File Name: portfolio performance measurement and benchmarking .zip
Louis K. Chan, Stephen G.
The measures are categorized based on the general way they are computed: asset selection vs. We show that several categories have been exhausted while some others feature very heterogeneous ways to assess performance within the same sets of objectives. Introduction Since the introduction of the Sharpe ratio in , many different measures of portfolio performance have been introduced in the scientific as well as practitioners literature. Yet, there exists no census of all of them. The most complete study so far is due to Le Sourd , but it mentions about fifty different measures1.
From an exhaustive review of the relevant literature, we have identified one hundred and one portfolio performance measures2. The main purpose of this paper is to provide a taxonomy of them. It naturally involves the identification of categories, in which we gather those measures that display common characteristics. Hence, we do not only provide an exhaustive list, but also a partition of the performance measurement area in homogenous categories.
Whenever there exists a performance measure that provides a proper generalization of any measure within the same category, then common sense dictates the usage of this particular measure and the abandonment of any other attempt to research further in that direction.
A general typology Insert exhibit 1 approximately here Exhibit 1 displays the structure of the simple binary classification tree proposed in this paper. In the first level, we distinguish the types of skills reflected in the measures, namely asset selection versus market timing. Measures that reflect asset selection are themselves split according to the individualization of performance.
Finally, in the category of risk-adjusted performance measures, all corresponding measures can be classified according to a double entry table. The first dimension represents the measure of value creation, whether it is an excess return or a gain potential.
The second dimension reports the type of performance translation, in relative ratio or absolute difference terms. Each category corresponds to a given section or sub-section. The sub-classifications are made according to how risk is measured.
Absolute risk 3. Sharpe ratio and close variations The original measure of this kind is the Sharpe ratio [Sharpe, ], defined as the ratio of the mean return in excess of the risk free rate over its standard deviation. Simplicity and ease of interpretation are the main strengths of this ratio4.
For these reasons, it is still widely used by financial institutions to compare the performance of mutual funds. Central to the usefulness of the Sharpe Ratio is the fact that an excess return represents the result of a "zero-investment strategy".
So, it represents the payoff from a unit of investment financed by borrowing. First, it does not quantify the value added, if any: it is only a ranking criterion. The risk free rate is constant and identical for lending and borrowing. In its computation, the choice of risk-free rate is important, as it affects rankings — though the impact is rather weak. The Sharpe ratio is an absolute measure that does not refer to a benchmark. Considering the point of view of the investor, his investment horizon must match the performance measurement period.
Furthermore, as it measures the total risk, Sharpe ratio is only suitable for investors who invest in only one fund. In case of aggregation of portfolios, its consolidation is not straightforward because of the covariance effects between volatilities.
Its interpretation is also difficult when it is negative: if risk increases, the Sharpe ratio also increases. With this measure, the values have a wider range in size, but do not give useful information in absolute. A problem rarely mentioned is the sampling error embedded in the values of the ratio. The estimate of the standard deviation is measured with statistical noise. Vinod and Morey  introduce the double Sharpe ratio, computed as the quotient of the Sharpe ratio estimate by its standard deviation.
To compute it, they use a bootstrapping methodology and generate a great number of resamplings from the original return sample. The assumption of a Gaussian returns distribution does not hold for many funds, in particular for hedge funds, so different statistical adaptations were proposed in the literature. Spurgin  shows that with the issuance of out-of-the-money options, the manager of a fund can enhance the Sharpe ratio by enhancing the mean-variance trade-off and altering the tail of his portfolio.
Mahdavi  introduces an adjusted Sharpe ratio ASR to evaluate assets whose return distribution is not normal. The approach is to transform the payoff so that its distribution will match that of the benchmark: once the return is transformed, the resulting Sharpe ratio of the asset can be directly compared to that of the benchmark, knowing the total payoffs from both instruments have exactly the same distributions.
He suggests a Sharpe ratio adapted to autocorrelation whose formula included a bias corrector. In fact, this is more a bias corrector than a true new measure. Even, the idea to multiply a performance measure by a bias corrector can be extended to every other performance measure.
The reference value in Sharpe ratio is the risk free rate. An interesting variation is proposed by Roy in , so fourteen years before Sharpe. He proposes to compare the return to a reserve return that is specific for the investor. Indeed, in many measures, authors use both the risk-free and the reserve return in the numerator. Despite all these statistical adaptations, most issues of the Sharpe ratio remain.
This explains why many variations of the Sharpe ratio were introduced. Other absolute risk measures 3. But most investors are only afraid of negative variations. The Sharpe ratio does not make any distinction between upside risk and downside risk. In the reward to half-variance index, introduced by Ang and Chua , the standard deviation is replaced by the half-variance which considers only the returns lower than the mean.
Pure downside-risk, i. Within this category, the most widely used measure is the Sortino ratio6 because of its flexibility. It combines previous measures, subtracting like Roy a reserve return in the numerator, and considering the same reserve return in the computation of the semi-variance at the denominator. Value at Risk is the measure selected by the investor who is mostly concerned by disasters, i.
Dowd [, ] calls it logically Sharpe ratio based on the Value at Risk. This measure also tackles one important drawback of the Sharpe ratio, its inability to distinguish between upside and downside risks. It also discriminates the irregular losses as opposed to repeated losses. It is particularly useful when making hedge decisions, as it permits to avoid the excessive use of micro hedges against individual risk exposures. The accurate numerical estimation of the VaR is computationally intensive and can be quite complex, especially needing large databases.
Its formula includes the third and fourth moments of the distribution, so also presenting the advantage to cover non normal distribution of returns. There are other issues related to the VaR. It is sensitive to the selected threshold, as conflicting results happen sometimes at different confidence levels.
As for any quantile measure, it is not sub- additive, which implies that portfolio diversification may lead to an increase of risk. It does not measure losses exceeding VaR, which are definitely of interest, even more than the VaR itself.
Finally, VaR has many local extremes, leading to unstable rankings. It assesses how deep is the loss in case of a disaster, and not anymore to estimate the threshold from where one can speak of disaster. They are too different to be attached to a specific group, and we list them with their main characteristics. This ratio is more robust to outliers than the Sharpe ratio. The Gini ratio, proposed by Yitzhaki , is the ratio between the excess return from the risk-free rate and its Gini coefficient.
Gini coefficient is a measure of dispersion that depends on the spread of values among themselves, rather than on the deviations about some fixed central point like the mean, as is computed the standard deviation. It is often used in the economics literature to measure income dispersion and the discriminatory power of rating models in credit risk management.
It shares many properties with the variance, but appears to be more informative for distributions that depart from normality. It also has the advantage of being linear. Young  introduces the Minimax ratio as the ratio between the expected excess return and the Minimax risk measure, the latter being the maximum loss over all past observations.
The Minimax ratio is easy to compute, but strongly affected by outliers in the historical data. Martin and Mc Cann  propose the Ulcer performance index. The denominator is the Ulcer index, computed as the quadratic mean of the percentage drops in value during the observed period; Ulcer index measures the depth and the duration of percentage drawdowns in price from earlier highs.
While remaining easy to compute, it presents a couple of concrete advantages compared to Sharpe ratio: it considers only downward changes, and the strings of losses that result in significant drawdowns in value are recognized.
Finally, the interest in finance to the stable modelling drives Rachev and Mittnik  to consider the stable ratio. Among many non-Gaussian distributions that are proposed in the literature to model asset returns that presents empirically an excess kurtosis, the stable Paretian distribution has unique distinctive characteristics that put it on the top of the list. The stable dispersion measure is the scale parameter of a stable Paretian distribution. The extension is here that performance is measured as a potential gain divided by a loss exposition.
The Bernardo-Ledoit gain-loss ratio has gained a lot of popularity thanks to Shadwick and Keating  who rebrand it under the name Omega. It is frequently used for hedge funds as it incorporates all the higher moments of the distribution.
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The portfolio performance evaluation involves the determination of how a managed portfolio has performed relative to some comparison benchmark. Performance evaluation methods generally fall into two categories, namely conventional and risk-adjusted methods. The most widely used conventional methods include benchmark comparison and style comparison. The risk-adjusted methods adjust returns in order to take account of differences in risk levels between the managed portfolio and the benchmark portfolio. The risk-adjusted methods are preferred to the conventional methods.
Explore a preview version of Portfolio Performance Measurement and Benchmarking right now. In order to make sound investment choices, investors must know the projected return on investment in relation to the risk of not being paid. Benchmarks are excellent evaluators, but the failure to choose the right investing performance benchmark often leads to bad decisions or inaction, which inevitably results in lost profits. The first book of its kind, Portfolio Performance Measurement and Benchmarking is a complete guide to benchmarks and performace evaluation using benchmarks. In one inclusive volume, readers get foundational coverage on benchmark construction, as well as expert insight into specific benchmarks for asset classes and investment styles. Starting with the basics—such as return calculations and methods of dealing with cash flows—this thorough book covers a wide variety of performance measurement methodologies and evaluation techniques before moving into more technical material that deconstructs both the creation of indexes and the components of a desirable benchmark.
Chapter 2 reviews the classical measures of portfolio performance developed between features explicit performance benchmarks for measuring the relative.
In service of this goal, we have been publishing net to LP medians and quartile breakpoints for key metrics like internal rate of return IRR , total value to paid-in capital TVPI , and distributions to paid-in capital DPI for decades. Over time, and as more investors allocate capital to private equity, the market has evolved to become increasingly sophisticated and competitive. In this context, fund-level net to LP benchmarks, while still necessary, are not always sufficient to the task. Enter investment-level benchmarking: aggregated pools of investments organized by year of investment, sector, geography, and so on.
Not a MyNAP member yet? Register for a free account to start saving and receiving special member only perks. The purpose of performance measurement is to help organizations understand how decision-making processes or practices led to success or failure in the past and how that understanding can lead to future improvements. Key components of an effective performance measurement system include these:. Clearly defined, actionable, and measurable goals that cascade from organizational mission to management and program levels;.
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