JOURNAL OF ECONOMICS AND FINANCE EDUCATION • Volume 2 • Number • Winter 2013

Capture Ratios: A Popular Method of Measuring Portfolio Performance in Practice

Don R. Cox and Delbert C. Goff 1

ABSTRACT

We provide a brief introduction to a simple measure of portfolio risk and return, the capture ratio, which is widely used in practice, but rarely noted in finance textbooks or literature. We describe the ratio and provide examples of its rather widespread use in the investing profession. Finally, we show a specific example of calculating capture ratios using a computer spreadsheet. Finance professors and their students can benefit from basic knowledge of this common practical performance measurement tool.

Introduction

Finance and investments textbooks typically discuss multiple measures of portfolio risk and return that are also commonly used in practice. Among the most commonly noted measures are alpha, beta, the standard deviation of returns, the Sharpe ratio, the Treynor ratio, tracking error, and the information ratio. There are other measures of portfolio performance that are used in practice, but are generally not covered in textbooks. Among the most popular of these alternative measures are the “up-market capture” and “down- market capture” ratios. Through our experience serving on advisory boards for endowment funds and working with investment professionals we have had the opportunity to see the frequency with which capture ratios are used in practice. And, through our research we have discovered other evidence suggesting that capture ratios are widely used in practice by investment advisors and consultants. There is, however, a dearth of information from academic research and/or textbooks on the capture ratios. The purpose of this paper is to provide a description of capture ratios and explain how they are used in practice. This information will be helpful for finance professors who want to make certain that their students are familiar with portfolio performance measures widely used in practice. We do not propose that capture ratios are theoretically superior to other measures of performance, but simply that any measure so widely presented and used in practice is worthy of attention by our peers. An example of the calculations that can be shared with students is given.

1 Don R. Cox, Professor of Finance, [email protected], and Delbert C. Goff, Professor of Finance, [email protected], Department of Finance, Banking & Insurance, Appalachian State University, Boone, NC 28608.

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JOURNAL OF ECONOMICS AND FINANCE EDUCATION • Volume 2 • Number • Winter 2013

What Are Capture Ratios?

Capture ratios provide information on how investment portfolios (and thereby investment managers) perform in up and down markets. The up capture ratio is a measure of a portfolio’s performance during periods where the benchmark portfolio is up. For example, an up capture ratio of 110 percent indicates that, on average, the portfolio outperforms the benchmark by 10 percent during periods when the benchmark is up. An up capture that is less than 100% indicates that the portfolio underperformed the benchmark during period when the benchmark returns were positive. Investment managers strive to have an up capture ratio that is high. The down capture ratio measures portfolio performance during periods when the benchmark returns are negative. For example, a down capture ratio of 80% indicates that, on average, the portfolio captured only 80% of the negative returns of the benchmark. Investment managers strive for a down capture ratio that is less than 100%, or at least less than their up capture ratio. The up capture ratio is calculated by dividing the annualized returns of the portfolio during periods that the benchmark returns are positive by the annualized returns of the benchmark during the periods the same periods. The first step in calculating the up capture ratio is to identify the periods (e.g., months or quarters) when the returns to the benchmark are positive. Next, annualize the returns for the benchmark and returns for the portfolio during the positive benchmark periods. Finally, calculate the ratio. That is:

Annualized returns of portfolioduring periods with positivebenchmark returns Up Capture  Annualized returns of benchmark during periods with positivebenchmark returns

The formula for calculating the up capture ratio is:

1  nup  y  1 r  1  i   i1  Up Capture  1  nup  y  1 s  1  k   k1 

Where: nup = number of positive benchmark returns sk = k-th positive benchmark return ri = portfolio return for the same period as the i-th positive benchmark return y = number of years, counting periods of positive benchmark returns only

For the down capture calculation, portfolio and benchmark returns from the negative benchmark return periods are used instead of returns from the positive benchmark return periods (Zephyr Associates, Inc., 2011).

How Widely Are Capture Ratios Used in Practice?

We have had the opportunity to interact with investment professionals in a variety of settings and we have observed that they frequently include capture ratios in reports about manager or fund performance. In particular, we have seen capture ratios being highlighted in presentations related to the comparison, evaluation and selection of investment managers, and in presentations illustrating the type of important analysis information that an advisor can provide to an investing client. Our personal observations include multiple financial advisors/consultants from a wide variety of major investment firms – including Merrill

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JOURNAL OF ECONOMICS AND FINANCE EDUCATION • Volume 2 • Number • Winter 2013

Lynch, UBS, Morgan Stanley, Deutsche Bank, Wells Fargo, and Smith Barney – as well as many smaller or independent advisors. A study by Nelson (2009) reports the results of surveys on investment screens used by financial planners. For 2008, 43.0% of respondents indicated occasional use of capture ratios, 42.0% indicated frequent use of capture ratios, and 15.0% indicated that they always used capture ratios (for 2009 respondents reported use of 58.6%, 30.1%, and 11.1%, respectively). These results provide significant recent evidence that capture ratios are widely accepted and widely used in practice by investment professionals. Finally, although we have not conducted a comprehensive search, we have frequently run across mutual fund annual reports and/or fact sheets that use capture ratios as part of the risk and return information presented by the fund. Just a few examples include the Alger China-US. Growth Fund, the Allianz AGIC Convertible Fund, the Wells Fargo Strategic Large Cap Growth Fund, and the Managers Special Equity Fund. In the September 2010 Management Commentary and Annual Report for the Oppenheimer Global Opportunities Fund, Frank Jennings, the portfolio manager for the fund states: “…we believe the best measures of our risk are what we refer to as upside and downside capture…. Over the last three years, the fund has performed better than the index in up markets, and almost equal to the index in down markets…We will seek to maintain this attractive risk/reward relationship for investors over the long term.”

What Is the Appeal of Capture Ratios?

As previously noted, there are numerous other measures of manager performance and risk (Sharpe ratio, Treynor ratio, information ratio, standard deviation, beta, etc.). Despite the array of measures, most of them depend in some way on the statistical measurement of variance. This presents two potential concerns: (a) measures that do not have a clear intuitive understanding by many non-professional investors, and (b) measures that treat the “pleasure” from gains as symmetrical with the “pain” from losses (based on models assuming behavior driven by expected utility). As proposed by Kahneman and Tversky (1979) and others, real-world investors often display “loss aversion” whereby they are more sensitive to losses than to gains. Capture ratios address both of these issues. A ratio that attempts to simply measure the percentage, or proportion, of market gains and losses that are captured by an investment manager is an idea that does not require any real understanding of statistical theory. Also, a measure that examines relative gains and relative losses separately may be useful for investors that display some degree of loss aversion, and even for different investors with different degrees of loss aversion.

Textbook and Literature Review

We searched 13 textbooks for information on capture ratios and could find no information on capture ratios in any of the textbooks examined. Table 1 lists the textbook searched. The only book that we found that provides coverage of capture ratios is Investment Manager Analysis by Frank J. Travers. This book is not a traditional textbook as the target audience appears to be professionals and not academics. Investment Manager Analysis provides a description of how to use and interpret the capture ratios, but it does not clearly explain and demonstrate how the ratios are calculated.

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JOURNAL OF ECONOMICS AND FINANCE EDUCATION • Volume 2 • Number • Winter 2013

Table 1 - Textbooks Searched For Information on Capture Ratios

Textbook Title Authors Essentials of Investments, Eighth Edition Bodie, Zvi; Kane, Alex; Marcus, Alan J. Fundamentals of Investing, Eleventh Edition Gitman, Lawrence J.; Joehnk, Michael D.; Smart, Scott B. Fundamentals of Investments, Fifth Edition Jordan, Bradford D.; Miller, Thomas W. Fundamentals of Investment Management, 9th Hirt, Geoffrey; Block, Stanley Edition Investments, 9th Edition Bodie, Zvi; Kane, Alex; Marcus, Alan Investments: An Introduction, 9th Edition Mayo, Herbert Investments: Analysis and Behavior, 2nd Edition Hirschey, Mark; Nofsinger, John Investments: Analysis and Management, 11th Jones, Charles P. Edition Investment Analysis and Portfolio Management, 9th Reilly, Frank; Brown, Keith Edition Managing Investment Portfolios Maginn, John; Tuttle, Donald; Pinto, Jerald; McLeavey, Dennis Modern Portfolio Theory and Investment Analysis, Elton, Edwin; Gruber, Martin; Brown, Stephen; 8th Edition Goetzmann, William Portfolio Construction, Management, and Strong, Robert A. Protection, 5th Edition Running Money: Professional Portfolio Stewart, Scott; Piros, Christopher; Heisler, Jeffrey Management

We could find no research in academic journals regarding capture ratios.

Example of Capture Ratio Calculations

Capture ratios can be easily calculated using a computer spreadsheet. Table 2 shows the calculation of up capture and down capture ratios using two years of monthly data. The benchmark portfolio is the S&P 500 index. The first step in the calculation is to identify the up (down) months for the index and add one to the return to enable the calculation of compound returns. This is accomplished in columns E (G) using a simple IF function [=IF(C3>0,1+C3,"") for the up capture and =IF(C3<0,1+C3,"") for the down capture]. In column F (H) one plus the portfolio returns is calculated for the months that the benchmark portfolio is up (down) using an IF function [=IF(E3="","",1+D3) for the up months and likewise for the down months]. Finally the up capture is calculated by calculating the annualized compound returns for the up months for the portfolio and for the benchmark and taking the ratio as follows:

=(PRODUCT(F3:F26)^(1/(COUNT(F3:F26)/12))-1)/(PRODUCT(E3:E26)^(1/(COUNT(E3:E26)/12))-1).

The down capture is calculated in a similar manner using the data in columns G and H.

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JOURNAL OF ECONOMICS AND FINANCE EDUCATION • Volume 2 • Number • Winter 2013

Table 2 - Calculating Capture Ratios with a Spreadsheet Program

A B C D E F G H

1 Monthly Returns Up Capture Calculations Down Capture Calculations 1 + Return on 1 + Return on 1 + Return on Portfolio 1 + Return on Portfolio 2 Benchmark During Benchmark During S&P During Up Benchmark Up During Down Benchmark Year Month 500 Portfolio Months Months Months Down Months 3 Jan -6.00% -4.36% 0.9400 0.9564 4 Feb -3.25% -2.17% 0.9675 0.9783 5 Mar -0.43% -0.36% 0.9957 0.9964 6 Apr 4.87% 6.23% 1.0487 1.0623 7 May 1.30% 2.55% 1.0130 1.0255 8 Jun -8.43% -5.55% 0.9157 0.9445

9 2008 Jul -0.84% -1.24% 0.9916 0.9876 10 Aug 1.45% -0.88% 1.0145 0.9912 11 Sep -8.91% -6.43% 0.9109 0.9357 12 Oct -16.80% -18.97% 0.8320 0.8103 13 Nov -7.18% -7.81% 0.9282 0.9219 14 Dec 1.06% 2.48% 1.0106 1.0248 15 Jan -8.43% -6.66% 0.9157 0.9334 16 Feb -10.65% -9.93% 0.8935 0.9007 17 Mar 8.76% 8.53% 1.0876 1.0853 18 Apr 9.57% 10.28% 1.0957 1.1028 19 May 5.59% 6.34% 1.0559 1.0634 20 Jun 0.20% -1.25% 1.0020 0.9875

21 2009 Jul 7.56% 7.62% 1.0756 1.0762 22 Aug 3.61% 3.98% 1.0361 1.0398 23 Sep 3.73% 4.80% 1.0373 1.0480 24 Oct -1.86% -0.52% 0.9814 0.9948 25 Nov 6.00% 5.92% 1.0600 1.0592 26 Dec 1.93% 1.95% 1.0193 1.0195 27 Up Capture Down Capture 28 106.3% 92.1%

The results for this example indicate that the portfolio had a greater return than the benchmark during the up market months. Also, the portfolio return during down months was less negative than the return on the benchmark during the down market months. When using the capture ratios the question may arise as to how many years of data should be used in the analysis. There is not a standard rule of thumb on the length of the observation period except that it should be long enough to capture a full market cycle including up and down market periods. Although capture ratios are most often presented as separate upside and downside values as described herein, in some instances an overall capture ratio is presented. An overall capture ratio is simply a ratio of the two ratios; that is, the upside capture divided by the downside capture. The general interpretation of such an overall capture ratio is that higher values are better, and as a rule of thumb, a value above 1.0 is desirable (meaning the manager captured proportionately more of the market gains than they did the market declines), and a value less than 1.0 is undesirable (meaning the manager captured proportionately more of the market declines than they did the market gains).

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Conclusion

We identify and describe a simple measure of portfolio risk and return, the capture ratio, which is widely used in practice, but rarely noted in finance textbooks or literature. We provide a brief description of the ratio and examples of its rather widespread use in the investing profession. Finally, we provide a specific example of calculating capture ratios using a computer spreadsheet. Hopefully, this brief introduction to capture ratios will be useful to other finance professors that may have had little exposure to this tool and wish to introduce another portfolio risk and return measure to students.

References

Bodie, Z., Kane, A., & Marcus, A. 2010. Essentials of Investments, 8th Edition. New York: McGraw-Hill Higher Education.

Bodie, Z., Kane, A., & Marcus, A. 2011. Investments, 9th Edition. New York: McGraw-Hill Higher Education.

Elton, E., Gruber, M., Brown, S., & Goetzmann, W. 2007. Modern Portfolio Theory and Investment Analysis, 8th Edition. Hoboken: John Wiley & Sons, Inc.

Hirschey, M., & Nofsinger, J. 2009. Investments: Analysis and Behavior, 2nd Edition. New York: McGraw Hill/Irwin.

Jones, C. P. 2007. Investments: Analysis and Management, 11th Edition. Hoboken: John Wiley & Sons, Inc.

Kahneman, D., & Tversky, A. 1979. “Prospect Theory: An Analysis of Decision Under Risk.” Econometrica, 47(2), 263-292.

Maginn, J., Tuttle, D., Pinto, J., & McLeavey, D. 2007. Managing Investment Portfolios, 3rd Edition. Hoboken: John Wiley & Sons, Inc.

Mayo, H. 2008. Investments: An Introduction, 9th Edition. Mason: Thompson South-Western.

Nelson, C. 2006. “How Planners Screen Investments.” Journal of Financial Planning (3rd Quarter), 8-9.

OppenheimerFunds, Inc. 2010, September. Oppenheimer Global Opportunities Fund Annual Report. Retrieved from OppenheimerFunds, Inc. Web site: https://www.oppenheimerfunds.com/digitalAssets/ee2ff8d31060f010VgnVCM100000e82311ac____-4.pdf

Reilly, F., & Brown, K. 2008. Investment Analysis and Portfolio Management, 9th Edition. New York: South-Western.

Stewart, S., Piros, C., & Heisler, J. 2010. Running Money: Professional Portfolio Management. New York: McGraw-Hill/Irwin.

Strong, R. A. 2009. Portfolio Construction, Management, and Protection, 5th Edition. Mason: South- Western.

Travers, F. J. 2004. Investment Manager Analysis. Hoboken: John Wiley & Sones, Inc.

Zephyr Associates, Inc. 2011. Zephyr Associates, Inc. Retrieved February 24, 2011, from Up and Down Capture: http://www.styleadvisor.com/content/and-down-capture

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