QARMA-Beta-t-EGARCH versus ARMA-GARCH: an application to S&P 500

Statistical performance and out-of-sample forecast precision of ARMA-GARCH and QARMA-Beta-t-EGARCH are compared. We study daily returns on the Standard and Poor’s 500 (S&P 500) index and a random sample of 50 stocks from the S&P 500 for period May 2006 to July 2010. Competing models are estimated for periods before and during the US financial crisis of 2008. Out-of-sample point and density forecasts are performed for periods during and after the US financial crisis. The results provide evidence of the superior in-sample statistical and out-of-sample predictive performance of QARMA-Beta-t-EGARCH.     

When Do Opening Stock Returns Tend to be Higher?

Abstract

In this study, I make an effort to formulate a trading rule that would make use of some systematic interday patterns in individual stocks’ opening returns. I analyze intraday price data on all the stocks that were S&P 500 Index constituents during the period from 1993 to 2012. I document that if the general market direction of the previous day's opening session is controlled for, then a stock's opening return tends to be higher if, on the previous trading day, its opening return was relatively high (either positive, or higher than the same day's opening market return) and its open-to-close return was relatively low (either non-positive, or lower than or equal to the same day's open-to-close market return). Finally, for the sampling period, I construct two different investment portfolios involving a long position in the stocks on the days when, according to the findings, their opening returns are expected to be high and a short position in the stocks on the days when, according to the findings, their opening returns are expected to be low. Both portfolios are found to yield significantly positive returns, providing evidence for the practical applicability of the documented patterns in opening stock prices.     

Score-driven Markov-switching EGARCH models: an application to systematic risk analysis

We introduce new Markov-switching (MS) dynamic conditional score (DCS) exponential generalized autoregressive conditional heteroscedasticity (EGARCH) models, to be used by practitioners for forecasting value-at-risk (VaR) and expected shortfall (ES) in systematic risk analysis. We use daily log-return data from the Standard & Poor’s 500 (S&P 500) index for the period 1950–2016. The analysis of the S&P 500 is useful, for example, for investors of (i) well-diversified US equity portfolios; (ii) S&P 500 futures and options traded at Chicago Mercantile Exchange Globex; (iii) exchange traded funds (ETFs) related to the S&P 500. The new MS DCS-EGARCH models are alternatives to of the recent MS Beta-t-EGARCH model that uses the symmetric Student’s t distribution for the error term. For the new models, we use more flexible asymmetric probability distributions for the error term: Skew-Gen-t (skewed generalized t), EGB2 (exponential generalized beta of the second kind) and NIG (normal-inverse Gaussian) distributions. For all MS DCS-EGARCH models, we identify high- and low-volatility periods for the S&P 500. We find that the statistical performance of the new MS DCS-EGARCH models is superior to that of the MS Beta-t-EGARCH model. As a practical application, we perform systematic risk analysis by forecasting VaR and ES.

Abbreviation Single regime (SR); Markov-switching (MS); dynamic conditional score (DCS); exponential generalized autoregressive conditional heteroscedasticity (EGARCH); value-at-risk (VaR); expected shortfall (ES); Standard & Poor's 500 (S&P 500); exchange traded funds (ETFs); Skew-Gen-t (skewed generalized t); EGB2 (exponential generalized beta of the second kind); NIG (normal-inverse Gaussian); log-likelihood (LL); standard deviation (SD); partial autocorrelation function (PACF); likelihood-ratio (LR); ordinary least squares (OLS); heteroscedasticity and autocorrelation consistent (HAC); Akaike information criterion (AIC); Bayesian information criterion (BIC); Hannan-Quinn criterion (HQC).     

Forecasting the S&P 500 index volatility

This study introduces a new pre-differencing transformation for the AR1MA model for forecasting S&P 500 index volatility. The out of sample forecasting performance of the ARIMA model using the new pre-differencing transformation is compared with the out of sample forecasting performance of the mean reversion model and the GARCH model. The ARIMA model using the new pre-differencing transformation introduced in this study is found to be superior to both the mean reversion model and the GARCH model in forecasting monthly S&P 500 index volatility for the forecast comparison periods used in this study.     

Sustainable competitive advantage and stock performance: the case for wide moat stocks

‘In business, I look for economic castles protected by unbreachable “Moats”’. Warren Buffett Companies that have sustainable competitive advantages should be able to create a barrier (Moat) to prevent or lessen competition from other firms. The wider the Moat the greater the barrier and the more secure the company’s profitability. Using the Morningstar classification of ‘Wide Moat’ stocks, we construct annually rebalanced equal- and value-weighted portfolios to analyse their performance in order to determine if they deliver superior performance relative to standard benchmark portfolios. The period for our analysis extends from June 2002 through May 2014. We find that the ‘Wide Moat’ portfolios outperform both the S&P 500 and Russell 3000 indices generating higher average monthly and annualized returns, Sharpe Ratio, Sortino Ratio, Treynor Ratio, Omega Ratio, Upside Potential Ratio, M², M² Alpha, and cumulative returns. When we compute alpha using Carhart four-factor and Fama–French five-factor models, we find that ‘Wide Moat’ portfolios had significantly positive risk-adjusted alphas with both the models. ‘Wide Moat’ portfolios also lost less value during the 2007–2009 financial crisis compared to both S&P 500 and Russell 3000. In conclusion, we find that ‘Wide Moat’ stocks have created significant value for their investors over the course of our study.     

S&P 500 Affiliation and Stock Price Informativeness

Abstract

When firms are added to a stock index, more information should be discovered, traded on, and incorporated into their stock prices, making them more informative. We test this hypothesis using a large sample of additions to the S&P 500 index. Using two alternative statistical tests, we find that the stocks added experience more random, less predictable return and, thus, appear to be priced more efficiently information-wise. We further find concurrent increases in institutional ownership and investor awareness, which tend to contribute to the higher pricing efficiency, adding to the literature. These findings should be of interest to academics and practitioners.     

QUANTILE FORECASTS OF FINANCIAL RETURNS USING REALIZED GARCH MODELS*

This article applies the realized generalized autoregressive conditional heteroskedasticity (GARCH) model, which incorporates the GARCH model with realized volatility, to quantile forecasts of financial returns, such as Value‐at‐Risk and expected shortfall. Student's t‐ and skewed Student's t‐distributions as well as normal distribution are used for the return distribution. The main results for the S&P 500 stock index are: (i) the realized GARCH model with the skewed Student's t‐distribution performs better than that with the normal and Student's t‐distributions and the exponential GARCH model using the daily returns only; and (ii) using the realized kernel to take account of microstructure noise does not improve the performance.     

On the asymmetric impact of macro–variables on volatility

We extend the GARCH–MIDAS model to take into account possible different impacts from positive and negative macroeconomic variations on financial market volatility: a Monte Carlo simulation which shows good properties of the estimator with realistic sample sizes. The empirical application is performed on the daily S&P500 volatility dynamics with the U.S. monthly industrial production and national activity index as additional (signed) determinants. We estimate the Relative Marginal Effect of macro variable movements on volatility at different lags. In the out-of-sample analysis, our proposed GARCH–MIDAS model not only statistically outperforms the competing specifications (GARCH, GJR-GARCH and GARCH–MIDAS models), but shows significant utility gains for a mean-variance investor under different risk aversion parameters. Attention to robustness is given by choosing different samples and estimating the model in an international context (six different stock markets).     

The risk-return relation and VIX: evidence from the S&P 500

A significantly positive risk-return relation for the S&P 500 market index is detected if the squared implied volatility index (VIX) is allowed for as an exogenous variable in the conditional variance equation of the parsimonious GARCH(1,1) model. This result holds for both daily and weekly observations, for extended conditional mean and variance specifications, and is robust to sub-samples. We show that the conditional variance obtained from the GARCH model with VIX has better predictive ability for realized volatility than the conditional variance from GARCH without VIX and VIX itself, thereby documenting an important information content of VIX for conditional variance. The results are interpreted as evidence that adding VIX squared in the conditional variance equation yields a better measure of conditional variance which, subsequently, uncovers a strong risk-return relation.     

Pricing and hedging options with GARCH-stable proxy volatilities

This article considers modelling nonnormality in return with stable Paretian (SP) innovations in generalized autoregressive conditional heteroskedasticity (GARCH), exponential generalized autoregressive conditional heteroskedasticity (EGARCH) and Glosten-Jagannathan-Runkle generalized autoregressive conditional heteroskedasticity (GJR-GARCH) volatility dynamics. The forecasted volatilities from these dynamics have been used as a proxy to the volatility parameter of the Black–Scholes (BS) model. The performance of these proxy-BS models has been compared with the performance of the BS model of constant volatility. Using a cross section of S&P500 options data, we find that EGARCH volatility forecast with SP innovations is an excellent proxy to BS constant volatility in terms of pricing. We find improved performance of hedging for an illustrative option portfolio. We also find better performance of spectral risk measure (SRM) than value-at-risk (VaR) and expected shortfall (ES) in estimating option portfolio risk in case of the proxy-BS models under SP innovations.

Abbreviation: generalized autoregressive conditional heteroskedasticity (GARCH), exponential generalized autoregressive conditional heteroskedasticity (EGARCH) and Glosten-Jagannathan-Runkle generalized autoregressive conditional heteroskedasticity (GJR-GARCH)     

Investment horizon effect on asset allocation between value and growth strategies

How does the optimal risk exposure of assets change as their investment horizons increase? Does this impact investment portfolio decision-making, in particular, optimal asset allocation between value and growth strategies over various investment horizons? This paper adopts a new approach to address these questions by examining portfolio allocation between value and growth stocks over various investment horizons. This new approach is based on wavelet analysis, which decomposes the returns of a particular investment strategy across multiple investment horizons. The key empirical results show that the success of pursuing the value strategy (short-selling growth stocks and going long on value stocks) is impacted by the approach used to classify value and growth stock returns. We explore two common alternatives: Fama-French versus Standard & Poor's (S&P) 500/Barra portfolios. The results using Fama-French portfolios show that as the investment horizon increases, the optimal mean allocation of investors tilts heavily away from growth stocks, particularly for lower and moderate levels of risk aversion. Interestingly, for S&P 500/Barra portfolios the allocation weights between value and growth do not vary much.     

Markov regime-switching Beta-t-EGARCH

We suggest a Markov regime-switching (MS) Beta-t-EGARCH (exponential generalized autoregressive conditional heteroscedasticity) model for U.S. stock returns. We compare the in-sample statistical performance of the MS Beta-t-EGARCH model with that of the single-regime Beta-t-EGARCH model. For both models we consider leverage effects for conditional volatility. We use data from the Standard Poor’s 500 (S&P 500) index and also a random sample that includes 50 components of the S&P 500. We study the outlier-discounting property of the single-regime Beta-t-EGARCH and MS Beta-t-EGARCH models. For the S&P 500, we show that for the MS Beta-t-EGARCH model extreme observations are discounted more for the low-volatility regime than for the high-volatility regime. The conditions of consistency and asymptotic normality of the maximum likelihood estimator are satisfied for both the single-regime and MS Beta-t-EGARCH models. All likelihood-based in-sample statistical performance metrics suggest that the MS Beta-t-EGARCH model is superior to the single-regime Beta-t-EGARCH model. We present an application to the out-of-sample density forecast performance of both models. The results show that the density forecast performance of the MS Beta-t-EGARCH model is superior to that of the single-regime Beta-t-EGARCH model.     

On the correlation between stocks and art market returns

We estimate the correlation between the returns of an S&P 500-based portfolio and Renoir paintings. Unlike previous studies that relied on single-point estimates of the correlation to explore the merits of adding art assets to a portfolio of stocks, we rely on a wild bootstrap algorithm to determine confidence intervals for the correlation estimates. We find that these confidence intervals are so wide (a situation not peculiar to our example) that it seems impossible to make absolute remarks about the merits of adding art-related assets to stocks portfolios. Moreover, our results suggest that previous conclusions regarding the correlation between art and stocks should be taken with some scepticism.     

Value at risk forecasting for volatility index

Forecasts of values at risk (VaRs) are made for volatility indices such as the VIX for the US S&P 500 index, the VKOSPI for the KOSPI (Korea Stock Price Index) and the OVX (oil volatility index) for crude oil funds, which is the first in the literature. In the forecasts, dominant features of the volatility indices are addressed: long memory, conditional heteroscedasticity, asymmetry and fat-tails. An out-of-sample comparison of the VaR forecasts is made in terms of violation probabilities, showing better performance of the proposed method than several competing methods which consider the features differently from ours. The proposed method is composed of heterogeneous autoregressive model for the mean, GARCH model for the volatility and skew-t distribution for the error.     

Are U.S. growth and value stocks similarly integrated with the world markets? A test across business cycles

Utilizing the bivariate GARCH-in-mean methodology, this study examines the strength of global risk premia using 10 major foreign stock markets with two style-based, large-cap U.S. index funds and S&P500, for the period 1993–2014. We incorporated seven U.S. business cycles. The foreign risk premium was found to be significantly strong for both growth and value stocks, and the S&P500 index, indicating that U.S. integration within global market is strong and persistent over the past 20 years. We report distinct risk characteristics owing to global linkages, for the two style-based U.S. funds over different business cycles. The foreign risk premium for growth stocks is mostly positive and especially high during contractions; in contrast, the value stocks demand more premiums during expansions. The growth and value linkages with foreign countries also vary quite substantially over the business cycles. A possible sign of convergence is the decreasing difference between value and growth foreign risk premiums, post-2001, perhaps indicative of greater domestic and global market integration. Our results support a solid, continuing trend of U.S. integration within global markets, with an influential role of business cycles.     

Modelling the risk–return relation for the S&P 100: The role of VIX

A significantly positive risk–return relation for the S&P 100 market index is detected if the implied volatility index (VIX) is allowed for as an exogenous variable in the conditional variance equation. This result holds for 4 alternative GARCH specifications, irrespective of the conditional distribution, and regardless of whether the conditional mean equation includes a constant term. This finding is robust to sub-samples, and to using VIX innovations to control for dividend yield and trading volume effects. Monte Carlo evidence suggests that if VIX is not included, the risk–return relation is more likely to be negative or weak, in line with several previous studies. If VIX is included, the distribution of the risk–return parameter has more than 99% of its mass in the area of positive values. We conclude that VIX carries important forward-looking information which improves the precision of the conditional variance estimation and, subsequently, reveals a significantly positive relation.     

Financing R&D in mature companies: An empirical analysis

We study financing patterns of publicly traded R&D-intensive manufacturing firms in Israel. We further characterize R&D-intensive firms by size, physical capital intensity, and whether they issued stocks in the United States, asking whether these features are associated with particular financing patterns. To address these issues, we present, for the first time, adjusted flow of funds charts that treat R&D expenses as a capital outlay (rather than an operating cost that reduces profits, as standard accounting principles prescribe). We also address the question of how R&D inputs should be measured - using R&D expenses or R&D personnel. We construct both expenditure- and personnel-based R&D measures for each firm in our sample, and investigate to what extent these measures are mutually consistent.     

Improving market timing of time series momentum in the Chinese stock market

ABSTRACT

This paper is the first study to present firm-level evidence that the time-series momentum (TSMOM) strategies with look-back-period k of 10 to 200 days outperform the buy-and-hold strategy (BH) on individual stocks in the Chinese stock market. We document that the optimal k* generating the best performance is different across assets and varies over time. We hence propose a model to predict the asset-specific and time-dependent k*, and examine the performance of the TSMOM strategies with the predicted k*. Our analysis shows that using the time-varying predicted k* substantially improves the predictability of the TSMOM strategies. Our new model and findings shed the light on trading strategy for both academia and applied investment practitioners.     

Correlations and volatility spillovers across commodity and stock markets: Linking energies,food, and gold

This paper employs a VAR-GARCH model to investigate the return links and volatility transmission between the S&P 500 and commodity price indices for energy, food, gold and beverages over the turbulent period from 2000 to 2011. Understanding the price behavior of commodity prices and the volatility transmission mechanism between these markets and the stock exchanges are crucial for each participant, including governments, traders, portfolio managers, consumers, and producers. For return and volatility spillover, the results show significant transmission among the S&P 500 and commodity markets. The past shocks and volatility of the S&P 500 strongly influenced the oil and gold markets. This study finds that the highest conditional correlations are between the S&P 500 and gold index and the S&P 500 and WTI index. We also analyze the optimal weights and hedge ratios for commodities/S&P 500 portfolio holdings using the estimates for each index. Overall, our findings illustrate several important implications for portfolio hedgers for making optimal portfolio allocations, engaging in risk management and forecasting future volatility in equity and commodity markets.     

Modeling volatility and conditional correlations between socially responsible investments,gold and oil

Socially responsible investing (SRI) is one of the fastest growing areas of investing. While there is a considerable literature comparing SRI to various benchmarks, very little is known about the volatility dynamics of socially responsible investing. In this paper, multivariate GARCH models are used to model volatilities and conditional correlations between a stock price index comprised of socially responsible companies, oil prices, and gold prices. The dynamic conditional correlation model is found to fit the data the best and used to generate dynamic conditional correlations, hedge ratios and optimal portfolio weights. From a risk management perspective, SRI offers very similar results in terms of dynamic conditional correlations, hedge ratios, and optimal portfolio weights as investing in the S&P 500. For example, SRI investors can expect to pay a similar amount to hedge their investment with oil or gold as investors in the S&P 500 would pay. These results can help investors and portfolio managers make more informed investment decisions.