Ruminations on Investment Performance Measurement

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1 eufm_ eufm00v.cls (0/0/ v. Standard LaTeX document class) --0 : EUFM eufm_ Dispatch: --0 CE: N/A Journal MSP No. No. of pages: 0 PE: Yvonne Ling 0 0 European Financial Management, 0 doi: 0./j.-0X.0.00.x Ruminations on Investment Performance Measurement Wayne E. Ferson Marshall School of Business, University of Southern California, 0 Troudale Parkway Suite, Los Angeles, CA 00, USA ferson@marshall.usc.edu Abstract This is a summary of a keynote address to the European Financial Management Symposium on Asset Management in April 0. It makes five observations about the state of the art in investment performance measurement. First, the traditional alphas used in performance measurement are not to be trusted as normative indicators for when to buy or sell funds, but Stochastic Discount Factor (SDF) alphas are better. Traditional alphas can be equivalent to the correct SDF alphas, but this requires that an Appropriate Benchmark be used. Third, mean variance efficient portfolios are almost never Appropriate Benchmarks. Fourth, Sharpe ratios can be justified as performance measures, if they are properly used. Finally, current holdings-based approaches to performance measurement are also flawed, but I offer some suggestions for improving them. Keywords: mutual funds, hedge funds, bond funds, stochastic discount factors, portfolio holdings, bootstrap, market efficiency, portfolio management JEL classification: G, G, G. Introduction It is a great honour to deliver a keynote address to the European Financial Management Symposium. In this address I collect and summarise some of the ideas that I have been thinking about and have presented in some form, in a stream of recent papers (Ferson (00, 0), Ferson and Lin (0), Ferson and Mo (0) and Aragon and Ferson, 00). I make several observations about the state of the art in investment performance measurement. First, the traditional alphas used in the literature are not to be trusted as normative indicators for when to buy or sell funds, but Stochastic Discount Factor I would like to acknowledge financial support from the Ivadelle and Theodore Johnson Chair in Banking and Finance at the Marshall School of Business, University of Southern California. This address collects and summarises some of the ideas in a stream of recent research, including Ferson (00), Ferson (0), Ferson and Lin (0), Ferson and Mo (0) and Aragon and Ferson (00). Q Q C 0 Blackwell Publishing Ltd

2 eufm_ eufm00v.cls (0/0/ v. Standard LaTeX document class) --0 : 0 0 Wayne E. Ferson (SDF) alphas are better. Traditional alphas can be equivalent to the correct SDF alphas, but this requires that an Appropriate Benchmark be used. Despite a traditional focus on mean variance efficient portfolios, these are almost never appropriate benchmarks. However, seemingly in contrast to conventional wisdom, Sharpe ratios can be justified as performance measures when they are used properly, by comparing the Sharpe ratio of the fund to be evaluated with the Sharpe ratio of an Appropriate Benchmark. Finally, current holdings-based approaches to performance measurement are also flawed, although under certain conditions they can be equivalent to the correct SDF alpha. These conditions are strong and unlikely to be met in practice, so I offer suggestions for how to improve the implementation of holdings-based performance measures. The remainder of this paper is organised as follows. Section reviews the problems with traditional alphas and the argument that the stochastic discount factor (SDF) alpha is a superior performance measure. Section describes the Appropriate Benchmark and shows that mean variance efficient portfolios are almost never Appropriate Benchmarks. Section shows how Sharpe ratios can be justified as performance measures. Section describes how current holdings-based measures are flawed and presents an illustration of how these flaws may be addressed. Section concludes.. Traditional Alphas and SDF alphas. Troubles with traditional alphas Studies of investment performance routinely use various traditional measures of alpha, referring to CAPM alpha, three-factor alpha or four-factor alpha, assuming the reader hardly requires a definition. Despite the familiarity with these traditional alphas, the literature has only partially resolved a basic question: Given a fund with a positive (negative) alpha, will an investor want to buy (sell) that fund? The simplest intuition for the attractiveness of a positive alpha is taught with the CAPM, where a combination of a positive-alpha fund, the market portfolio and cash can beat the market in a mean variance sense (higher mean return given the variance). Dybvig and Ross (b) show that if a fund has a positive alpha measured relative to a benchmark, then buying some of the fund at the margin will result in a higher Sharpe ratio than that of the benchmark, if the benchmark excess return is positive. The literature also offers many examples where a traditional alpha is not a reliable buysell indicator. When there is differential information, the portfolio of a better-informed manager expands the opportunity set of the less-informed client, so the client would generally like to use the managed portfolio return. The problem is, the client might wish to short the fund even if it has a positive alpha (Chen and Knez, ). As Dybvig and Ross (a) and Grinblatt and Titman () show, a market timing manager with true ability can generate a negative alpha. We can find positive alphas when performance is neutral but leverage or options are used (e.g. Jagannathan and Korajczyk (), Leland, ) or we can find negative alphas when performance is neutral but you don t account for public information (Ferson and Schadt, ). Goetzmann et al. (00) show how option-like strategies can lead to absurd measured performance. Roll () and Green () give examples of arbitrary alphas when the benchmark used to define alpha is not mean variance efficient. Dybvig and Ross (a) and Hansen and Richard () show that a portfolio can be mean variance efficient given the informed manager s knowledge, but appear mean variance inefficient to the uninformed client. Glode (0) argues C 0 Blackwell Publishing Ltd Q Q Q

3 eufm_ eufm00v.cls (0/0/ v. Standard LaTeX document class) --0 : 0 0 Ruminations on Investment Performance Measurement that investors may wish to buy a fund even when it has a negative traditional alpha. Thus, the existing literature suggests that traditional alphas are not reliable signals for an investor s decision on whether to buy or sell a fund. But, if alpha doesn t indicate attractive investments, why do we routinely use it in the current literature as if it did?. The right SDF alpha The stochastic discount factor (SDF) approach appeared as early as Beja (), and became the common language of empirical asset pricing during the 0s. Glosten and Jagannathan () and Chen and Knez () were the first to develop SDF alphas for fund performance. A stochastic discount factor, m t+, is a scalar random variable, such that the following equation holds: E(m t+ R t+ Z t ) = 0, () where R t+ is the vector of the underlying asset gross returns (payoff at time t+ divided by price at time t), is an N-vector of ones and Z t denotes the investment client s or public information at time t. The elements of the vector m t+ R t+ maybeviewedas risk adjusted gross returns. The returns are risk adjusted by discounting them, or multiplying by the stochastic discount factor, m t+, so that the expected present value per dollar invested is equal to one dollar. An investment manager forms a portfolio of the assets with gross return R pt+ = x( t ) R t+, where x( t ) is the vector of portfolio weights and t is the manager s information at the beginning of the period, at time t. If t is more informative than Z t, the portfolio R pt+ may not be priced through equation (). That is, the manager may record abnormal performance, or nonzero alpha. (In what follows I will drop the time subscripts unless they are needed for clarity.) Define the SDF alpha for portfolio p as follows: α p = E(mR p Z). () In general, the SDF alpha is a function of the information Z, known to the investment client at the beginning of the period. If R Bt+ is any zero-alpha benchmark, equations () and () imply that the SDF alpha may also be written as: α p E(m [R p R B ] Z). Ferson and Lin (0) provide conditions under which the SDF alpha is a reliable guide for normative investment choice. The SDF is based on the client s utility function, assumed to be time-additive in a multiperiod model, where the indirect value function is J(W,s) and the SDF is m t+ = βj w (W t+,s t+ )/u c (C t ). Subscripts denote derivatives and s is a vector of state variables. The model presents the client with the opportunity to buy or sell a managed portfolio with return R p = x( ) R. The client adjusts to this new opportunity by changing her consumption and portfolio choices, until alpha is zero at the new optimum. The optimal amount purchased is proportional to the SDF alpha of the fund as defined by Equation (). Thus, the right alpha which provides a reliable buy-sell signal is the SDF alpha and it is, in general client-specific. This raises the question: Are there conditions under which the traditional alphas can be trusted? That is the subject of the next section. The manipulation proof performance measure of Goetzmann et al. (00) is a special case of this analysis, using a single period model and a specific utility function. C 0 Blackwell Publishing Ltd

4 eufm_ eufm00v.cls (0/0/ v. Standard LaTeX document class) --0 : 0 0 Wayne E. Ferson. The Appropriate Benchmark In empirical practice, a traditional alpha is almost always measured as the expected return of the fund in excess of a benchmark, E(R p R B Z). A classical example is Jensen s (, ) alpha, which follows from the Capital Asset Pricing Model (CAPM, Sharpe, ). Jensen s alpha is the expected excess return of the fund over a benchmark that combines the risk-free asset and the market index so as to have the same beta as the fund to be evaluated: α p = E[R p {β p R m + ( β p )R f }]. Jensen s alpha is also the intercept in a time-series regression of R p R f on R m R f. Jensen s alpha would be a reliable measure of performance if it coincided with the right, SDF alpha. What are the conditions under which this will occur? Ferson (00) defines an Appropriate Benchmark as one that has the same covariance with the relevant SDF as the portfolio to be evaluated. Thus, an appropriate benchmark has the same risk as the fund from the client s perspective. To see this, take the definition of the SDF alpha and rewrite it as: α p = E[m(R p R B ) Z] = E(m Z)E(R p R B Z) + Cov(m, R p R B Z). () The term E(m Z) is identical for all funds, and essentially translates the measures through time. E(m Z) is the price of a risk-free, one period bond and is measured at the beginning of the period, while the returns are measured at the end of the period. We see that the expected return in excess of a benchmark is essentially equivalent to the SDF alpha, if and only if Cov(m,R p Z) = Cov(m,R B Z); that, is, only if R B is an Appropriate Benchmark. When will the market portfolio-based benchmark of the CAPM be an Appropriate Benchmark? When the SDF is linear in the market portfolio return, the SDF approach is equivalent to the CAPM (e.g. Ferson, ). This situation is also equivalent to assuming that the client has a quadratic utility function defined over the benchmark return. The foreshadows the next result, which states that mean variance efficient portfolios are almost never Appropriate Benchmarks.. Mean-variance efficient benchmarks are almost never appropriate benchmarks The literature on traditional alphas is strongly influenced by the CAPM and often focuses on mean variance efficient benchmarks. For example, in the CAPM the market portfolio-based benchmark is mean variance efficient. Grinblatt and Titman () discuss mean variance efficient benchmarks. Chen and Knez () and Dalhquist and Soderlind () used mean variance efficient benchmarks and SDF alphas. Ferson (0) shows, using the SDF approach, that mean variance efficient portfolios are almost never appropriate. The argument is briefly reviewed here. A portfolio R B is minimum variance efficient if and only if it maximises the correlation to the SDF (e.g. Ferson, ). That is, we can write the SDF as: m = a + br B + u, with E(uR Z) = 0, if and only if R B is minimum variance efficient in the set of assets R, conditional on the information Z (the coefficients a and b may be functions of Z). The fund s portfolio, R p, has Cov(R p,m Z) = bcov(r p,r B Z) + Cov(R p,u Z). Therefore, if The Appropriate Benchmark is a special case of the more general Otherwise Equivalent portfolio defined by Aragon and Ferson (00), which considers aspects of the problem other than risk, such as costs and taxes. Q C 0 Blackwell Publishing Ltd

5 eufm_ eufm00v.cls (0/0/ v. Standard LaTeX document class) --0 : 0 0 Ruminations on Investment Performance Measurement R B is an Appropriate Benchmarks it implies Cov(R p,u Z) = 0. This occurs in two possible situations: (i) R B is conditionally minimum variance efficient in the more inclusive set of assets (R, R p ), in which case alpha is always zero and not very useful (Roll, ); or (ii) the SDF is exactly linear in R B (u = 0). This implies that the utility function behind the SDF is a quadratic function of R B. The quadratic utility, as is well-known, has a number of unappealing characteristics, such as increasing absolute risk aversion and satiation, and so is not very attractive. Nevertheless, outside of this setting a mean-variance efficient portfolio is not an Appropriate Benchmark.. Justifying the Sharpe Ratio The Sharpe ratio (Sharpe, ) for a portfolio p is defined as: SR p = E(r p )/σ (R p ), () where r p R p R f is the return of the portfolio p, net of the return, R f, to a safe asset or cash and σ (R p ) is the standard deviation or volatility of the portfolio return. The Sharpe ratio measures the degree to which a portfolio is able to yield a return in excess of the risk-free return to cash, per unit of volatility risk. The Sharpe ratio is traditionally thought to be inappropriate when returns are highly nonnormal. For example, Leland () shows that it is important to consider higher moments of the distributions if the performance measure is to accurately capture an investor s utility. Goetzmann et al. (00) show that by selling put options at fair market prices one can generate very high Sharpe ratios without investment skill. They also give an example where a manager with forecasting skill can have a low Sharpe ratio. Lo (00) presents examples where high frequency trading can generate high Sharpe ratios. Despite these perceived limitations, the Sharpe ratio is simple and is often used in practice as a measure of portfolio performance. Ferson (0) shows that, under certain conditions, the Sharpe ratio can be motivated as a valid performance measure. The argument is briefly reviewed here. The trick is to compare the Sharpe ratio of a fund with that of an Appropriate Benchmark. If the fund s Sharpe ratio exceeds that of the benchmark, we have: E(R p R f )/σ (R p ) > E(R B R f )/σ (R B ). () Let ρ be the correlation between the fund s return and the benchmark return, R B, and assume that the correlation is positive. Because the correlation is less than.0, it implies E(R p R f ) > [ρσ(r p )/σ (R B )] E(R B R f ). Recognising [ρσ(r p )/σ (R B )] as the regression beta of the fund s excess return on that of the benchmark, we see that that α p = E(R pt ) E[R ft + β p (R Bt R ft )] > 0; that is, the fund s expected return in excess of an Appropriate Benchmark portfolio that combines R B with cash, is positive. The Sharpe ratio is invariant to the use of leverage at a fixed risk-free rate. Thus, comparing the Sharpe Ratio of a managed fund to that of an Appropriate Benchmark, the Sharpe ratio of the fund is larger than that of the benchmark only if the SDF alpha is positive. This result suggests some interesting questions for future work. For example, there may be limiting situations under high-frequency trading where the Sharpe ratio of a fund can become infinite in the limit. In such cases a well-specified Appropriate Benchmark should also become infinite, and the difference between the two Sharpe ratios might still be useful. C 0 Blackwell Publishing Ltd Q

6 eufm_ eufm00v.cls (0/0/ v. Standard LaTeX document class) --0 : 0 0 Wayne E. Ferson. Holdings-based Performance Measures Grinblatt and Titman () derive a holdings-based measure in a single-period model where the returns and managers information are jointly normally distributed. Assuming nonincreasing absolute risk aversion on the part of the manager, they show that: Cov{x( ) r} > 0, () where x( ) is the optimal weight vector. Equation () says that the sum of the covariances between the weights of a manager with private information,, and the returns for the securities in a portfolio is positive. The idea is that a manager who increases the fund s portfolio weight in securities before they perform well, or who anticipates and avoids losers, has investment ability. It is important to note that under the normality assumption that justifies this result, a manager never gets a signal that volatility is going to change. From the definition of covariance we can implement () by demeaning the weights or the returns: Cov{x( ) r} = E{[x( ) E(x( ))] r} = E{x( )[r E(r)]}. Copeland and Mayers () demean returns, while Brinson et al. () and Grinblatt and Titman () demean the weights, introducing a set of benchmark weights, x B, as: Cov{x( ) r} = E{[x( ) x B ] r. With benchmark weights, the benchmark portfolio implied by the measure is r B = x B r, and E{[x( ) x B ] r is the average difference in the hypothetical returns of the fund and the benchmark portfolio. Ferson and Khang (00) develop the Conditional Weight-based Measure of performance (CWM), where controls for changes in expected returns and volatility are introduced through a set of lagged instruments, Z t. The CWM = E{x(Z, ) [r E(r Z)]}, where x(z, ) denotes the portfolio weight vector at the beginning of the period. The weights may depend on the public information, denoted by Z. In weight-based measures the return of the fund is a hypothetical return, since it is constructed using a snapshot of the fund s actual weights at the end of a period (usually, at the end of a quarter or half-year) and the subsequent returns of the securities. These hypothetical returns reflect no trading within the quarter, no trading costs or management fees. Typically, the benchmark pays no costs either. Holdingsbased performance measures are thus fairly clean measures of managerial ability before costs, but they ignore the effects of interim trading between the reporting dates, and they may be subject to biases such as window dressing, where managers move to more favourable-looking positions before holdings reporting dates. Studies use fund holdings data for more than weight-based performance measures. A simple example is the return gap measure of Kacperczyk et al. (00), defined as r p x( ) r, where r p is the return reported by the fund. The return gap reflects trading within the quarter, trading costs and funds expenses. Cremers and Petajisto (00) propose a measure of active portfolio management, the Active Share: (/) x x B, the mean absolute difference between the fund s portfolio weights and those of its benchmark. Recent research has brought in the wide range of available data on the characteristics of the securities held by funds, allowing many creative analyses. This is a leading edge in fund performance research and Ferson (0) provides a review. Daniel et al. (DGTW, ) combine holdings, returns and characteristics of the stocks held by the fund. For a given fund, a benchmark is formed by matching the characteristics of each stock i in the portfolio held by the fund with benchmark portfolios, R t bi constructed for each stock to have matching characteristics. This is similar to the matching-firm approach used in some corporate finance studies. Specifically, each C 0 Blackwell Publishing Ltd

7 eufm_ eufm00v.cls (0/0/ v. Standard LaTeX document class) --0 : 0 0 Ruminations on Investment Performance Measurement security in the fund s portfolio is assigned to one of groups, depending upon its size, book-to-market ratio and lagged return. The benchmark for each stock is a valueweighted portfolio of the stocks in the characteristic group. DGTW () start with the Grinblatt and Titman () performance measure, introducing a set of benchmark weights equal a fund s actual holdings reported k periods before: x i,t k, to obtain: DGTW t+ = i x it ( Ri,t + R bi t + ) + i ( xit Rt bi + x i,t krt bi + (t k)) + bi(t k) x i,t k Rt + () i bi(t k) where R t+ is the benchmark return associated with security i at time t-k. The assumption, in order to have an Appropriate Benchmark, is that matching the characteristics of each stock implies a benchmark with the same covariance with m t+. However, as we will see shortly, this is not enough to justify the measure. The first term in () is interpreted as selectivity, the second term as characteristic timing and the third as the return attributed to style exposure. While the sum of the components is equal to, and thus has the same theoretical justification as the Grinblatt and Titman () measure, the individual terms are ad hoc, and no theoretical justification for their interpretation is known.. The flaws of current holdings-based measures First consider how a manager with superior information generates alpha. Substitute R p = x( ) R into () and use the definition of covariance to se that: α p = E(mR x( ) Z) = E(mR Z) E(x( ) Z) + Cov(mR x( ) Z) = Cov(mR x( ) Z). () Moving between the second and third lines, we use the facts that E(mR Z) is a vector of ones and that weights x( ) sum to one. Equation () shows that the SDF alpha is the sum of the covariances of the manager s weights with the future abnormal returns of the assets, mr. This is not what the literature on holdings-based performance has typically done. Instead of Cov(mR x( ) Z) studies have computed versions of Cov(R x( ) Z), leaving out the risk adjustment. Thus, the right way to do holdings-based performance measures in future work is to introduce risk adjustment. There are, of course, conditions under which the current approach to holdings based performance measurement can be justified, as shown by Ferson (0). The argument is summarised here. Assuming R B is an Appropriate Benchmark with Cov(m; [R p R B ] Z) = 0, we can expand Equation () as: αp = E(m Z){E(x( ) x B Z) E(R Z) + Cov(x( ) x B R Z)}, () and the first term is zero when E(x( )-x B Z) = 0. We then see that Equation () reduces to Cov([x( )-x B ] R Z), which is the measure that current holdings-based studies are built around. Summarising, current holdings-based measures can be justified, in the sense that they are equivalent to the SDF alpha, under three conditions: (i) The return defined by the benchmark weights, r B = x B r, is an Appropriate Benchmark return; (ii) the weight also satisfy E(x( ) Z) = x B ; and (iii) the alpha of the return r B = x B ris C 0 Blackwell Publishing Ltd

8 eufm_ eufm00v.cls (0/0/ v. Standard LaTeX document class) --0 : 0 0 Wayne E. Ferson zero. These represent a strong set of conditions that are unlikely to hold in practice. I conclude that it is probably better to just do the risk adjustment, as in Cov(mR x( ) Z), than it is to struggle to justify the existing measures. Grinblatt and Titman () show that Equation () holds only when all of the fund s holdings are used in the calculation. For example, a manager with information may overweight some assets and underweight others for hedging purposes, and if one side of the hedge is omitted the measure can be misleading. It is generally not justified to apply holdings-based measures to subsets of stocks. This problem is analogous to the problem of measuring the correct market portfolio in the CAPM.. An example of holdings-based performance with proper risk adjustment Ferson and Mo (0) provide an example of a holdings-based performance measure with proper risk adjustment. Using Equation (), they assume the SDF is given by linear factor models following Cochrane (): m = a b r B. This is admittedly a very strong assumption, and I present it here as an illustration. Consider a factor model regression for the excess returns of the N underlying securities: r = a + βr B + u, (0) where β is the N K matrix of regression betas and E(ur B ) = 0. Define the vector of abnormal, or idiosyncratic returns as the sum of the intercept plus residuals: v = a + u. (A similar decomposition is used by Kacperczyk et al., 0). A fund forms a portfolio using weights, x, and the excess returns are: r p = x r = (x β)r B + x v. Let w = x β be the asset allocation weights on the factor portfolios. Substituting into the definition of alpha in Equation (), and using the assumption that r B has zero alphas, Ferson and Mo (0) obtain: α p = acov(w r B ) b E{[r B r B E(r B r B )]w}+e{(a b r B )x v}. () The first term of () captures market level timing through the covariance between the portfolio weights and the subsequent factor returns. This is essentially the Grinblatt and Titman () measure applied at the asset allocation level. The second term captures volatility timing, through the relation between the portfolio weights and the second moment matrix of benchmark returns. Busse () finds evidence that volatility timing behavior may be present in US equity funds. The third term of () captures selectivity ability. This analysis shows that the original Grinblatt and Titman measure is misspecified in the presence of timing behaviour, suffering from a missing variables bias. This is because as noted above, their measure is developed under joint normality with homoskedasticity, so an informed manager never gets a signal that conditional volatility will change. Since the components of the DGTW measure sum to the Grinblatt and Titman measure, that measure also suffers from a potential missing variables bias.. Conclusions This address offers several observations on the state of the art in investment performance measurement, and a number of suggestions for improving the art. The traditional alphas used in performance measurement are not to be trusted as normative indicators for when to buy or sell funds, but Stochastic Discount Factor (SDF) alphas are better. One challenge for future research is to develop clientele-specific measures of performance in the SDF C 0 Blackwell Publishing Ltd

9 eufm_ eufm00v.cls (0/0/ v. Standard LaTeX document class) --0 : 0 0 Ruminations on Investment Performance Measurement framework, capturing the marginal utilities of different kinds of investors. Traditional alphas can be equivalent to the correct SDF alphas, but this requires that an Appropriate Benchmark be used. Mean variance efficient portfolios are almost never Appropriate Benchmarks. Interestingly, when the Sharpe ratios of funds are compared with those of Appropriate Benchmarks, they can be justified as performance measures. I offer a perspective on current holdings-based performance measures. Current implementations of these measures are flawed because they do not properly adjust for risk, except under very stringent assumptions. I conclude that future work on these measures should do the risk adjustment properly, and review one illustrative example. References Aragon, G. and Ferson, W., Portfolio performance evaluation, Foundations and Trends in Finance, Vol. :, 00, pp.. Beja, A.., The structure of the cost of capital under uncertainty, Review of Economic Studies, Vol,, pp.. Bhattacharya, S. and Pfleiderer, P., Delegated portfolio management, Journal of Economic Theory, Vol.,, pp.. Brinson, G., Hood, L. and Bebower, G., Determinants of portfolio performance, Financial Analysts Journal, Vol.,, pp.. Busse, J., Volatility timing in mutual funds: evidence from daily returns, Review of Financial Studies, Vol.,, pp. 00. Chen, Z., and Knez, P.J., Portfolio performance measurement: theory and applications, Review of Financial Studies, Vol.,, pp.. Cochrane, J.H., A cross-sectional test of an investment-based asset pricing model, Journal of Political Economy, Vol. 0,, pp.. Connor, G. and Korajczyk, RA., Performance measurement with the arbitrage pricing theory: a new framework for analysis, Journal of Financial Economics, Vol.,, pp.. Copeland, T. and Mayers D., The value line enigma ( ): a case study of performance evaluation issues, Journal of Financial Economics, Vo. 0,, pp.. Cornell, B., Asymmetric information and portfolio performance measurement, Journal of Financial Economics, Vol.,, pp. 0. Cremers, M. and Petajisto, A., How active is your fund manager? A new measure that predicts performance, Review of Financial Studies, Vol., 00, pp.. Daniel, K., Grinblatt, M., Titman, S. and Wermers, R., Measuring mutual fund performance with characteristic-based benchmarks, Journal of Finance, Vol.,, pp. 0. Dybvig, P. H. and Ingersoll, J.E., Mean variance theory in complete markets, Journal of Business, Vol.,, pp.. Dybvig, P. H., and Ross, S. A., The analytics of performance measurement using and a security market line, Journal of Finance, Vol., a, pp.. Dybvig, P. H. and Ross, S. A., Differential information and performance measurement using and a security market line, Journal of Finance, Vol., b, pp.. Farnsworth, H. K., Ferson, W., Jackson, D. and Todd, S., Performance evaluation with stochastic discount factors, Journal of Business, Vol., 00, pp.. Ferson, W., Theory and empirical testing of asset pricing models, in Jarrow, Maksimovic and Ziemba, eds, Finance, Handbooks in Operations Research and Management Science (Elsevier, ), pp. 00. Ferson, W., Investment performance evaluation, Annual Reviews of Financial Economics, Vol., 0, pp. 0. Ferson, W., Investment performance: a review and synthesis, in G. Constantinides, M. Harris and R. Stulz, eds, Handbook of Economics and Finance, forthcoming. C 0 Blackwell Publishing Ltd Q

10 eufm_ eufm00v.cls (0/0/ v. Standard LaTeX document class) --0 : Wayne E. Ferson Ferson, W. and Khang, K., Conditional performance measurement using portfolio weights: evidence for pension funds. Journal of Financial Economics, Vol., 00, pp.. Ferson, W. and Lin., J., Alpha and performance measurement: the effect of investor heterogeneity, Working Paper (University of Southern California, 0). Ferson, W. and Mo, H., Performance measurement with market and volatility timing and selectivity, Working Paper (University of Southern California. 0). Ferson, W., and Schadt, R., Measuring fund strategy and performance in changing economic conditions, Journal of Finance, Vol.,, pp.. Glosten, L. and Jagannathan, R., A contingent claims approach to performance evaluation, Journal of Empirical Finance, Vol.,, pp.. Goetzmann, W., Ingersoll, J. and Ivkovic, Z, Monthly measurement of daily timers, Journal of Financial and Quantitative Analysis, Vol., 000, pp. 0. Goetzmann, W., Ingersoll, J., Spiegel, M. and Welch, I., Portfolio performance manipulation and manipulation-proof measures, Review of Financial Studies, Vol., 00, pp.. Grinblatt, M. and Titman, S., Mutual fund performance: an analysis of quarterly portfolio holdings, Journal of Business, Vol., a, pp.. Grinblatt, M. and Titman, S., Portfolio performance evaluation: old issues and new insights, Review of Financial Studies, Vol., b, pp.. Grinblatt, M. and Titman, S., Performance measurement without benchmarks: an examination of mutual fund returns, Journal of Business, Vol. 0,,. Hansen, L. P. and Richard, S., The role of conditioning information in deducing testable restrictions implied by dynamic asset pricing models, Econometrica, Vol.,, pp.. Jagannathan, R. and Korajczyk, R., Assessing the market timing performance of managed portfolios, Journal of Business, Vol.,, pp.. Jensen, M. C., The performance of mutual funds in the period, Journal of Finance, Vol.,, pp.. Jensen, M. C., Optimal utilization of market forecasts and the evaluation of investment performance, in G. P. Szego and K. Shell, eds, Mathematical Methods in Finance (North-Holland Publishing Company, ). Jobson, J.D. and Korkie, R., Potential performance and tests of portfolio efficiency, Journal of Financial Economics, Vol. 0,, pp.. Kacperczyk, M.C., Sialm, C. and Zheng, L., Unobserved actions of mutual funds, Review of Financial Studies, Vol., 00, pp.. Kacperczyk, M.C, Van Nieuwerburgh, S. and Veldkamp, L., Time-varying manager skill, Working Paper (New York University, 0). Leland, H., Performance beyond mean-variance: performance measurement in a nonsymmetric world, Financial Analysts Journal, Vol.,, pp.. Roll, R., Ambiguity when performance is measured by the security market line. Journal of Finance, Vol.,, pp. 0. Sharpe, W.F., Capital asset prices: a theory of market equilibrium under conditions of risk. Journal of Finance, Vol.,, pp.. Sharpe, W.F., Asset allocation: management style and performance measurement, Journal of Portfolio Management, Vol.,, pp.. Wermers, R., Mutual fund performance: an empirical decomposition into stock-picking talent, style, transactions costs and expenses, Journal of Finance, Vol., 000, pp.. C 0 Blackwell Publishing Ltd

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12 USING e-annotation TOOLS FOR ELECTRONIC PROOF CORRECTION Required software to e-annotate PDFs: Adobe Acrobat Professional or Adobe Reader (version.0 or above). (Note that this document uses screenshots from Adobe Reader X) The latest version of Acrobat Reader can be downloaded for free at: Once you have Acrobat Reader open on your computer, click on the Comment tab at the right of the toolbar: This will open up a panel down the right side of the document. The majority of tools you will use for annotating your proof will be in the Annotations section, pictured opposite. We ve picked out some of these tools below:. Replace (Ins) Tool for replacing text.. Strikethrough (Del) Tool for deleting text. Strikes a line through text and opens up a text box where replacement text can be entered. Highlight a word or sentence. Click on the Replace (Ins) icon in the Annotations section. Type the replacement text into the blue box that appears. Strikes a red line through text that is to be deleted. Highlight a word or sentence. Click on the Strikethrough (Del) icon in the Annotations section.. Add note to text Tool for highlighting a section to be changed to bold or italic.. Add sticky note Tool for making notes at specific points in the text. Highlights text in yellow and opens up a text box where comments can be entered. Highlight the relevant section of text. Click on the Add note to text icon in the Annotations section. Type instruction on what should be changed regarding the text into the yellow box that appears. Marks a point in the proof where a comment needs to be highlighted. Click on the Add sticky note icon in the Annotations section. Click at the point in the proof where the comment should be inserted. Type the comment into the yellow box that appears.

13 USING e-annotation TOOLS FOR ELECTRONIC PROOF CORRECTION. Attach File Tool for inserting large amounts of text or replacement figures.. Add stamp Tool for approving a proof if no corrections are required. Inserts an icon linking to the attached file in the appropriate pace in the text. Click on the Attach File icon in the Annotations section. Click on the proof to where you d like the attached file to be linked. Select the file to be attached from your computer or network. Select the colour and type of icon that will appear in the proof. Click OK. Inserts a selected stamp onto an appropriate place in the proof. Click on the Add stamp icon in the Annotations section. Select the stamp you want to use. (The Approved stamp is usually available directly in the menu that appears). Click on the proof where you d like the stamp to appear. (Where a proof is to be approved as it is, this would normally be on the first page).. Drawing Markups Tools for drawing shapes, lines and freeform annotations on proofs and commenting on these marks. Allows shapes, lines and freeform annotations to be drawn on proofs and for comment to be made on these marks.. Click on one of the shapes in the Drawing Markups section. Click on the proof at the relevant point and draw the selected shape with the cursor. To add a comment to the drawn shape, move the cursor over the shape until an arrowhead appears. Double click on the shape and type any text in the red box that appears. For further information on how to annotate proofs, click on the Help menu to reveal a list of further options: