings based on the three different Information Ratios as illustrated in both scatter plots of Figure 10. While there are noticeable differences between Information Ratios based on the Dow Jones Industrial Average and those based on the S&P 500, the changes in rankings when using the Russell 1000 versus the S&P 500 are quite small. The selection of an appropriate benchmark is, therefore, an important step during performance analyses in general. Still, the results can only provide very limited guidance as to how to select the right benchmark. One can, however, conclude that benchmark indices that cover a large part of the investment universe of the specific fund category (for example, the Russell 1000 or S&P 500) are superior to indices that are only based on a few securities and certain industry sectors (for example, the Dow Jones Industrial Average). It should also be noted that the Dow Jones Industrial Average has been criticized for its equal weighting of stocks, lack of revision of its constituents following changes in the market environment, and a missing framework that describes admission criteria. The final decision for or against a benchmark should always be based on the experience of the performance evaluator.