True Market Portfolio Research Articles

Real Economy Portfolio: The Market Risk Premium as a Source of Alpha

We all know that the stock market does not perfectly reflect the overall economy. The author shows that this fact has exciting implications for active equity management. If standard cap-weighted benchmarks fail to reflect the economy, they contain uncompensated risks and will underperform the true market portfolio. Although we can never hold the true market portfolio because of nontraded human capital and other constraints, the author builds a sector-level model that captures returns to labor, capital, and intermediate inputs in the entire US economy. A portfolio designed to replicate these exposures generates statistically significant alpha that is distinct from existing factors. TOPICS:Security analysis and valuation, portfolio construction, performance measurement Key Findings ▪ The market risk premium refers to all assets in the economy, and even broad stock market indexes are an imperfect proxy. ▪ We leverage classic results from input–output analysis and international trade theory to construct a real economy portfolio from listed equities that better replicates the underlying economy. The key is to upweight labor-intensive and under-represented economic activities. ▪ The real economy portfolio has delivered significant alpha that is distinct from known factors.

Optimizing the True Market Portfolio

Optimizing the True Market Portfolio

Is the CAPM a Biased Estimator of Market Risk?

The Capital Asset Pricing Model (CAPM) is often used to determine an appropriate return on equity for regulated utilities. However, the CAPM will sometimes produce unrealistically high or low results during times of excess market volatility. I hypothesize that these results do not indicate a failure in the model itself. Instead, they are caused by the traditional implementation of the CAPM and the underlying definition of risk used by many financial theorists.My paper uses 1997-2001 data to provide an empirical comparison of betas generated in a manner consistent with the capital asset pricing model (CAPM betas) to betas generated using a method based on market losses (“Alternative Betas”). I use psychological literature and a mathematical example to suggest that when a loss-based notion of risk is used, only those observations in which the market declines constitute market risk; and that the CAPM is a systematically biased estimator of market risk because the variability of gains receive the same weight as the variability of losses.In the CAPM world, there are only two types of risk: market risk (measured by beta), and firm-specific risk; with the assumption that only market risk will be rewarded since firm specific risk can be diversified away. The CAPM assumes that the market is mean-variance efficient; predicts that the constant term will be 0; and predicts that a security's risk premium is proportional to both beta and the risk premium of the market portfolio (Bodie, 1996). Mathematically, the risk premium is equal to β[E(rM) − rf], where rM is the market return and rf is the risk-free rate.In the 30 years since the initial publication of the CAPM, there have been numerous criticisms of the model in the financial literature. Studies have suggested that the CAPM is not testable because the composition of the true market portfolio is unknown (Roll, 1977); the constant term is positive and significant (Miller and Scholes, 1972); the estimated risk premium is significantly lower than the actual risk premium (Black, Jensen, and Scholes, 1972); non-systematic risk has a significant effect on excess returns (Lintner, 1965b); and the expected return-beta relationship is not fully consistent with empirical observations (Fama and MacBeth, 1973).

Why Track Inefficiency?

Benchmarks play an important role in assessing performance as a part of the investment process. Modern portfolio theory suggests that the benchmark of the true market portfolio on the efficient frontier is unknown. However, the S&amp;P 500 Index is often used as a proxy for the U.S. domestic equity market portfolio. In this study, the authors examine the efficiency of the S&amp;P 500.The results imply that more efficient subsets of the S&amp;P 500 are easily constructed by randomly selecting stocks across industry sectors within the S&amp;P 500. The implications of the study suggest portfolios consisting of fewer stocks equally weighted across industries are more efficient than the S&amp;P 500 Index. <b>TOPICS:</b>Portfolio theory, equity portfolio management, portfolio construction

The non-relevance of the elusive holy grail of asset pricing tests: The “true” market portfolio does not alter CAPM validity conclusions

Abstract Empirical evaluations of CAPM usually attach a caveat that rejection is conditional on the choice of market proxy. We explore the criticality of the proxy choice disclaimer. Using different proxies and comprehensive simulations of the unobserved “true” market in Fama–MacBeth tests of CAPM, we find that the significance ( t -statistics) corresponding to betas remain consistently unaltered, even if the proxy is a small fraction of or has a low correlation with the true market. The constancy of t -statistics persists in a simulated true-CAPM world as well: if CAPM is indeed valid, the choice of proxy is unlikely to reject it erroneously. Identity of the elusive true market portfolio and the choice of representative proxy cannot overturn conclusions on validity of CAPM based on Fama–MacBeth tests. Roll’s Critique, incontrovertible in theory, may be quite forgiving in practice – CAPM cannot be resurrected by a “closer” approximation of the elusive true market portfolio when it has commonly been rejected.

Intra- and Interobserver Agreement and Impact of Arterial Input Selection in Perfusion CT Measurements Performed in Squamous Cell Carcinoma of the Upper Aerodigestive Tract

CT Perfusion (CTP) has shown potential for assessing head and neck tumors. Our purposes were to assess the inter- and intraobserver agreement of CTP measurements and to investigate whether the selection of arterial input, ipsilateral versus contralateral to the tumor or left-versus-right external carotid artery (ECA), may affect CTP measurements in patients with squamous cell carcinoma (SCCA) of the upper aerodigestive tract. Twenty-six patients with SCCA were enrolled in this prospective study and underwent CTP. Data were analyzed by 2 expert readers and by an inexperienced reader for interobserver agreement and by the 2 expert readers for intraobserver agreement assessment, by using the ECA ipsilateral to tumor site as arterial input. All 3 readers repeated their analysis by using the ECA contralateral to tumor site as arterial input. Inter- and intraobserver agreement was assessed by using the Bland-Altman approach; CTP measurements by using ipsilateral-versus-contralateral or left-versus-right ECA were compared by using the Wilcoxon signed rank test. The geometric mean of the ratios (95% limits of agreement) for inter- and intraobserver agreement ranged from 0.96 (0.75-1.23) to 1.00 (0.92-1.10) for blood flow (BF), from 0.88 (0.63-1.21) to 1.00 (0.88-1.14) for blood volume (BV), from 0.96 (0.64-1.44) to 0.98 (0.76-1.27) for mean transit time (MTT), and from 0.85 (0.41-1.76) to 1.14 (0.70-1.86) for permeability surface area product (PS). Significantly higher tumor PS and MTT for 2 readers and lower tumor BF for 1 of 3 readers were observed when the arterial input was placed in the left ECA. BF, BV, and MTT demonstrated higher inter- and intraobserver agreement than PS. The selection of arterial input, right-versus-left ECA, may determine changes in CTP measurements in patients with SCCA of the upper aerodigestive tract.

Properties of Portfolio-Based Estimates of Market Risk Premia

We use simulation to assess the performance of conventional financial econometric methods in recovering accurate estimates of market risk premia. In this study, we focus particular attention on the properties of standard cross-sectional risk premium estimation methods using portfolios and make several contributions. First, we confirm a general finding reported elsewhere that standard cross-sectional regression methods can produce accurate point estimates of market risk premia under ideal conditions, but they typically have very large standard errors. Our simulations show that existing standard error adjustments generally have limited practical importance. We propose a bootstrap approach and show that it can produce suitable standard errors. Second, when the market index is misspecified, we demonstrate that the biases in market risk premium estimates can be huge, even when the market proxy is highly correlated with the true market portfolio. We show that the pure cross-sectional method, in which in-sample mean excess returns are regressed against in-sample portfolio betas, is generally superior to the Fama-MacBeth method in estimating market risk premia with the least bias. We also demonstrate that the optimal number of portfolios to use in cross-sectional regressions depends critically on the estimation method, the accuracy of the market proxy, and whether the aim is to compute the best point estimate of the market risk premium or the standard error of the estimate. Finally, as an alternative to the cross-sectional method, we find that the mean of an excess index return provides a more efficient estimate of the market risk premium compared with a cross-sectional estimate, but only when the market index employed for both closely approximates the true market portfolio.

Une méthode asymptotique pour tester la validité du modèle d’équilibre d’actifs financiers (MEDAF) avec pour exemple la bourse de Paris

One of the problems in testing the validity of the two-parameter CAPM is the determination of an efficient proxy market portfolio to represent the true market portfolio. We test the mean-variance efficiency of a pre-specified market portfolio by using a method proposed by Roll (1976) for testing the linear relation between the rate of return of an asset and its beta, and hence the mean-variance efficiency of a proxy market portfolio. This procedure exploits the asymptotic exact linearity condition of the rate of return and beta by measuring the rate of decrease of cross-sectional residual variance with respect to increasing time-series sample size. The technique is applied to samples of companies on the Paris Stock Exchange for the period 1969-1978: 144 companies and twenty-nine different time series. The results indicate that although the sum of the squared residuals of a CAPM-type regression declines as the number of time observations increases, the sum of the squared residuals does not approach zero as the temporal sample size increases, as would be required for the market proxy of our pre-specified sample to be efficient.

Self-consistent asset pricing models

We discuss the foundations of factor or regression models in the light of the self-consistency condition that the market portfolio (and more generally the risk factors) is (are) constituted of the assets whose returns it is (they are) supposed to explain. As already reported in several articles, self-consistency implies correlations between the return disturbances. As a consequence, the alphas and betas of the factor model are unobservable. Self-consistency leads to renormalized betas with zero effective alphas, which are observable with standard OLS regressions. When the conditions derived from internal consistency are not met, the model is necessarily incomplete, which means that some sources of risk cannot be replicated (or hedged) by a portfolio of stocks traded on the market, even for infinite economies. Analytical derivations and numerical simulations show that, for arbitrary choices of the proxy which are different from the true market portfolio, a modified linear regression holds with a non-zero value α i at the origin between an asset i's return and the proxy's return. Self-consistency also introduces “orthogonality” and “normality” conditions linking the betas, alphas (as well as the residuals) and the weights of the proxy portfolio. Two diagnostics based on these orthogonality and normality conditions are implemented on a basket of 323 assets which have been components of the S&P500 in the period from January 1990 to February 2005. These two diagnostics show interesting departures from dynamical self-consistency starting about 2 years before the end of the Internet bubble. Assuming that the CAPM holds with the self-consistency condition, the OLS method automatically obeys the resulting orthogonality and normality conditions and therefore provides a simple way to self-consistently assess the parameters of the model by using proxy portfolios made only of the assets which are used in the CAPM regressions. Finally, the factor decomposition with the self-consistency condition derives a risk-factor decomposition in the multi-factor case which is identical to the principal component analysis (PCA), thus providing a direct link between model-driven and data-driven constructions of risk factors. This correspondence shows that PCA will therefore suffer from the same limitations as the CAPM and its multi-factor generalization, namely lack of out-of-sample explanatory power and predictability. In the multi-period context, the self-consistency conditions force the betas to be time-dependent with specific constraints.

Equilibrium “Anomalies”

AbstractMany empirical “anomalies” are actually consistent with the single beta capital asset pricing model if the empiricist utilizes an equity‐only proxy for the true market portfolio. Equity betas estimated against this particular inefficient proxy will be understated, with the error increasing with the firm's leverage. Thus, firm‐specific variables that correlate with leverage (such as book‐to‐market and size) will appear to explain returns after controlling for proxy beta simply because they capture the missing beta risk. Loadings on portfolios formed on relative leverage and relative distress completely subsume the powers of the Fama and French (1993) returns to small minus big market capitalization (SMB) portfolios and returns to high minus low book‐to‐market (HML) portfolios factors in explaining cross‐sectional returns.

Calculating the misspecification in beta from using a proxy for the market portfolio

This study investigates the effects of the market portfolio being unknown on the estimation of beta in the CAPM. Providing an analysis of the impact of using a proxy for the market portfolio when the market portfolio is known. This allows one to ask and answer ‘if what’ questions, such as if portfolio A is the true market portfolio, what happens to beta if one uses portfolio B as a proxy for A. It is shown that for a given universe of investible assets, frequently used equally weighted and value weighted portfolios are far from the Markowitz market portfolio and thus the betas calculated with the equally weighted and value weighted portfolios are quite different from those obtained with the Markowitz portfolio. These calculations are based on sequential assumptions that one portfolio is a proxy whilst another is the actual market.

Reviving Beta? Bayesian Test of Efficiency and the CAPM

In this paper, we employ a Bayesian framework to test the CAPM while explicitly accounting for the unobservability of the true market portfolio. We derive the posterior model odds ratio for comparing the view that the proxy is perfect (exact efficiency) to the view that its correlation with the market portfolio is less than one (approximate efficiency). We also compare the prior and the posterior expected correlation between the proxy and the market portfolio using a new methodology to choose priors that is both analytically tractable and intuitive. In marked contrast to the existing literature, the main result is that, in general, the data do not provide clear evidence against the CAPM. Posterior correlations are generally high enough to suggest that a belief in approximate efficiency is reasonable. These new results illustrate the importance of carefully choosing priors, and they show that even apparently innocuous assumptions can have unforeseen consequences.

Estudo Empírico Sobre a Eficiência da Carteira Teórica do Índice Bovespa

The use of proxies for the market portfolio is a common practice in the finance field. Some scientific studies covering the basics of the theory of capital markets depend on the consideration of the market portfolio, which is treated as the benchmark portfolio for the entire capital market, especially when using theories derived from the so-called "portfolio theory", whose precursor was Harry Markowitz (1952, 1959), who created the basis for nearly everything that is studied in relation to investment decisions under uncertainty. Markowitz made an important contribution in the field of study of the relationship between risk and return, defining key concepts such as diversification effect, the efficient set and the tangency portfolio among others. His first study in the field of modern finance theory was an article published in 1952 in The Journal of Finance, entitled Portfolio Selection. Later, in 1959 he wrote a book on the subject with the same title as the original article. Despite the fact that capital market modern theory defines and uses the market portfolio, especially when dealing with the equilibrium model of bond prices called the capital asset pricing model (CAPM) as it is known, it is impossible to observe the true market portfolio. It is understood as market portfolio that portfolio which is formed by all assets that could be traded in the economy. Therefore, it comprehends all the so-called financial assets which involve primary rights on future cash flows and other assets representing wealth from the standpoint of the investor, such as real estate, artwork, rarities etc. It's easy to see how difficult it is if not impossible from a practical standpoint, to build the market portfolio, even periodically. As to organized markets, it is easier to get the value and asset prices as it happens, for example, with the stock market. But in other markets, even when lacking a clearing system, it is impossible to assert correct values to the assets traded. Inevitably what ends up happening is the creation of proxies, i.e., approximate representations of real market portfolio, especially when studying empirically or applying in practice the theories related to capital markets. Roll (1977), in his famous critique to the empirical tests of CAPM, argues it is impossible to observe the market portfolio, which in turn implies a lack of objectivity to conclude the validity of the model quoted. The CAPM empirical tests eventually end up being, according to Roll, efficiency tests of the market portfolio, once the mentioned model requires that such tests, to which all titles are referenced, be efficient in terms of mean and variance. In this study we try to evaluate the Bovespa index portfolio performance, which is the main market index used in Brazil in terms of risk and return. It would be desirable that the proxy of our market was a good representation of the true market portfolio, which means to position itself on the efficient frontier related to the risky assets traded in our market. However, by the construction methodology of the index theoretical portfolio it is difficult to imagine that the same is part of such frontier. The efficiency of the index was statistically tested using procedures detailed in the article.

THE BENCHMARK BETA, CAPM, AND PRICING ANOMALIES

THE area of finance owes, in a large measure, its emergence as a scientific discipline to the advent of the capital asset pricing model (CAPM) which describes the determination of asset prices in an equilibrium framework. It is noted that in the classical CAPM of Sharpe (1964), Lintner (1965), and Mossin (1966), the structure of capital market equilibrium is presented in a highly parsimonious way, relating the equilibrium asset returns to a single risk factor, namely, the market beta. This parsimonious approach enables the equilibrium asset pricing relationship to be expounded in a simple and intuitively appealing way, thereby helping the CAPM to become one of the dominant paradigms in modern finance. Recently, however, the CAPM appears to have lost some of its earlier appeal for at least two reasons. First, Roll (1977) casts a serious doubt on the testability of the CAPM. As is well known, Roll forcefully argued that the only testable implication of the CAPM is the mean-variance efficiency of the market portfolio, and that the model is really neither testable nor applicable unless the true market portfolio is known. Because of the Roll critique, the CAPM is widely regarded as a theory without clear observational consequences. Second, researchers such as Friend and Blume (1970), Banz (1981), and Reinganum (1981) documented various asset pricing 'anomalies' unexplained by the CAPM. Friend and Blume, for instance, found that Jensen's alpha, which is supposedly a 'risk-adjusted' performance measure, is strongly inversely related to the level of beta risk. Banz and Reinganum, on the other hand, found that stock returns are negatively related to firm size even after controlling for the effect of beta risk. The Roll critique prompted several researchers to devise alternative ways of testing the CAPM taking into account the unobservability of the market portfolio. Kandel and Stambaugh (1987) and Shanken (1987), for instance, developed and tested the joint hypothesis that the true market portfolio is mean-variance efficient and that the proxy and true market portfolios are highly correlated. Their test results generally rejected the hypothesis for the assumed correlation of.7 or higher. Gibbons and Ferson (1985), on the other hand, tested a restriction derived from the temporal behavior of conditional expected returns and failed to reject a single-factor pricing hypothesis. While their findings are inconclusive so far, these researchers and others made serious attempts to mitigate the Roll critique (see footnote 1, base of next page). In contrast, however, no serious efforts were made to explain various asset pricing anomalies in terms of the unobservability of the market portfolio. In the present

Multivariate proxies and asset pricing relations

Abstract A framework is developed in which inferences can be made about the validity of an equilibrium asset pricing relation, even though the central aggregate in this relation is unobservable. A multivariate proxy for the true market portfolio, consisting of an equal-weighted stock index and a long-term government bond index, is employed in an investigation of the Sharpe-Lintner CAPM. The empirical evidence suggests that we can reject the joint hypothesis that (a) CAPM is valid, and (b) multiple correlation between the true market portfolio and proxy assets exceeds 0.7. Connections to the equilibrium factor pricing literature are also explored.

The Arbitrage Pricing Theory: Is it Testable?

ABSTRACTThis paper challenges the view that the Arbitrage Pricing Theory (APT) is inherently more susceptible to empirical verification than the Capital Asset Pricing Model (CAPM). The usual formulation of the testable implications of the APT is shown to be inadequate, as it precludes the very expected return differentials which the theory attempts to explain. A recent competitive‐equilibrium extension of the APT may be testable in principle. In order to implement such a test, however, observation of the return on the true market portfolio appears to be necessary.

The Arbitrage Pricing Theory: Is it Testable?

This paper challenges the view that the Arbitrage Pricing Theory (APT) is inherently more susceptible to empirical verification than the Capital Asset Pricing Model (CAPM). The usual formulation of the testable implications of the APT is shown to be inadequate, as it precludes the very expected return differentials which the theory attempts to explain. A recent competitive-equilibrium extension of the APT may be testable in principle. In order to implement such a test, however, observation of the return on the true market portfolio appears to be necessary.

A critique of the asset pricing theory's tests Part I: On past and potential testability of the theory

Testing the two-parameter asset pricing theory is difficult (and currently infeasible). Due to a mathematical equivalence between the individual return/‘beta’ linearity relation and the market portfolio's mean-variance efficiency, any valid test presupposes complete knowledge of the true market portfolio's composition. This implies, inter alia, that every individual asset must be included in a correct test. Errors of inference inducible by incomplete tests are discussed and some ambiguities in published tests are explained.