Covariance Of Returns Research Articles

Asset Pricing Models in China Stock Market

Harry Markowitz (1959) develops mean-variance Based on this model, Sharpe (1964), Lintner (1965) and Black (1972) build CAPM. However, empirical findings are not in favor of CAPM. Then，Merton (1973) generalizes CAPM and proposes ICAPM. Afterwards, Fama and French (1996) take the idea of Ross (1976)'s arbitrage pricing theory and construct a three-factor model. The three-factor model explains the covariation in average returns. The purpose of this study is to explore explanatory power of asset pricing models to investor behavior in China stock market. Findings of this study are that Fama French three-factor model better explains time-series variation in stock return than CAPM based on different sample data. Size effect exists in Shanghai and China stock market. However, value effect is found only in Shanghai stock market. This study also shows that unlike Fama French (1996), firms with low E/P ratios tend to have higher returns and firms with higher E/P ratios tend to have lower returns in Shanghai stock market. Robustness tests show that Fame French three-factor model is robust.

Can Stochastic Discount Factor Models Explain the Cross Section of Equity Returns?

We propose a multivariate test based on no-arbitrage conditions under the stochastic discount factor approach, which compares cross-sectional variation in equity returns to the cross-sectional variation in their conditional covariance with the discount factors. Using the multivariate generalized heteroskedasticity in mean model to estimate the 25 portfolios formed on size and book-to-market ratio, together each with its own arbitrage condition, we find that the no-arbitrage test rejects the consumption-based capital asset pricing model (C-CAPM). Although the conditional covariances of returns with consumption exhibit negative variation across size, they do not vary across the book-to-market ratio. Thus, the C-CAPM can capture size effect, but not value effect. Allowing the coefficients on the consumption covariances to be different largely improves the fit of the C-CAPM, however. The value effect appears to be associated with book-to-market ratio as well as size. Book-to-market ratio separately does not generate information about average returns that cannot be explained by the C-CAPM. One possible explanation for this extra dimension of risk is the investment growth prospect of firms. Low book-to-market ratio firms may be expected to have higher rates of growth while small firms may also be expected to behave similarly.

Can stochastic discount factor models explain the cross-section of equity returns?

We propose a multivariate test of the capital asset pricing model (C-CAPM) of the cross-sectional variation in equity returns in which we compare cross-sectional variation in equity returns to the cross-sectional variation in their conditional covariance with stochastic discount factors. We use a multivariate generalized heteroskedasticity in mean model to estimate 25 portfolios that are formed on size and the book-to-market ratio. Each portfolio is allowed to have its own no-arbitrage condition. We find that although the conditional covariances of returns with consumption exhibit negative variation across size, they do not vary across the book-to-market ratio. Thus, C-CAPM can capture the size effect, but not the value effect. The fit is, however, improved by allowing the coefficients on the consumption covariances to be different. The value effect appears to be associated with the book-to-market ratio as well as size. On its own the book-to-market ratio does not generate additional information about average returns to C-CAPM. A possible explanation for these findings is that both small and low book-to-market ratio firms are expected to have higher rates of growth.

Optimizing agricultural land-use portfolios with scarce data—A non-stochastic model

The theory of portfolio selection has often been applied to help improve economic decisions about the environment. Applying this theory requires information on the covariance of uncertain returns between all combinations of the economic options and also assumes that returns are normally distributed. As it is usually difficult to fulfill all data requirements and assumptions, this paper proposes a variant of robust portfolio optimization as an alternative that needs less pre-information. The approach considers future uncertainties in a non-stochastic fashion through possible deviations from the nominal return of land-use alternatives. Maximizing the economic return of the land-use portfolio is conditional on meeting an inclusive set of constraints. These demand that a pre-defined return threshold is achieved by the robust solution for each uncertainty scenario considered. Based on data for eight agricultural crops common in the Ecuadorian lowlands, a comparison with portfolios generated by classical stochastic mean-variance optimization shows greater land-use diversification (through increased Shannon indices), but only moderate expected economic loss of non-stochastic robust land-use portfolios. We conclude that non-stochastic derivation of land-use portfolios is a good alternative to the classical stochastic model, in situations where information on economic input parameters is scarce.

Price-Dividend Ratio Factor Proxies for Long-Run Risks

We show that several asset pricing models that rely on long-run risks imply that the state of the economy can be captured by factors derived from the price-dividend ratios of stock portfolios. We find two factors with small growth and large value tilts are important for this purpose, thereby relating the Fama-French model and the Bansal-Yaron and Merton intertemporal asset pricing models. As predicted by the model, these price-dividend ratio factors track consumption volatility and predict future consumption and stock dividends, and the covariance of returns with their innovations explains the cross-section of average returns of several stock portfolios. (JEL G19)

A new spread estimator

A new estimator of bid-ask spreads is presented. When the trade direction is known, any estimate of the spread is associated with a unique series of conjectural mid-prices derived by adjusting the observed transaction price by half the estimated spread. It is shown that the covariance of successive conjectural mid-price returns is maximised (or least negative) when the estimated spread is equal to the true spread. A search procedure to maximise this covariance may therefore be used to estimate the true spread. The performance of this estimator under various conditions is examined both theoretically and with Monte Carlo simulations. The simulations confirm the theoretical results. The performance of the estimator is good.

The impact of oil price shocks on the stock market return and volatility relationship

This paper examines the impact of structural oil price shocks on the covariance of U.S. stock market return and stock market volatility. We construct from daily data on return and volatility the covariance of return and volatility at monthly frequency. The measures of daily volatility are realized-volatility at high frequency (normalized squared return), conditional-volatility recovered from a stochastic volatility model, and implied-volatility deduced from options prices. Positive shocks to aggregate demand and to oil-market specific demand are associated with negative effects on the covariance of return and volatility. Oil supply disruptions are associated with positive effects on the covariance of return and volatility. The spillover index between the structural oil price shocks and covariance of stock return and volatility is large and highly statistically significant.

The Impact of Oil Price Shocks on the Stock Market Return and Volatility Relationship

This paper examines the impact of structural oil price shocks on the covariance of U.S. stock market return and stock market volatility. We construct from daily data on return and volatility the covariance of return and volatility at monthly frequency. The measures of daily volatility are realized-volatility at high frequency (normalized squared return), conditional-volatility recovered from a stochastic volatility model, and implied-volatility deduced from options prices. Positive shocks to aggregate demand and to oil-market specific demand are associated with negative effects on the covariance of return and volatility. Oil supply disruptions are associated with positive effects on the covariance of return and volatility. The spillover index between the structural oil price shocks and covariance of stock return and volatility is large and highly statistically significant.

New estimates of time-varying currency betas: A trivariate BEKK approach

This paper examines the conditional time-varying currency betas from five developed markets and four emerging markets. We employ a modified trivariate BEKK-GARCH-in-mean model of Engle and Kroner (1995) to estimate the time-varying conditional variance and covariance of returns of stock index, the world market portfolio and changes in bilateral exchange rate between the US dollar and the local currency. It is found that currency betas are more volatile than those of the world market betas. Currency betas in emerging markets are more volatile than those in the developed markets. Moreover, we find evidence of long-memory in currency betas. The usefulness of time-varying currency betas are illustrated by two applications.

A Bayesian High-Frequency Estimator of the Multivariate Covariance of Noisy and Asynchronous Returns

A multivariate positive definite estimator of the integrated covariance matrix of noisy and asynchronously observed asset returns is proposed. We adopt a Bayesian Dynamic Linear Model where microstructure noise is interpreted as measurement error, and asynchronous trading as missing observations in an otherwise synchronous series. Missing observations are treated as any other parameter, as typical in a Bayesian framework. An augmented Gibbs algorithm is used since all full conditionals are available and its convergence and robustness are discussed. A realistic simulation study compares our estimator with existing alternatives, under different liquidity and microstructure noise conditions. The results suggest that our estimator is superior in terms of RMSE particularly under severe conditions, such as portfolios of assets with heterogeneous liquidity and high level of microstructure noise. The application to the empirical dataset of ten tick-by-tick stock price series confirms the simulation results.

Estimating time-varying currency betas with contagion: New evidence from developed and emerging financial markets

This paper examines the conditional time-varying currency betas from five developed and six emerging financial markets with contagion and spillover effects. We employ a trivariate asymmetric BEKK-type GARCH-in-Mean (MGARCH-M) approach to estimate the time-varying conditional variance and covariance of returns of stock market index, the world market portfolio and bilateral exchange rate between the US dollar and the local currency. The results show that the world market and currency risks are not only priced in the stock markets, but also time-varying. It is found that currency betas are much more volatile than the world market betas, and currency betas in the emerging markets are more volatile than those in the developed markets. We find empirical evidence of contagion effect and spillovers between stock market and foreign exchange market during the recent global financial crisis, and the effect is stronger in the emerging markets than that in the developed markets. Two applications are provided to illustrate the usefulness of time-varying currency betas.

Forward-Looking Measures of Higher-Order Dependencies with an Application to Portfolio Selection

This paper provides implied measures of higher-order dependencies between assets. The measures exploit only forward-looking information from the options market and can be used to construct an implied estimator of the covariance, co-skewness, and co-kurtosis matrices of asset returns. We show that higher-order dependencies vary heavily over time and identify the economic factors driving them. Furthermore, we run a portfolio selection exercise and show that investors can benefit from using the new estimator. They obtain a better risk-adjusted out-of-sample performance by up to 14% per year compared to when they use various historical and partially implied benchmark estimators.

Expected return, time-varying risk, and hedging demand in the US REITs market

This paper explores the time-varying relationship between the return and risk for the portfolios in the US real estate investment trusts (REITs) market. Three classes of REITs portfolios are sorted on size, momentum and book-to-market. The empirical results place a positive trade-off between the return and predictable covariation in all REITs portfolios. Furthermore, this paper examines the significance of intertemporal hedging demand in each REITs portfolio by extending the Intertemporal Capital Asset Pricing model (ICAPM) with a set of prevailing macroeconomic variables and financial market indicators, which indicate that the predictable movements in return could be attributed to the change in covariances with these innovations. The conclusive results show that innovations in inflation rate, de-trended short-term interest rate, Fama-French momentum factor, S&P/Case-Shiller home price index, and Barclay Capital long-term government/corporate bond index play a crucial role in hedging demand for REITs portfolios.

Measuring the Risk-Return Tradeoff with Time-Varying Conditional Covariances

We examine the prediction of Merton's intertemporal CAPM that time varying risk premiums arise from the conditional covariances of returns on assets with the return on the market and other state variables. We find a positive and significant price of risk for the covariance with the market return that is driven by the time series variation in the conditional covariances, and the risk-premium on the market remains positive and significant after controlling for additional state variables. Our method estimates the risk-return tradeoff in the ICAPM using multiple portfolios as test assets.

Global Minimum Variance Portfolio: A Horse Race of Volatilities

We conduct a horse race using three asset return volatility estimates: the sample variance, the exponential smoother used by RiskMetrics, and the generalized autoregressive conditional heteroskedasticity (GARCH). Our results are performed in both univariate and multivariate analysis. Our goal is to test whether using econometric tools achieves better economic performance. Economic performance is captured by portfolio performance as in DeMiguel et al (2009), who use three metrics to evaluate portfolios: risk-return, Sharpe-ratio, and turnover. Our portfolio of interest is the global minimum variance (GMV) portfolio since its inputs are determined solely by the variances and covariances of the asset returns. Computing the three portfolio performances for the three volatility candidate, we provide an evidence in support of the GARCH approach; however, this edge is undermined by greater portfolio turnover and larger estimation error, when the number assets in the portfolio is large.

Pricing deviation, misvaluation comovement, and macroeconomic conditions

We measure an individual stock’s misvaluation based on the deviation of its price from predicted intrinsic value. Both under- and overvalued stocks identified by this misvaluation measure exhibit greater valuation uncertainty and arbitrage difficulty, and the misvaluation measure strongly predicts stock returns incremental to size, book-to-market ratio, past returns, and various return anomalies. Based on the misvaluation measure, we form a misvaluation factor and find that stock return covariances with this factor possess significant and robust return predictive power. We further show that the misvaluation factor predicts future economic conditions, providing additional insight into the real effect of systematic misvaluation in the stock market.

Estimating Time-Varying Currency Betas: New Evidence from Nine Developed and Emerging Markets

This paper examines the conditional time-varying currency betas from five developed markets and four emerging markets. We employ BEKK multivariate GARCH models of Engle and Kroner (1995) to estimate the time-varying conditional variance and covariance of returns of stock index, the world market portfolio and changes in bilateral exchange rate between the US dollar and the local currency. It is found that currency betas are more volatile than those of the world market betas. Currency betas in emerging markets are more volatile than those in the developed markets. Moreover, we find evidence of long-memory in currency betas. The usefulness of time-varying currency betas are illustrated by two applications.

Do Hedge Funds Exploit Rare Disaster Concerns?

We find hedge funds that have higher return covariation with a disaster concern index, which we develop through out-of-the-money puts on various economic sector indices, earn significantly higher returns in the cross section. We provide substantial evidence that these funds have better skills in exploiting the market's ex ante rare disaster concerns (SED), which may not realize as disaster shocks ex post. In particular, high-SED funds on average outperform low-SED funds by 0.96% per month, but have less exposure to disaster risk. They continue to deliver superior future performance when SED is estimated using the disaster concern index purged of disaster risk premium, and have leverage-managing and extreme-market-timing abilities. We also provide strong evidence against alternative interpretations.

Who Participates in Corporate Income Tax Consolidation? Evidence from Japan

When a group of affiliated corporations have the option to file a single tax return based on a combined income, what types of groups would take up the option? This study empirically analyses decisions to participate in a single-jurisdiction consolidated tax filing. The data consists of 2,782 Japanese corporate groups headed by publicly-traded corporations observed over 2002-2007. Results indicate higher likelihood of participation among groups characterised by low correlation in returns among group members, high variance in returns, large number of subsidiaries, and losses accumulated in parents. The significant influence of variance and covariance of returns suggests that a consolidation scheme improves the efficiency of corporate income tax through reducing profit shifting.

Jump robust two time scale covariance estimation and realized volatility budgets

We estimate the daily integrated variance and covariance of stock returns using high-frequency data in the presence of jumps, market microstructure noise and non-synchronous trading. For this we propose jump robust two time scale (co)variance estimators and verify their reduced bias and mean square error in simulation studies. We use these estimators to construct the ex-post portfolio realized volatility (RV) budget, determining each portfolio component’s contribution to the RV of the portfolio return. These RV budgets provide insight into the risk concentration of a portfolio. Furthermore, the RV budgets can be directly used in a portfolio strategy, called the equal-risk-contribution allocation strategy. This yields both a higher average return and lower standard deviation out-of-sample than the equal-weight portfolio for the stocks in the Dow Jones Industrial Average over the period October 2007–May 2009.