Decomposing the VIX: Implications for the predictability of stock returns

The VIX index is not only a volatility index but also a polynomial combination of all possible higher moments in market return distribution under the risk-neutral measure. This paper formulates the VIX as a linear decomposition of four fundamentally different elements: the realized variance (RV), the variance risk premium (VRP), the realized tail (RT), and the tail risk premium (TRP), respectively. Using an innovative and nonparametric tail risk measure, we find that approximately one-third of the VIX's formation is attributed to the TRP. In addition to VRP, RT and TRP are crucial components for predicting future returns on equity portfolios.     

Forecasting financial market volatility: Sample frequency vis-à-vis forecast horizon

This paper explores the return volatility predictability inherent in high-frequency speculative returns. Our analysis focuses on a refinement of the more traditional volatility measures, the integrated volatility, which links the notion of volatility more directly to the return variance over the relevant horizon. In our empirical analysis of the foreign exchange market the integrated volatility is conveniently approximated by a cumulative sum of the squared intraday returns. Forecast horizons ranging from short intraday to 1-month intervals are investigated. We document that standard volatility models generally provide good forecasts of this economically relevant volatility measure. Moreover, the use of high-frequency returns significantly improves the longer run interdaily volatility forecasts, both in theory and practice. The results are thus directly relevant for general research methodology as well as industry applications.     

Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles

We model consumption and dividend growth rates as containing (1) a small long‐run predictable component, and (2) fluctuating economic uncertainty (consumption volatility). These dynamics, for which we provide empirical support, in conjunction with Epstein and Zin's (1989) preferences, can explain key asset markets phenomena. In our economy, financial markets dislike economic uncertainty and better long‐run growth prospects raise equity prices. The model can justify the equity premium, the risk‐free rate, and the volatility of the market return, risk‐free rate, and the price–dividend ratio. As in the data, dividend yields predict returns and the volatility of returns is time‐varying.     

Stock Market Volatility and Economic Factors

This paper examines the ability of rational economic factors to explain stock market volatility. A simple model of the economy under uncertainty identifies four determinants of stock market volatility: uncertainty about the price level, the riskless rate of interest, the risk premium on equity and the ratio of expected profits to expected revenues. In initial tests these variables have significant explanatory power and account for over 50 per cent of the variation in market volatility from 1929 to 1989. When the regression coefficients are allowed to vary over time using cluster regression, the four factors explain over 90 per cent of the variation in market volatility. The results are useful in explaining the past behavior of stock market volatility and in forecasting future volatility.     

Forecasting volatility of the U.S. oil market

We examine the information content of the CBOE Crude Oil Volatility Index (OVX) when forecasting realized volatility in the WTI futures market. Additionally, we study whether other market variables, such as volume, open interest, daily returns, bid-ask spread and the slope of the futures curve, contain predictive power beyond what is embedded in the implied volatility. In out-of-sample forecasting we find that econometric models based on realized volatility can be improved by including implied volatility and other variables. Our results show that including implied volatility significantly improves daily and weekly volatility forecasts; however, including other market variables significantly improves daily, weekly and monthly volatility forecasts.     

Inferring volatility dynamics and risk premia from the S&P 500 and VIX markets

We estimate a flexible affine model using an unbalanced panel containing S&P 500 and VIX index returns and option prices and analyze the contribution of VIX options to the model’s in- and out-of-sample performance. We find that they contain valuable information on the risk-neutral conditional distributions of volatility at different time horizons, which is not spanned by the S&P 500 market. This information allows enhanced estimation of the variance risk premium. We gain new insights on the term structure of the variance risk premium, present a trading strategy exploiting these insights, and show how to improve S&P 500 return forecasts.     

Risk,uncertainty, and asset prices

We identify the relative importance of changes in the conditional variance of fundamentals (which we call “uncertainty”) and changes in risk aversion in the determination of the term structure, equity prices, and risk premiums. Theoretically, we introduce persistent time-varying uncertainty about the fundamentals in an external habit model. The model matches the dynamics of dividend and consumption growth, including their volatility dynamics and many salient asset market phenomena. While the variation in price–dividend ratios and the equity risk premium is primarily driven by risk aversion, uncertainty plays a large role in the term structure and is the driver of countercyclical volatility of asset returns.     

Fund Volatility Index using equity market state prices

The Fund Volatility Index (FVX) is proposed as a forward measure of volatility with applications in fund hedging and risk management. The method applies equity market state prices to individual fund pay‐offs. FVX is validated as a predictor of short‐term realised volatility for 30 exchange traded funds. Performance of the method is compared with existing methods using a data set of 14 925 non‐traded funds. FVX has lower bias and higher forecast accuracy than existing methods. As a more general measure, it allows for incorporation of terms to capture individual fund skewness and projection of higher moments of returns.     

Leverage and the Cross‐Section of Equity Returns

Building on theoretical asset pricing literature, we examine the role of market risk and the size, book‐to‐market (BTM), and volatility anomalies in the cross‐section of unlevered equity returns. Compared with levered (stock) returns, unlevered market beta plays a more important role in explaining the cross‐section of unlevered equity returns, even after controlling for size and BTM. The size effect is weakened, while the value premium and the volatility puzzle virtually disappear for unlevered returns. We show that leverage induces heteroskedasticity in returns. Unlevering returns removes this pattern, which is otherwise difficult to address by controlling for leverage in regressions.     

Announcement Effects and Asymmetric Volatility in Industry Stock Returns: Evidence from Taiwan

This study employs financial econometric models to examine the asymmetric volatility of equity returns in response to monetary policy announcements in the Taiwanese stock market. The meetings of the board of directors at the Central Bank of the Republic of China (Taiwan) are considered for testing the announcement effects. The asymmetric generalized autoregressive conditional heteroskedasticity (GARCH) model and the smooth transition autoregression with GARCH model are used to measure equity returns' asymmetric volatility. We conclude that the asymmetric volatility of countercyclical equity returns can be identified. Our findings support the leverage effect of stock price changes for most industry equity returns in Taiwan.     

Common Volatility: An Empirical Investigation of Closed-End Country Funds

The study of international integration of equity markets has received a great deal of interest. This paper investigates whether returns of forty-one closed-end country funds share a common volatility process with three comparable return series: the underlying net asset value (NAV), U.S. stock market returns, and foreign stock market returns. Country funds are a natural setting to test for international market integration, as they are traded in the U.S. market, whereas their underlying assets are traded in foreign stock markets. Our results indicate that only a few emerging markets' country funds share common volatility processes with their comparable asset returns. This, in turn, suggests weak linkages through the second moment of related assets.     

Herding and market volatility

In this paper, we explore the impact of investor herding behavior on stock market volatility. We adopt a direct herding measure based on the variation of cross-sectional stock betas. The measure can be readily separated into positive and adverse components, whereby investors herd towards and away from the market portfolio, respectively. Using A-shares listed in the Chinese equity market from August 2005 to March 2021, we show that the market volatility is Granger caused by the measure, and that there exists an asymmetric effect between positive and adverse herding on volatility. Furthermore, we provide robust evidence that the information contained in the herding measure helps generate significantly improved volatility forecasts and add economic value to investors. Our paper not only contributes to the volatility forecasting literature but also advances our understanding of herding in the equity market.     

The cross-section of average delta-hedge option returns under stochastic volatility

Existing evidence indicates that average returns of purchased market-hedge S&P 500 index calls, puts, and straddles are non-zero but large and negative, which implies that options are expensive. This result is intuitively explained by means of volatility risk and a negative volatility risk premium, but there is a recent surge of empirical and analytical studies which also attempt to find the sources of this premium. An important question in the line of a priced volatility explanation is if a standard stochastic volatility model can also explain the cross-sectional findings of these empirical studies. The answer is fairly positive. The volatility elasticity of calls and puts is several times the level of market volatility, depending on moneyness and maturity, and implies a rich cross-section of negative average option returns—even if volatility risk is not priced heavily, albeit negative. We introduce and calibrate a new measure of option overprice to explain these results. This measure is robust to jump risk if jumps are not priced.      

How is illiquidity priced in the Chinese stock market?

This study investigates the liquidity premium in the Chinese stock market. We found that the expected stock returns increase monotonically with the quintile sort on characteristic liquidity with descending patterns. The characteristic liquidity premium ranges from 0.82% to 1.28% per month, which is much higher than that of their US counterparts. Moreover, our multivariate decomposition approach highlights that characteristic illiquidity premiums can be explained mainly by size, idiosyncratic volatility and momentum. The net systematic liquidity premium reaches 0.84% per month, driven mainly by commonality beta. The finding shows that a liquidity-based strategy forecasts cross-section and time-series expected returns.     

Unconstrained estimates of the equity risk premium

Estimates of the equity risk premium implied by analyst forecasts—generally 2–4 %—are often significantly below realized equity returns of 6 %. Measurement error could result from conservative assumptions, reliance upon consensus rather than detailed forecasts, the use of market rather than target prices, and regression analysis, which can be influenced by a small number of observations. We address these potential sources of measurement error. Our estimates are consistent with subsequently realized returns and capture systematic risk exposure. Alternative techniques could capture another form of priced risk or identify firm characteristics associated with systematic mispricing. From 1999 to 2008, we estimate an average equity risk premium in the United States of 5.3 %. The estimate increases from 3.1 % for 1999–2000 to 5.9 % from 2001 to 2008, comparable to the historical average of realized equity returns.     

How Does Information Quality Affect Stock Returns?

Using a simple dynamic asset pricing model, this paper investigates the relationship between the precision of public information about economic growth and stock market returns. After fully characterizing expected returns and conditional volatility, I show that (i) higher precision of signals tends to increase the risk premium, (ii) when signals are imprecise the equity premium is bounded above independently of investors' risk aversion, (iii) return volatility is U-shaped with respect to investors' risk aversion, and (iv) the relationship between conditional expected returns and conditional variance is ambiguous.     

Cross section of option returns and idiosyncratic stock volatility

This paper presents a robust new finding that delta-hedged equity option return decreases monotonically with an increase in the idiosyncratic volatility of the underlying stock. This result cannot be explained by standard risk factors. It is distinct from existing anomalies in the stock market or volatility-related option mispricing. It is consistent with market imperfections and constrained financial intermediaries. Dealers charge a higher premium for options on high idiosyncratic volatility stocks due to their higher arbitrage costs. Controlling for limits to arbitrage proxies reduces the strength of the negative relation between delta-hedged option return and idiosyncratic volatility by about 40%.     

Combining long memory and level shifts in modelling and forecasting the volatility of asset returns

We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in most high-frequency measures of volatility, whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons.     

Asymmetry in return and volatility spillover between equity and bond markets in Australia

We document asymmetry in return and volatility spillover between equity and bond markets in Australia for daily returns during the period 1992–2006 using a bivariate GARCH modelling approach. Negative bond market returns spillover into lower stock market returns whereas good news originating in the equity market leads to lower bond returns. Bond market volatility spills over into the equity market but the reverse is not true. Transmission of bond volatility into equity volatility depends in a complex way upon the respective signs of the return shocks in each market.     

Volatility as an Asset Class: European Evidence

Abstract

Volatility movements are known to be negatively correlated with stock index returns. Hence, investing in volatility appears to be attractive for investors seeking risk diversification. The most common instruments for investing in pure volatility are variance swaps, which now enjoy an active over-the-counter (OTC) market. This paper investigates the risk-return tradeoff of variance swaps on the Deutscher Aktienindex and Euro STOXX 50 index over the time period from 1995 to 2004. We synthetically derive variance swap rates from the smile in option prices. Using quotes from two large investment banks over two months, we validate that the synthetic values are close to OTC market prices. We find that variance swap returns exhibit an option-like profile compared to returns of the underlying index. Given this pattern, it is crucial to account for the non-normality of returns in measuring the performance of variance swap investments. As in the US, the average returns of selling variance swaps are found to be strongly positive and too large to be compatible with standard equilibrium models. The magnitude of the estimated risk premium is related to variance uncertainty and past index returns. This indicates that the variance swap rate does not seem to incorporate all past information relevant for forecasting future realized variance.