Generalized parameter functions for option pricing

We extend the benchmark nonlinear deterministic volatility regression functions of Dumas et al. (1998) to provide a semi-parametric method where an enhancement of the implied parameter values is used in the parametric option pricing models. Besides volatility, skewness and kurtosis of the asset return distribution can also be enhanced. Empirical results, using closing prices of the S&P 500 index call options (in one day ahead out-of-sample pricing tests), strongly support our method that compares favorably with a model that admits stochastic volatility and random jumps. Moreover, it is found to be superior in various robustness tests. Our semi-parametric approach is an effective remedy to the curse of dimensionality presented in nonparametric estimation and its main advantage is that it delivers theoretically consistent option prices and hedging parameters. The economic significance of the approach is tested in terms of hedging, where the evaluation and estimation loss functions are aligned.     

Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices

Implicit in the prices of traded financial assets are Arrow–Debreu prices or, with continuous states, the state-price density (SPD). We construct a nonparametric estimator for the SPD implicit in option prices and we derive its asymptotic sampling theory. This estimator provides an arbitrage-free method of pricing new, complex, or illiquid securities while capturing those features of the data that are most relevant from an asset-pricing perspective, for example, negative skewness and excess kurtosis for asset returns, and volatility "smiles" for option prices. We perform Monte Carlo experiments and extract the SPD from actual S&P 500 option prices.     

Speculative trading and stock returns: A stochastic dominance analysis of the Chinese A-share market

The pricing of A-shares in China has long puzzled financial economists. This paper applies recent tests of stochastic dominance (SD) to examine whether differences in the return distributions of A- and B-shares in China are consistent with market efficiency. As SD is nonparametric, market efficiency can be examined without the joint test problem arising from misspecifications in the asset pricing benchmark. Our results show A-shares have second-order dominated B-shares from 1996 to 2005. This dominance was most significant during the market segmentation period, but has continued, albeit to a lesser extent even after the B-share market was opened to local investors in 2001. Our results are robust to using residual returns from an international asset pricing model instead of raw returns. We conclude that the superior performance of A-shares cannot be attributed to risk. The results are more likely due to a return bias caused by intense speculation among retail individuals under limited arbitrage.     

Systematic Risk and Empirical Research

We show here that risky asset returns generating processes stated in terms of factors which include both accounting and non-accounting based measures of risk (e.g. book to market ratios) imply, under fairly standard regularity conditions, that the Sharpe-Lintner-Black asset pricing model beta is a 'sufficient' statistic in the sense that it captures all important attributes of the returns generating process in a single number. We then derive the parametric relationship between betas based on inefficient index portfolios and betas based on the market or tangency portfolio. We demonstrate that the relationship between risky asset expected returns and betas computed on the basis of inefficient index portfolios is both consistent with the predictions of the Capital Asset Pricing Model and the multi-factor asset pricing models of Fama and French (1992, 1993, 1995 and 1996). The 'trick' is to realise that inefficient index portfolios are composed of the market portfolio and a collection of inefficient but self financing 'kernel' or 'arbitrage' portfolios. It then follows that there is a perfect linear cross sectional relationship between risky asset expected returns, betas based on inefficient index portfolios and the arbitrage portfolios. Hence, if we happen to stumble across variables that span the same subspace as the vectors representing the arbitrage portfolios, it is easy to create the illusion that risky asset expected returns depend on variables other than 'beta'.     

Portfolio allocation using multivariate variance gamma models

In this paper, we investigate empirically the effect of using higher moments in portfolio allocation when parametric and nonparametric models are used. The nonparametric model considered in this paper is the sample approach; the parametric model is constructed assuming multivariate variance gamma (MVG) joint distribution for asset returns.We consider the MVG models proposed by Madan and Seneta (1990), Semeraro (2008) and Wang (2009). We perform an out-of-sample analysis comparing the optimal portfolios obtained using the MVG models and the sample approach. Our portfolio is composed of 18 assets selected from the S&P500 Index and the dataset consists of daily returns observed from 01/04/2000 to 01/09/2011.     

Conditional beta pricing models: A nonparametric approach

We propose a two-stage procedure to estimate conditional beta pricing models that allows for flexibility in the dynamics of asset betas and market prices of risk (MPR). First, conditional betas are estimated nonparametrically for each asset and period using the time-series of previous data. Then, time-varying MPR are estimated from the cross-section of returns and betas. We prove the consistency and asymptotic normality of the estimators. We also perform Monte Carlo simulations for the conditional version of the three-factor model of Fama and French (1993) and show that nonparametrically estimated betas outperform rolling betas under different specifications of beta dynamics. Using return data on the 25 size and book-to-market sorted portfolios, we find that the nonparametric procedure produces a better fit of the three-factor model to the data, less biased estimates of MPR and lower pricing errors than the Fama–MacBeth procedure with betas estimated under several alternative parametric specifications.     

The specification of conditional expectations

This paper explores different specifications of conditional expectations. The most common specification, linear least squares, is contrasted with nonparametric techniques that make no assumptions about the distribution of the data. Nonparametric regression is successful in capturing some nonlinearities in financial data, in particular, asymmetric responses of security returns to the direction and magnitude of market returns. The technique is ideally suited for empirically modeling returns of securities that have complicated embedded options. The conditional mean and variance of the NYSE market return are also examined. Forecasts of market returns are not improved with the nonparametric techniques which suggests that linear conditional expectations are a reasonable approximation in conditional asset pricing research. However, the linear model produces a disturbing number of negative expected excess returns. My results also indicate that the relation between the conditional mean and variance depends on the specification of the conditional variance. Furthermore, a linear model relating mean to variance is rejected and these tests are not sensitive to the expectation generating mechanism nor the conditioning information. Rejections are driven by the distinct countercyclical variation in the ratio of the conditional mean to variance.     

Alternative beta risk estimators and asset pricing tests in emerging markets: The case of Pakistan

This paper tests and compares the applicability of two asset pricing models specifically, the CAPM and the Fama–French three factor models for an emerging stock market namely, Pakistan. The paper analyses a number of beta risk estimators, including OLS, the Dimson thin trading estimator, a trade-to-trade estimator and a sample selectivity estimator. To uncover any possible influence of the return interval and the type of the market index, the analysis is carried out on three data frequencies namely daily, weekly and monthly as well as for a value and an equally weighted market index. The alternative beta estimators appear to correct thin trading bias but their effects on asset pricing tests are not visible. Moreover contrary to the expectations the test results for monthly and weekly frequencies are not promising. Instead for daily data the cross-section of returns are explained by a number of risk factors and trading volume.     

Consumption Fluctuations and Expected Returns

This paper introduces a novel consumption-based variable, cyclical consumption, and examines its predictive properties for stock returns. Future expected stock returns are high (low) when aggregate consumption falls (rises) relative to its trend and marginal utility from current consumption is high (low). We show that the empirical evidence ties consumption decisions of agents to time variation in returns in a manner consistent with asset pricing models based on external habit formation. The predictive power of cyclical consumption is not confined to bad times and subsumes the predictability of many popular forecasting variables.     

Do industries matter in explaining stock returns and asset-pricing anomalies?

Industry returns cannot be explained fully by well-known asset pricing models. This study reveals that common factors extracted from industry returns carry significant risk premiums that go beyond the explanatory power of size, book-to-market (BM) ratios, and momentum. In particular, this study shows that (1) the small-firm effect is significant only for firms whose market capitalization is below their industry average; (2) the BM effect is an intra-industry phenomenon; (3) a one-year momentum effect is significant only for firms whose BM ratio is smaller than the industry average and limited to non-January months; and (4) there is seasonality in all effects that cannot be explained by risk-based asset-pricing models. Neither rational nor behavioral theories alone can explain industry returns, and it is perhaps too hasty to attribute asset pricing anomalies to a single driving force.     

Sources of Entropy in Representative Agent Models

We propose two data‐based performance measures for asset pricing models and apply them to models with recursive utility and habits. Excess returns on risky securities are reflected in the pricing kernel's dispersion and riskless bond yields are reflected in its dynamics. We measure dispersion with entropy and dynamics with horizon dependence, the difference between entropy over several periods and one. We compare their magnitudes to estimates derived from asset returns. This exercise reveals tension between a model's ability to generate one‐period entropy, which should be large, and horizon dependence, which should be small.     

Explaining abnormal returns in stock markets: An alpha-neutral version of the CAPM

This paper develops a behavioural asset pricing model in which traders are not fully rational as is commonly assumed in the literature. The model derived is underpinned by the notion that agents’ preferences are affected by their degree of optimism or pessimism regarding future market states. It is characterized by a representation consistent with the Capital Asset Pricing Model, augmented by a behavioural bias that yields a simple and intuitive economic explanation of the abnormal returns typically left unexplained by benchmark models. The results we provide show how the factor introduced is able to absorb the “abnormal” returns that are not captured by the traditional CAPM, thereby reducing the pricing errors in the asset pricing model to statistical insignificance.     

The evolution of capital asset pricing models

The capital asset pricing models (CAPM) has been the benchmark of asset pricing models and has been used to calculate asset returns and the cost of capital for more than four decades. Many researchers have tried to relax the original assumptions and generalize the static CAPM. We survey the important alternative theoretical models of capital asset pricing and provide a complete review of the evolution of asset pricing models. We also discuss the interrelationships among these models and suggest several possible directions for future research. Our results might be used as a guideline for future theoretical and empirical research in capital asset pricing.     

Common asset pricing factors in volatilities and returns in futures markets

Factor-based asset pricing models have been used to explain the common predictable variation in excess asset returns. This paper combines means with volatilities of returns in several futures markets to explain their common predictable variation. Using a latent variables methodology, tests do not reject a single factor model with a common time-varying factor loading. The single common factor accounts for up to 53% of the predictable variation in the volatilities and up to 14% of the predictable variation in the means. S&P500 futures volatility predicted by the factor model is highly correlated with volatility implied in S&P500 futures options. But both the factor and implied volatilities are significant in predicting future volatility. In derivatives pricing, both implied volatility from options and factors extracted from asset pricing models should be employed.     

Testing asset pricing models with changing expectations and an unobservable market portfolio

When the assumption of constant risk premiums is relaxed, financial valuation models may be tested, and risk measures estimated without specifying a market index or state variables. This is accomplished by examining the behavior of conditional expected returns. The approach is developed using a single risk premium asset pricing model as an example and then extended to models with multiple risk premiums. The methodology is illustrated using daily return data on the common stocks of the Dow Jones 30. The tests indicate that these returns are consistent with a single, time-varying risk premium.     

The restrictions on predictability implied by rational asset pricing models

This article shows how rational asset pricing models restrictthe regression-based criteria commonly used to measure returnpredictability. Specifically it invokes no-arbitrage argumentsto show that the intercept, slope coefficients, and R² in predictiveregressions must take specific values. These restrictions providea way to directly assess whether the predictability uncoveredusing regression analysis is consistent with rational pricing.Empirical tests reveal that the returns on the CRSP size decilesare too predictable to be compatible with a number of well-knownpricing models. However, the overall pattern of predictabilityacross these portfolios is reasonably consistent with what wewould expect under circumstances where predictability is rational.     

BUSINESS CYCLES AND STOCK MARKET RETURNS: EVIDENCE USING INDUSTRY-BASED PORTFOLIOS

Much evidence has emerged recently that suggests stock returns are predictable. In representative agent consumption-based asset pricing models, asset returns are related to aggregate output and consumption through changes in the intertemporal marginal rate of substitution. An alternative view is that the amount of variation required in the intertemporal marginal rate of substitution is too large to be rationally explained. We shed further light on this debate by investigating whether the stock returns of certain sectors of the economy can predict future market returns even after controlling for the information contained in the aggregate market index. In the consumption-based models, aggregate output and consumption affect the discount rates of all assets synchronously; no particular sectoral return should have any more predictive ability than the others. We find evidence that the stock returns of five industry-based portfolios have significant information about future market returns that is not in the market index. This stylized empirical result is not consonant with existing models relating output to stock returns.     

The Robustness of the APT to Alternative Estimators

We test the robustness of the APT to two alternative estimation procedures: the Fama and MacBeth (1973) two-step methodology; and the one-step procedure due to Burmeister and McElroy (1988). We find that the APT is indeed sensitive to the chosen estimator and assumptions about the factor structure of stock returns. We believe that our findings have implications for the estimation of asset pricing models in general.     

上市公司综合盈利水平与股票收益

本文基于2000-2017年上市公司的财务及股票交易数据,研究了上市公司综合盈利水平与股票收益之间的关系。我们使用目前资产定价文献中较新的偏最小二乘法和组合预测法,从12个衡量公司盈利能力的指标中提取了一个测度上市公司综合盈利水平的指标。研究结果显示,上市公司综合盈利水平能够显著预测未来股票收益。使用单因子偏最小二乘法、取12个月斜率的平均值构造的综合盈利水平最有效,以其构建的多空对冲投资组合能产生15%的年平均收益,夏普比率达到0.75。与此对应,组合预测法提取的上市公司综合盈利水平的预测能力稍低,但依然显著。在控制了其他公司特征变量后,综合盈利水平对于股票收益的解释能力依然稳健。本文还从经济机制的角度出发,探讨了综合盈利水平对收益的预测来源。我们发现,上市公司综合盈利水平与股票预期回报的正向关系在投资摩擦更低的组中更高,而在错误定价程度更高的组通常更低。这些结果支持了基于投资摩擦的Q理论,而与行为金融的错误定价理论相悖。