The Impact of Investment Constraints on Portfolio Performance Measurement: The Power Utility Function Case

This paper examines the effect of investment constraints on performance measurement of institutionally managed funds. Assuming that these funds have a power utility function and using an optimal portfolio choice model, one can show that the Security Market Line remains a valid benchmark for these constrained funds under the perfect market assumption. Relaxing the perfect market assumption, one can prove that a non-stationary constrained investment policy will bias traditional measures of timing ability differently across managers types. Finally, the magnitude of this bias is illustrated with a numerical example.     

A note on capital asset pricing and heterogeneous taxes

In this paper, we present a stylized model where we show how asset prices, i.e., required expected rates of returns, may be characterized in a world with heterogeneous asset taxes. Within a simple CAPM-like framework, we derive an after-tax beta equal to the pre-tax beta multiplied by a (non-obvious) asset specific tax adjustment. We further show in what sense the Security Market Line here can be replaced by a Security Market Fan. Well-known CAPM relations are obtained as special cases, and policy implications are analyzed.     

Mean-variance hedging for continuous processes: New proofs and examples

Let be a special semimartingale of the form and denote by the mean-variance tradeoff process of . Let be the space of predictable processes for which the stochastic integral is a square-integrable semimartingale. For a given constant and a given square-integrable random variable , the mean-variance optimal hedging strategy by definition minimizes the distance in between and the space . In financial terms, provides an approximation of the contingent claim by means of a self-financing trading strategy with minimal global risk. Assuming that is bounded and continuous, we first give a simple new proof of the closedness of in and of the existence of the F?llmer-Schweizer decomposition. If moreover is continuous and satisfies an additional condition, we can describe the mean-variance optimal strategy in feedback form, and we provide several examples where it can be computed explicitly. The additional condition states that the minimal and the variance-optimal martingale measures for should coincide. We provide examples where this assumption is satisfied, but we also show that it will typically fail if is not deterministic and includes exogenous randomness which is not induced by .     

Investment Policy Implications of the Capital Asset Pricing Model

The results of previous generalized Security Market Line (SML) tests of the Mean Variance (MV) and Linear Risk Tolerance (LRT) Capital Asset Pricing Models indicate that the models are empirically identical. A very widely accepted, but technically incorrect, explanation for the results is that with normal return distributions all expected utility maximizing riskaverse investors will pick MV portfolios. The paper shows that the generalized SML tests cannot distinguish between the MV model and a much wider variety of power utility LRT models than has previously been entertained. On the other hand, with approximately normal, or real world, return distributions the investment policies of the various models are shown to be different from each other, and from the MV policy in particular. To the extent the results of the portfolio selection calculations are robust, the results of, and implications drawn from, the tests of the macro pricing relations are not based on firm micro foundations.     

The Impact of Sampling Errors on the Choice of Portfolio Efficiency Analysis Rules with Borrowing and Lending of a Riskless Asset

This paper evaluates the impact of sampling errors on portfolio decisions using mean-variance and stochastic dominance rules where riskless borrowing and lending opportunities exist. The paper establishes criteria for comparing the alternative decision rules (for example, mean variance versus stochastic dominance) according to their effectiveness and the cost (in sampling error terms). Normal distributions are simulated using various assumed means, standard deviations, correlations, and sample sizes. These simulations enable one to evaluate the impact of sampling errors on the potential effectiveness of the empirical stochastic dominance and mean variance rules that include borrowing and lending of a riskless asset.     

The Expected Return and Exercise Time of Merton-style Real Options

We analyse the rate of return and expected exercise time of Merton-style options (1973) employed in many real option situations where the possibility of exercise is both perpetual and American in nature. Using risk-neutral and risk-adjusted pricing techniques, Merton-style options are shown to have an expected return that is a constant percentage of the option value and independent of the proximity to the critical exercise boundary. Merton options thus remain at the same point on the Security Market Line, unlike European options whose position and rate of return change dynamically. We also present formulae for the expected time and discounted times to exercise and analyse the dependency of these variables on volatility.     

Two Paradigms and Nobel Prizes in Economics: a Contradiction or Coexistence?

Abstract Markowitz and Sharpe won the Nobel Prize in Economics for the development of Mean‐Variance (M‐V) analysis and the Capital Asset Pricing Model (CAPM). Kahneman won the Nobel Prize in Economics for the development of Prospect Theory. In deriving the CAPM, Sharpe, Lintner and Mossin assume expected utility (EU) maximisation in the face of risk aversion. Kahneman and Tversky suggest Prospect Theory (PT) as an alternative paradigm to EU theory. They show that investors distort probabilities, make decisions based on change of wealth, exhibit loss aversion and maximise the expectation of an S‐shaped value function, which contains a risk‐seeking segment. Can these two apparently contradictory paradigms coexist? We show in this paper that although CPT (and PT) is in conflict to EUT, and violates some of the CAPM's underlying assumptions, the Security Market Line Theorem (SMLT) of the CAPM is intact in the CPT framework. Therefore, the CAPM is intact also in CPT framework.     

Testing and Aggressive Investment Strategy Using Value Line Ranks: A Reply

This paper answers the comments of readers of our earlier paper. Additional insight is gained by adding recent data to show the effect of following Value Line Investment Service recommendations in active stock market trading over the years 1974–81. We show that Value Line makes a statistically significant contribution, which cannot be explained by the Beta risk factor. We offer our results as an unexplained divergence from the Efficient Market Hypothesis, but with the tentative hypothesis that investment timing (i.e., the fact that the Efficient Market Hypothesis does not operate instantaneously) may explain much of the abnormality.     

Speculative Betas

The risk and return trade‐off, the cornerstone of modern asset pricing theory, is often of the wrong sign. Our explanation is that high‐beta assets are prone to speculative overpricing. When investors disagree about the stock market's prospects, high‐beta assets are more sensitive to this aggregate disagreement, experience greater divergence of opinion about their payoffs, and are overpriced due to short‐sales constraints. When aggregate disagreement is low, the Security Market Line is upward‐sloping due to risk‐sharing. When it is high, expected returns can actually decrease with beta. We confirm our theory using a measure of disagreement about stock market earnings.     

对证券一级市场审批制的反思

本文通过对世界证券市场形成及发展的模式、结构研究,并深入分析中国证券一级市场的建构,解析一级市场实操中出现的种种弊端,反思中国证券一级市场的发展方向.     

Benchmark Invariancy,Seasonality and APM-Free Portfolio Performance Measures

The Jobson-Korkie (1981) Z score and the positive period weighting (PPW) score of Grinblatt and Titman (1989) are applied to various benchmarks of market and mimicking portfolios to study the benchmark invariancy problem. Significantly different portfolio performance inferences are found for a sample of 146 equity mutual funds depending on the mean-variance efficiency of the portfolio benchmarks (mimicking portfolios versus market indices). Portfolio performance inferences are affected significantly by the number of factors, nonsynchronous trading adjustment, and the sizes of the firms used for factor extraction. The returns of the portfolio benchmarks exhibit significant monthly seasonalities, which, in turn, significantly influence mutual fund performance inferences.     

Robust optimal strategies for an insurer with reinsurance and investment under benchmark and mean-variance criteria

In this paper, an ambiguity-averse insurer (AAI) whose surplus process is approximated by a Brownian motion with drift, hopes to manage risk by both investing in a Black–Scholes financial market and transferring some risk to a reinsurer, but worries about uncertainty in model parameters. She chooses to find investment and reinsurance strategies that are robust with respect to this uncertainty, and to optimize her decisions in a mean-variance framework. By the stochastic dynamic programming approach, we derive closed-form expressions for a robust optimal benchmark strategy and its corresponding value function, in the sense of viscosity solutions, which allows us to find a mean-variance efficient strategy and the efficient frontier. Furthermore, economic implications are analyzed via numerical examples. In particular, our conclusion in the mean-variance framework differs qualitatively, for certain parameter ranges, with model-uncertainty robustness conclusions in the framework of utility functions: model uncertainty does not always result in an agent deciding to reduce risk exposure under mean-variance criteria, opposite to the conclusions for utility functions in Maenhout and Liu. Our conclusion can be interpreted as saying that the mean-variance problem for the AAI explains certain counter-intuitive investor behaviors, by which the attitude to risk exposure, for an AAI facing model uncertainty, depends on positive past experience.     

Evaluation of linear asset pricing models by implied portfolio performance

We present a theoretical perspective that motivates the use of the Generalized Least Squares R-Square, prominently advocated by Lewellen et al. [Lewellen, J., Nagel, S., Shanken, J., forthcoming. A skeptical appraisal of asset-pricing tests. Journal of Financial Economics], as an evaluation measure for multivariate linear asset pricing models. Adapting results from Shanken [Shanken, J., 1985. Multivariate tests of the zero-beta CAPM. Journal of Financial Economics 14, 327–348] and Kandel and Stambaugh [Kandel, S., Stambaugh, R.F., 1995. Portfolio inefficiency and the cross-section of expected returns. Journal of Finance 50, 157–184], we provide various interpretations and a graphical account in mean-variance space of this measure, facilitating a better understanding of its properties. We furthermore relate it to another leading evaluation metric, the HJ-distance of Hansen and Jagannathan [Hansen, L.P., Jagannathan, R., 1997. Assessing specification errors in stochastic discount factor models. Journal of Finance 52, 557–590]. Additionally, we present a comparison between these evaluation measures using mean-variance mathematics in risk-return space, and we provide a simple formula for calculating both model evaluation measures that involves only the parameters of the mean-variance asset and factor frontiers.     

An explicit bound on individual assets' deviations from APT pricing in a finite economy

Ross's Arbitrage Pricing Theory (APT) is a tractible and reasonable alternative to the mean-variance model. Nonetheless, understanding of the theory has been obscured by the complexity of the sequence economy models used for motivation. By contrast, we give a simple and direct derivation of the APT in a finite economy. Using an explicit bound on the deviations from APT prices across assets, a coarse calculation shows that theoretical deviations from APT pricing are negligible in our economy.     

我国金融市场中基准利率的选择北大核心

本文从资产定价角度给出了基准利率选择的理论框架,并对我国市场中的利率体系进行研究。我们发现,在均值一方差标准下,银行间隔夜同业拆借利率和银行间隔夜国债回购利率并不是最有效的;银行间同业拆借市场与银行间国债回购市场内部各利率与期限之间的关系不是单调的;银行间同业拆借市场利率与银行间国债回购利率之间并不存在绝对的占优关系;相比之下,存款利率尤其是活期存款利率最有效从而更适合作为其他资产定价的依据,应该成为我国目前金融市场的基准利率。最后,本文给出了相应的建议。     

Exact distribution-free tests of mean-variance efficiency

This paper develops exact distribution-free tests of unconditional mean-variance efficiency. These new tests allow for unknown forms of non-normalities, conditional heteroskedasticity, and other non-linear temporal dependencies among the absolute values of the error terms in the asset pricing model. Exactness here rests on the assumption that the joint temporal error density is symmetric around zero. This still leaves open the possibility of return distribution asymmetry via coskewness with the benchmark portfolio. A simulation study shows that the new tests have very good power relative to that of many commonly used tests. The inference procedures developed are further illustrated by tests of the mean-variance efficiency of a market index using a 42-year sample of monthly returns on ten U.S. equity portfolios.     

Econometrical analysis of the sample efficient frontier

The efficient frontier is a parabola in the mean-variance space which is uniquely determined by three characteristics. Assuming that the portfolio asset returns are independent and multivariate normally distributed, we derive tests and confidence sets for all possible arrangements of these characteristics. Note that all of our results are based on the exact distributions for a finite sample size. Moreover, we determine a confidence region of the whole efficient frontier in the mean-variance space. It is shown that this set is bordered by five parabolas.     

Relative Performance Evaluation of Mutual Funds: A Non-Parametric Approach

We propose an alternative mutual fund performance index which addresses the benchmark problem and controls for economies of scale in managing mutual funds. We advance a new concept of 'return-cost' efficiency as another important element in evaluating portfolio management, in addition to the mean-variance efficiency concept. Our index based on a non-parametric estimation is shown to be similar to the Sharpe index with multiple slopes (or factors). We have shown that all fund categories, except income funds, have similar average efficiency scores after controlling for economies of scale. Most funds operate in increasing returns to scale and seem to be successful in holding mean-variance efficient portfolios, but unsuccessful in allocating transaction costs efficiently, evidenced by excessive turnovers and loads.     

Tests of the foreign exchange risk premium using the expected second moments implied by option pricing

This paper utilizes the second moment expectations implied by currency option pricing to demonstrate that these expectations are systematically related to expected return differentials across assets denominated in different currencies. Because the measured deviations from uncovered interest rate parity are tied to variables which theory links to the risk premium, the results provide substantial evidence that a risk premium does indeed exist, as opposed to the alternative of a violation of rational expectations. However, like previous attempts, the data do not support an explicit mean-variance formulation of the risk premium.     

International portfolio selection and efficiency analysis

In the risk-return tradeoff, the traditional mean-variance analysis has been widely used for studies of international portfolio efficiency and diversification. Without prior knowledge about either the parametric structure of assets' return distributions or the form of investors' preference functions, the variance may no longer serve as a suitable risk proxy. This article examines international portfolio efficiency and diversification effects through mean-variance and various distribution-free (or less restrictive) risk-return measures. We show empirically that the mean-variance model is appropriate for large or well-diversified portfolios, but may provide biased results for single assets and less diversified portfolios. While stochastic dominance stands as theoretically the most appropriate method of international portfolio selection and efficiency analysis, the lack of optimal search algorithms reduces its practical usefulness. Very little gain is obtained by using the Gini-mean-difference risk measure as compared to the semivariance measure. The semivariance measure is a powerful and convenient discriminator of risky prospects, while stochastic dominance can serve as a benchmark to justify portfolio efficiency.