Options Trading and the CAPM

This article studies equilibrium asset pricing when agents facenonnegative wealth constraints. In the presence of these constraintsit is shown that options on the market portfolio are nonredundantsecurities and the economy's pricing kernel is a function ofboth the market portfolio and the nonredundant options. Thisimplies that the options should be useful for explaining riskyasset returns. To test the theory, a model is derived in whichthe expected excess return on any risky asset is linearly related(via a collection of betas) to the expected excess return onthe market portfolio and to the expected excess returns on thenonredundant options. The empirical results indicate that thereturns on traded index options are relevant for explainingthe returns on risky asset portfolios.     

Constructing Asset Pricing Models With Specific Factor Loadings

We demonstrate how one can build pricing formulae in which factors other than beta may be viewed as determinants of asset returns. This is important conceptually as it demonstrates how the additional factors can compensate for a market portfolio proxy that is mis‐specified, and also shows how such a pricing model can be specified ex ante. The procedure is implemented by first selecting an ‘orthogonal’ portfolio which falls on the mean‐variance efficient frontier computed from the empirical average returns, variances and covariances on the equity securities of a large sample of firms. One then determines the inefficient index portfolio which leads to a vector of betas that when multiplied by the average return on the orthogonal portfolio, and which when subtracted from the vector of average returns for the firms comprising the sample, yields an error vector that is equal to the vector of numerical values for the variables that are to form the basis of the asset pricing formula. There will then be a perfect linear relationship between the vector of average returns for the firms comprising the sample, the vector of betas based on the inefficient index portfolio and such other factors that are deemed to be important in the asset pricing process. We illustrate computational procedures using a numerical example based on the quality of information contained in published corporate financial statements.     

Equilibrium "Anomalies"

Many 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.     

Where do betas come from? Asset price dynamics and the sources of systematic risk

In this article we break asset's betas with common factors intocomponents attributable to news about future cash flows, realinterest rates, and excess returns. To achieve this decomposition,we use a vector autoregressive time-series model and an approximatelog-linear present value relation. The betas of industry andsize portfolios with the market are largely attributed to changingexpected returns. Betas with inflation and industrial productionreflect opposing cash flow and expected return effects. We alsoshow how asset pricing theory restricts the expected excessreturn components of betas.     

Are the Latent Variables in Time-Varying Expected Returns Compensation for Consumption Risk?

Multibeta asset pricing models are examined using proxies for economic state variables in a framework which exploits time-varying expected returns to estimate conditional betas. Examples include multiple consumption-beta models and models where asset returns proxy for the state variables. When the state variables are not specified, the tests indicate two or three time-varying expected risk premiums in the sample of quarterly asset returns. Conditional betas relative to consumption generate less striking evidence against the model than betas relative to asset returns, but both the consumption and the market variables fail to proxy for the state variables.     

On the Cross-sectional Relation between Expected Returns and Betas

There is an exact linear relation between expected returns and true “betas” when the market portfolio is on the ex ante mean-variance efficient frontier, but empirical research has found little relation between sample mean returns and estimated betas. A possible explanation is that market portfolio proxies are mean-variance inefficient. We categorize proxies that produce particular relations between expected returns and true betas. For the special case of a zero relation, a market portfolio proxy must lie inside the efficient frontier, but it may be close to the frontier.     

Cashflow news,the value premium and an asset pricing view on European stock market integration

The decomposition of national CAPM market betas of European countries’ value and growth portfolio returns into cashflow and discount rate news driven components reveals that i) high average returns on value portfolios are associated with disproportionately high sensitivity to national cashflow news which corroborates recent evidence for the U.S. and ii) two-beta variants of national CAPMs capture the cross-sectional dispersion in European stock returns. The latter finding is suggestive of relatively well integrated stock markets among the core European countries and reflects basic asset pricing theory. One (national) discount factor should price any (international) asset.     

Linear beta pricing with efficient/inefficient benchmarks and short-selling restrictions

We provide two security pricing models that can be used when short sales of risky securities are not permitted. The first model uses a benchmark located on the expected return-standard deviation efficient frontier without short sales and presents security expected returns as a weighted linear function of two betas, one induced by the benchmark and the other adjusting for the short-sale constraints. The second model uses a benchmark that is inefficient relative to the efficient frontier, does not allow short sales, and expresses security returns as a weighted linear function of three betas:one induced by the inefficient benchmark, and the other two adjusting simultaneously for the short-sales restrictions and the benchmark's inefficiency.These results complement the linear pricing models that link expected returns and betas by allowing, for efficient or inefficient expected return-standard deviation, benchmarks with restricted short sales.     

An analysis of the importance of S&;P 500 discretionary constituent changes

The main purpose of this paper is to investigate the impact of the S&P 500 index committee’s decisions to change the constituent firms in the index on benchmark risk measures. The index is managed and changed discretionally by the index committee to make it as representative of the market condition as possible. In addition, the index constantly changes due to important corporate events such as bankruptcies, mergers and acquisitions, and spin-offs. We reconstruct market portfolios by retaining all discretionally deleted firms in a 3 and 5 year periods. We estimate betas at every deletion date in terms of reconstructed market portfolios; we found that these estimate betas are significantly different from the betas obtained from the constantly updated S&P 500 portfolio. We also found that such portfolios are less representative of the business cycle than the actual S&P 500 portfolio. Finally, we found that the portfolio returns obtained by retaining all discretionally deleted firms deviate significantly from the returns of the actual S&P 500 index over the studied period, October 1989 to December 2007.     

Risky asset pricing based on safety first fund management

We study a portfolio selection model based on Kataoka's safety-first criterion (KSF model in short). We assume that the market is complete but without risk-free asset, and that the returns are jointly elliptically distributed. With these assumptions, we provide an explicit analytical optimal solution for the KSF model and obtain some geometrical properties of the efficient frontier in the plane of probability risk degree z _α and target return r _α. We further prove a two-fund separation and tangency portfolio theorem in the spirit of the traditional mean-variance analysis. We also establish a risky asset pricing model based on risky funds that is similar to Black's zero-beta capital asset pricing model (CAPM, for short). Moreover, we simplify our risky asset pricing model using a derivative risky fund as a reference for market evaluation.     

Changes in Expected Security Returns,Risk, and the Level of Interest Rates

Regressions of security returns on treasury bill rates provide insight about the behavior of risk in rational asset pricing models. The information in one-month bill rates implies time variation in the conditional covariances of portfolios of stocks and fixed-income securities with benchmark pricing variables, over extended samples and within five-year subperiods. There is evidence of changes in conditional “betas” associated with interest rates. Consumption and stock market data are examined as proxies for marginal utility, in a general framework for asset pricing with time-varying conditional covariances.     

Sentiment-scaled CAPM and market mispricing

This study explores the conditional version of the capital asset pricing model on sentiment to provide a behavioural intuition behind the value premium and market mispricing. We find betas (β) and the market risk premium to vary over time across different sentiment indices and portfolios. More importantly, the state β derived from this sentiment-scaled model provides a behavioural explanation of the value premium and a set of anomalies driven by mispricing. Different from the static β–return relation that gives a flat security market line, we document upward security market lines when plotting portfolio returns against their state βs and portfolios with higher state βs earn higher returns.     

Trading Volume: Implications of an Intertemporal Capital Asset Pricing Model

We derive an intertemporal asset pricing model and explore its implications for trading volume and asset returns. We show that investors trade in only two portfolios: the market portfolio, and a hedging portfolio that is used to hedge the risk of changing market conditions. We empirically identify the hedging portfolio using weekly volume and returns data for U.S. stocks, and then test two of its properties implied by the theory: Its return should be an additional risk factor in explaining the cross section of asset returns, and should also be the best predictor of future market returns.     

Equity market valuation of human capital and stock returns

We investigate whether and how well firms’ stock market valuations reflect their employees’ collective skills and effectiveness relative to that of their industry peers and competitors. We devise a relative stock market valuation measure of human capital intangibles (EVHC) and find that portfolios of low EVHC firms systematically outperform portfolios of high EVHC firms by an average 1.34% per month. However, this is primarily a small firms effect, because for large firms the excess returns of the arbitrage portfolio that is long on the low EVHC stocks and short on the high EVHC stocks is zero. Our results suggest that reliance on human capital intangibles may proxy for risk not fully accounted for by conventional asset pricing models, or alternatively, that the market cannot correctly price human capital intangibles for small size firms.     

Heteroskedasticity in Stock Returns

We use predictions of aggregate stock return variances from daily data to estimate time-varying monthly variances for size-ranked portfolios. We propose and estimate a single factor model of heteroskedasticity for portfolio returns. This model implies time-varying betas. Implications of heteroskedasticity and time-varying betas for tests of the capital asset pricing model (CAPM) are then documented. Accounting for heteroskedasticity increases the evidence that risk-adjusted returns are related to firm size. We also estimate a constant correlation model. Portfolio volatilities predicted by this model are similar to those predicted by more complex multivariate generalized-autoregressive-conditional-heteroskedasticity (GARCH) procedures.     

Sources of risk and expected returns in global equity markets

This paper empirically examines multifactor asset pricing models for the returns and expected returns on eighteen national equity markets. The factors are chosen to measure global economic risks. Although previous studies do not reject the unconditional mean variance efficiency of a world market portfolio, our evidence indicates that the tests are low in power, and the world market betas do not provide a good explanation of cross-sectional differences in average returns. Multiple beta models provide an improved explanation of the equity returns.     

A dynamic model of active portfolio management with benchmark orientation

This paper studies optimal dynamic portfolios for investors concerned with the performance of their portfolios relative to a benchmark. Assuming that asset returns follow a multi-linear factor model similar to the structure of Ross (1976) [Ross, S., 1976. The arbitrage theory of the capital asset pricing model. Journal of Economic Theory, 13, 342–360] and that portfolio managers adopt a mean tracking error analysis similar to that of Roll (1992) [Roll, R., 1992. A mean/variance analysis of tracking error. Journal of Portfolio Management, 18, 13–22], we develop a dynamic model of active portfolio management maximizing risk adjusted excess return over a selected benchmark. Unlike the case of constant proportional portfolios for standard utility maximization, our optimal portfolio policy is state dependent, being a function of time to investment horizon, the return on the benchmark portfolio, and the return on the investment portfolio. We define a dynamic performance measure which relates portfolio’s return to its risk sensitivity. Abnormal returns at each point in time are quantified as the difference between the realized and the model-fitted returns. Risk sensitivity is estimated through a dynamic matching that minimizes the total fitted error of portfolio returns. For illustration, we analyze eight representative mutual funds in the U.S. market and show how this model can be used in practice.     

Index tracking with utility enhanced weighting

Passive index investing involves investing in a fund that replicates a market index. Enhanced indexation uses the returns of an index as a reference point and aims at outperforming this index. The motivation behind enhanced indexing is that the indices and portfolios available to academics and practitioners for asset pricing and benchmarking are generally inefficient and, thus, susceptible to enhancement. In this paper we propose a novel technique based on the concept of cumulative utility area ratios and the Analytic Hierarchy Process (AHP) to construct enhanced indices from the DJIA and S&P500. Four main conclusions are forthcoming. First, the technique, called the utility enhanced tracking technique (UETT), is computationally parsimonious and applicable for all return distributions. Second, if desired, cardinality constraints are simple and computationally parsimonious. Third, the technique requires only infrequent rebalancing, monthly at the most. Finally, the UETT portfolios generate consistently higher out-of-sample utility profiles and after-cost returns for the fully enhanced portfolios as well as for the enhanced portfolios adjusted for cardinality constraints. These results are robust to varying market conditions and a range of utility functions.     

Market proxies as factors in linear asset pricing models: Still living with the roll critique

A new model misspecification measure for linear asset pricing models is proposed for the case where misspecification maps to latency of one of the pricing factors; in this case, the market return. This measure is suited both for testing models that include the market return as a pricing factor in a traditional sense (i.e., whether the chosen model does or does not price a collection of risky assets) and ranking those models (i.e., determining which model performs best). The proposed measure is used in pricing portfolios reflecting the size, value, and momentum premia. The conditional CAPM of Jagannathan and Wang (1996) is found to best the performance of both the simple CAPM and the ICAPM of Petkova (2006). Moreover, it is discovered that winner stocks in a momentum portfolio may have higher market betas than loser stocks.     

The Causal Effect of Limits to Arbitrage on Asset Pricing Anomalies

We examine the causal effect of limits to arbitrage on 11 well-known asset pricing anomalies using the pilot program of Regulation SHO, which relaxed short-sale constraints for a quasi-random set of pilot stocks, as a natural experiment. We find that the anomalies became weaker on portfolios constructed with pilot stocks during the pilot period. The pilot program reduced the combined anomaly long–short portfolio returns by 72 basis points per month, a difference that survives risk adjustment with standard factor models. The effect comes only from the short legs of the anomaly portfolios.