Essential Performance Metrics to Evaluate and Interpret Investment Returns Wealth Management Services
Alpha, beta, Sharpe ratio: these metrics are ubiquitous tools of the investment community. Used correctly, they can help investors better evaluate their investment decisions. Used incorrectly, they may lead to erroneous conclusions. Effectively evaluating an investment goes beyond observing short-term absolute returns. Numerous measures can help decipher the full implications of various investment choices by examining factors such as return, risk and performance of the portfolio. This report identifies and explains popular performance metrics and utilizes a hypothetical case study to illustrate evaluation techniques that may help determine whether an investment manager has succeeded in effectively implementing their investment objectives. Understanding the metrics in this report will help to holistically interpret portfolio performance and will assist in the manager evaluation and selection process. It is important to note that these metrics are not an exclusive means for evaluating investment performance. Other qualitative factors, such as an investor s investment objectives and appetite for risk and the manager s investment technique and philosophy, should be taken into consideration during the selection and evaluation process. Each metric will be illustrated using the following hypothetical case study assumptions: Two hypothetical managers, Manager A and Manager B, have similar investment styles and measure their performance against the same hypothetical benchmark. The risk-free rate of return is 3.00%. The most recent annual returns for each manager and the benchmark are listed below. Year Benchmark Manager A Manager B 1 4.00% 5.00% 2.00% 2 20.00 15.00 28.00 3-5.00-2.00-8.00 4 5.00 7.00 4.00 Please refer to opposite page for case study summary. In the hypothetical above, all returns are provided gross of fees. It is important to remember that investment management fees would otherwise reduce the performance that an investor would experience.
Case Study Summary The metrics provide some valuable insight when evaluating both managers: Although Manager B produced a greater arithmetic return, Manager A produced the greater geometric (compounded) return. Both managers provided positive excess return above the benchmark. Manager A was more consistent (less risky) than Manager B and the benchmark, as evidenced by the lower standard deviation and beta. Manager A was more defensive (lower downside capture ratio), while Manager B was more aggressive (higher upside capture ratio). Manager A was more successful in outperforming on a risk-adjusted basis, measured by a positive alpha and higher Sharpe ratio. Manager A provides a greater probability of continuing to outperform the benchmark, given the higher information ratio. The returns of the managers were highly correlated to the selected benchmark, further validating their alpha and beta metrics. Formula Key r i : rate of return x i : interim return x avg : average of all returns n : number of years R p : return of portfolio R f : risk-free rate of return R m : return of market R b : return of benchmark AR i : interim active return AR avg : average active return p : standard deviation of portfolio m : standard deviation of market w fund, i : weight of asset i in the fund w index, i : weight of asset i in the index COV p,m : covariance of portfolio and market COV A,B : covariance of portfolio A and portfolio B = n i=1 (a i -a avg ) (b i -b avg ) n-1 Conclusion An enhanced understanding of performance metrics can help advisors evaluate different investment options for their clients, and, when used correctly, can help them better communicate their recommendations and inspire investor confidence. These metrics do not, however, provide a complete perspective alone, and should be used in conjunction with a manager s qualitative characteristics (investment philosophy, process, portfolio holdings, etc.) in the evaluation and selection process.
Metric Measuring Returns Arithmetic Mean Rp Geometric Return Rg Excess Return ER Description The arithmetic mean, or simple average, treats each year s return as an isolated event and excludes the impact of compounding. The arithmetic mean is calculated by summing the returns for each time period, and dividing by the number of periods. The geometric average treats returns as part of a continuous, single experience and includes the impact of compounding. The geometric or time-weighted return is measured by linking periodic returns through multiplication. Excess return measures the amount by which an investment outperforms its respective benchmark. Excess return is the unadjusted, or absolute, difference between the manager s results, measured arithmetically, and the benchmark returns, both positive and negative. What it Measures The average return over an investment period. The compounded return over an investment period. The manager s return compared to the benchmark over an investment period. How to Interpret All else equal, a higher arithmetic return is better. All else equal, a higher geometric return is better. A positive excess return indicates the manager outperformed the benchmark; a higher excess return is better. Important Considerations Often the starting point for evaluating performance, this is likely to be the return investors calculate by themselves. The arithmetic mean is an input to calculate other ratios, such as Sharpe ratio and Alpha, described later. Most money managers report their returns using the geometric average because it reflects the actual growth or reduction of dollars in a portfolio more accurately than the arithmetic mean. The geometric average will always be expressed as a lower percentage than the arithmetic average, assuming a varied return sequence and a time period greater than one year. While the metric can be useful as a functional screening tool, it ignores an important issue the level of risk assumed to achieve those results. Formula r 1 + r 2 +... +r n n 1 n [(1+r 1 )(1+r 2 )...(1+r n )] -1 R p - R b Case Study Refer to case study assumptions and summary sections for additional information. Benchmark: 6.00% Manager A: 6.25% Manager B: 6.50% Manager B earned a higher arithmetic return. Benchmark: 5.63% Manager A: 6.08% Manager B: 5.72% Manager A earned a higher geometric return. Manager A: 0.25% Manager B: 0.50% Both managers provided excess return, but Manager B had higher excess return.
Measuring Risk Measuring Risk-Adjusted Returns Standard Deviation Beta β Alpha Sharpe Ratio SR Standard deviation indicates the consistency of a manager s returns. It is a measure of total volatility, both systematic (market related) and non-systematic (security specific). It is calculated by selecting a series of returns; finding the difference or variance around the mean of those returns; summing the squared deviations from the mean; and dividing by the number of observations (minus one degree of freedom for a sample). Beta is a measure of sensitivity to the market benchmark. It measures the volatility of a security or portfolio relative to the market as a whole (systematic risk only). It is calculated as the covariance between a portfolio and the market divided by the market variance. Jensen s alpha is the portfolio s risk-adjusted performance or value added by a manager. Alpha is the incremental return between a manager s actual results and the expected results, given the level of risk. The Sharpe ratio measures the efficiency of a portfolio. It quantifies the return received in exchange for risk assumed. It is calculated by taking the return of a portfolio above a risk-free rate divided by the portfolio standard deviation. The overall volatility of the manager relative to its average return. The volatility of the manager relative to the overall market. The manager s return in excess of what would be forecasted by the portfolio s market exposure. The efficiency of the portfolio, defined as the return net of cash per unit of volatility around a portfolio s average return. A lower standard deviation indicates more consistent performance and lower risk; a higher standard deviation indicates less consistency and higher risk. The greater the standard deviation, the more varied the return sequence. A beta of 1.0 indicates that a manager would respond similarly to the market. A beta greater than 1.0 indicates that a portfolio would be more responsive to movements in the market, while a beta below 1.0 indicates a more muted response. A positive alpha indicates that a selected portfolio has produced returns above the expected level at the same level of risk, and a negative alpha suggests the portfolio underperformed given the level of risk assumed. The higher the Sharpe ratio, the better. Standard deviation is the expected variance of future returns on either side of the average, based on behavior of past performance, and does not differentiate between returns above or below the mean. Aggressive investors may choose portfolios with higher betas, while defensive investors may focus on lower beta investments. For a given level of risk, a higher value added by a manager is desirable. It helps equalize returns of managers within the same asset class so they can be compared on a riskadjusted basis. n (x i -x avg ) 2 i=1 n-1 COV p,m m 2 R P - [R f +β p (R m -R f )] R p - R f p Benchmark: 10.36% Manager A: 6.99% Manager B: 15.26% Manager A was more consistent (less risky) than both Manager B and the benchmark, as measured by a lower standard deviation. Manager A: 0.67 Manager B: 1.47 Manager A was more defensive; Manager B was more aggressive. Manager A: 1.25% Manager B: -0.90% Manager A outperformed on a riskadjusted basis indicated by a higher, positive alpha. Manager B underperformed on a risk-adjusted basis indicated by a negative alpha. Benchmark: 0.29 Manager A: 0.46 Manager B: 0.23 Manager A had a more efficient portfolio than Manager B.
Measuring Performance Com R-Squared R2 Active Share AS Tracking Error TE R-squared, also referred to as the coefficient of determination, represents the dependence of one variable (the manager s return) on another variable (the benchmark return). It is calculated by squaring the correlation coefficient between the manager and the benchmark. Alternately, R-squared can be calculated by squaring beta, multiplying this term by the market variance and dividing by the manager s variance. Active share measures the percentage of the manager s portfolio holdings that are different from the benchmark. It is calculated using the weight of each stock held by the manager relative to the weight of each stock in the benchmark. For a manager that never shorts stock and never buys on margin, active share will be between 0% and 100%. Tracking error measures active risk or the variability of a portfolio s return compared to the benchmark. It is calculated as the standard deviation (consistency) of the active return, or alpha. The percentage of a manager s return directly attributable to the benchmark. The degree to which the manger is selecting stocks that are different from its benchmark. The volatility of the manager relative to its benchmark return. Many research professionals agree that an R- squared above.70 indicates a good fit between the manager and benchmark, validating the benchmark as suitable. Higher active share implies a greater amount of positions that are different from the benchmark, interpreted as a greater degree of stock picking. For an index or a passive manager, tracking error should be close to zero, while active managers, especially those that have produced significant excess return, usually have higher tracking errors. R-squared is used to select an appropriate benchmark. It helps identify the percentage of a manager s return that is specifically attributable to underlying benchmark volatility. The residual is active manager risk that may improve or reduce a manger s results based on their skills. A strong R- squared also provides confidence that the alpha and beta of the portfolio are reasonably accurate. A manger can only outperform a benchmark by taking positions that are different from the benchmark. Some amount of positive active share is a necessary but not sufficient condition for outperforming the benchmark. Investors can eliminate active risk by simply indexing their portfolios. Tracking error by itself is not necessarily good or bad. It can help identify the extent the investment experience may vary from the benchmark. A high tracking error may be useful in identifying potential style drift. ß 2 x m 2 p 2 ½ n w fund, i -w index, i i=1 n (AR i - AR avg ) 2 i=1 n-1 Manager A: 0.98 Manager B: 0.99 Both Manager A and Manager B have a good fit with the benchmark. Manager A: 65%* Manager B: 80%* * Because calculation of active share requires analysis of portfolio and benchmark holdings, which are not included in the case study, these results are estimated. Manager B engaged in a greater degree of stock picking relative to the benchmark than Manager A. Manager A: 3.59% Manager B: 5.07% Manager B s portfolio was more varied compared with the benchmark than Manager A s portfolio.
pared to a Benchmark Information Ratio IR Capture Ratio CR Correlation Coefficient ρ The information ratio provides guidance regarding a manager s ability to persistently produce returns above the benchmark. It is calculated by the excess return in the numerator divided by the tracking error, or consistency of excess return, in the denominator. The capture ratio is presented as two numbers, up-capture and down-capture. The downside capture ratio measures, on an absolute basis, how much of a benchmark s decline was captured by the portfolio. Downside capture ratio is calculated by dividing the portfolio performance by the benchmark performance during periods when the benchmark performance is negative. Upside capture ratio is similarly defined as the percentage portfolio return divided by the market return when the market rises. Correlation measures the relationship or association that two variables have to each other. It is calculated as the covariance between two investments divided by the product of their standard deviations. A manager s ability to add incremental value relative to incremental risk. The degree of under- or outperformance by a manager compared to the benchmark. The direction and degree of linear relation between two investments. A higher information ratio is desirable. Defensive portfolios would typically have downside capture ratios of less than 1.0. Aggressive portfolios would typically have upside capture ratios greater than 1.0. A high association between two variables means they tend to move in the same direction and a low association means they tend to diverge. A correlation of 1.0 represents perfect correlation, a correlation of -1.0 represents perfect negative correlation, and a correlation of 0.0 offers no predictive value. Some consider this metric a more sophisticated Sharpe ratio. Ideally, a manager would seek to add excess return in a consistent manner so that returns do not swing too far from their benchmark in any given period. The information ratio can be used to compare managers across asset classes. Capture ratios do not incorporate risk; they simply measure the under- or outperformance of a portfolio compared tothe benchmark. Blending assets that do not move in tandem may help reduce a portfolio s overall volatility. The correlation coefficient between two assets helps to determine the potential benefits of diversification. R p - R b TE Up (Down) Capture = Manager returns when benchmark is positive (negative) Benchmark returns when positive (negative) cov A, B A x B Manager A: 0.069 Manager B: 0.0986 Manager B s higher information ratio indicates a greater consistency in outperforming the benchmark. Manager A: 0.40 downside; 0.93 upside Manager B: 1.60 downside; 1.17 upside Manager A was more defensive (lower downside capture ratio), while Manager B was more aggressive (higher upside capture ratio). Correlation A, B : 0.97 Manager A and Manager B have high positive correlation, indicating the portfolios tend to move in tandem.
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