Testing excess returns on event days: Log returns vs. dollar returns

The results of academic and practitioners’ event studies are often translated from excess log returns into excess dollar returns. The prior literature argues for a difference between the statistical significance of excess log returns and that of excess dollar returns. In contrast, we show analytically and using simulations that specifying event study hypotheses in terms of excess dollar returns is equivalent to specifying them in terms of excess log returns. The prior literature’s result was due to a bias in the estimator of expected excess dollar returns, an incorrect assumption that it is approximately normally distributed, and a misapplication of the delta method.     

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.     

VIX and liquidity premium

Previous studies find as the VIX goes up, the return and the Sharpe ratio on liquidity provision increase. We argue these two phenomena are correlated because they depend on the same fundamentals: investors’ risk aversion, asset variances and asset correlations. Our theoretical model shows (1) when investors are more risk-averse, they expect a higher return for providing liquidity, (2) when assets are volatile, liquidity shocks create stronger trading demands and thus liquidity demanders pay a higher premium, and (3) when assets are highly correlated, the higher risk of spillover of liquidity shocks across assets raises the price of liquidity. An increase in any of these three factors, besides increasing the expected return and the Sharpe ratio of liquidity providers, leads to a higher value for the VIX index. Our empirical analyses show that one standard-deviation increase in each of these three factors raise liquidity providers’ expected daily return (annualized Sharpe ratio) by 0.16%, 0.38% and 0.40% (0.82, 1.27 and 2.10 units), respectively.     

Exchange Rates and FOMC Days

Federal Open Market Committee (FOMC) meeting days provide a natural laboratory for exploring the effects of policy uncertainty and learning on exchange rate determination. A reasonable hypothesis is that the meeting outcomes are price-relevant public information associated with a switch to an "informed-trading state." Evidence is provided by intradaily exchange rates for 10 FOMC meetings. A particularly interesting finding is that the informed-trading regime tends to emerge during the time that the FOMC meets. An extensive search of public news indicates that the informed trading cannot be explained as the response to public information.     

Global asset prices and FOMC announcements

This paper analyzes the impact of U.S. monetary policy announcement surprises on foreign equity indexes, short- and long-term interest rates, and exchange rates in 49 countries. We use two proxies for monetary policy surprises: the surprise change to the current target federal funds rate (target surprise) and the revision to the expected path of future monetary policy (path surprise). We find that different asset classes respond to different components of the monetary policy surprises. Global equity indexes respond mainly to the target surprise; exchange rates and long-term interest rates respond mainly to the path surprise; and short-term interest rates respond to both surprises. On average, a hypothetical surprise 25-basis-point cut in the federal funds target rate is associated with about a 1 percent increase in foreign equity indexes and a 5 basis point decline in foreign short-term interest rates. A surprise 25-basis-point downward revision in the expected path of future policy is associated with about a ½ percent decline in the exchange value of the dollar against foreign currencies and 5 and 8 basis point declines in short- and long-term interest rates, respectively. We also find that asset prices’ responses to FOMC announcements vary greatly across countries, and that these cross-country variations in the response are related to a country’s exchange rate regime. Equity indexes and interest rates in countries with a less flexible exchange rate regime respond more to U.S. monetary policy surprises. In addition, the cross-country variation in the equity market response is strongly related to the percentage of each country’s equity market capitalization owned by U.S. investors. This result suggests that investors’ asset holdings may play a role in transmitting monetary policy surprises across countries.     

Effect of credit rating changes on Australian stock returns

We study the impact credit rating revisions have on stock returns of Australian firms rated by Standard & Poor's and Moody's. Our evidence is consistent with that documented in the USA showing that only downgrades contain price‐relevant information. The reaction is most significant when the downgrade: (i) is unanticipated; (ii) is for an unregulated firm; and (iii) reduces the firm's rating by more than one category.     

Bank-Equity returns and changes in the discount rate

The ex ante value of discount window operations is modelled as an option providing financial institutions with a right to purchase reserves at potentially below market rates of interest. The value of this option varies according to terms specified by the Federal Reserve. Changes in the value of this option are linked to the equity returns of participating banks. An empirical method is proposed to separate the signal impacts of a discountrate change from the firm-specific impacts of changes in the hypothesized option value. Evidence consistent with changes in the value of the option is reported.     

VIX期权定价与校正

VIX期权作为波动率衍生品能为金融机构提供有效的市场风险对冲工具。文献中对VIX期权定价的实证分析误差都很大,原因在于模型的选取误差以及校正方法和样本选取不妥。通过在VIX模型中加入均值回复因素和跳因素,可以使VIX过程更加合理,也可以使VIX期权定价精度更高。通过对VIX期权市场中间报价进行校正,得到了4个文献模型的参数估计,并比较4个模型的定价精度和正向隐含波动率偏斜拟合效果。     

VIX option pricing and CBOE VIX Term Structure: A new methodology for volatility derivatives valuation

This study integrates CBOE VIX Term Structure and VIX futures to simplify VIX option pricing in multifactor models. Exponential and hump volatility functions with one- to three-factor models of the VIX evolution are used to examine their pricing for VIX options across strikes and maturities. The results show that using exponential volatility functions presents an effective choice as pricing models for VIX calls, whereas hump volatility functions provide efficient out-of-sample valuation for most VIX puts, in particular with deep in-the-money and deep out-of-the-money. Pricing errors for calls can be further reduced with a two-factor model.     

VIX futures term structure and the expectations hypothesis

Tests of the expectations hypothesis reveal that the slope of the VIX futures term structure predicts the direction but not the magnitude of the evolution of the short-end of the curve, but predicts neither the direction nor the magnitude of short-term changes in the long-end of the curve. Relative value seeking spread trades, constructed to exploit such violations, deliver excess returns with annualized Sharpe ratios equal or greater than those of volatility-writing strategies deployed by VIX ETN's for a majority of the 32 spread trade combinations tested. I demonstrate that profits from beta-neutral variations of the spread trades, which are not compensation for taking on equity downside risk by design, are propagated by inflows of capital into VIX futures markets, after controlling for factors that measure changes in the availability of hedge fund capital, risk appetite, and momentum. At the heart of profits, and by extension the term structure anomalies, is a disproportionally elevated basis propagated by long VIX demand that enters the futures market through ETN channels.     

Predicting stock returns in the presence of uncertain structural changes and sample noise

The predictive power of the dividend-price ratio has been the subject of intense scrutiny. Most studies on return predictability assume that predictor variables follow stationary processes with constant long-run means. Following recent evidence on the role of structural breaks in the dividend-price ratio mean, we propose an estimation method that explicitly incorporates uncertainty about the location and magnitude of structural breaks in the predictor that extracts the regime mean component of the dividend-price ratio. Adjusting for structural changes in the ratio’s mean and estimation error significantly improves predictive power of the dividend-price ratio as well as other standard predictors in sample and out of sample.     

Impact of macroeconomic announcements on implied volatility slope of SPX options and VIX

This paper examines the impact of macroeconomic announcements on the high-frequency behavior of the observed implied volatility skew of S&P 500 index options and VIX. We document that macroeconomic announcements affect VIX significantly and slope at a lesser extent. We also find evidence that good and bad announcements significantly and asymmetrically change implied volatility slope and VIX.     

A jump diffusion model for VIX volatility options and futures

Volatility indices are becoming increasingly popular as a measure of market uncertainty and as a new asset class for developing derivative instruments. Although jumps are widely considered as a salient feature of volatility, their implications for pricing volatility options and futures are not yet fully understood. This paper provides evidence indicating that the time series behaviour of the VIX index is well approximated by a mean reverting logarithmic diffusion with jumps. This process is capable of capturing stylized facts of VIX dynamics such as fast mean-reversion at higher levels, level effects of volatility and large upward movements during times of market stress. Based on the empirical results, we provide closed-form valuation models for European options written on the spot and forward VIX, respectively.     

Time-varying correlation between stock market returns and real estate returns

Direct investment in commercial or residential real estate is found to provide valuable diversification benefits for Australian investors though this is not so evident for indirect real estate investment vehicles like listed Australian real estate investment trusts (A-REIT). Further, multivariate analysis of Australian real estate and share market quarterly returns, spanning the period from the 3rd quarter 1986 to the 3rd quarter 2009, suggest that the correlation between real estate returns and share market returns is time-varying. Finally, while all of the asset class correlation coefficients increased with the Global Financial Crisis period this broad movement in asset class correlation is not evident in during the Wall Street Crash of 1987.     

Is There a Dead Spot? New Evidence on FOMC Decisions Before Elections

Using new data that chronicle the Fed's internal forecast of the output gap from 1973 to 1998, this paper tests for an electoral cycle in the decisions of the Federal Open Market Committee (FOMC). The paper provides evidence of a dead spot in the committee's decisions before presidential elections. For given values of these internal forecasts, the FOMC is less likely to decide to tighten monetary policy in the year preceding a presidential election than at other times.     

VIX term structure forecasting: New evidence based on the realized semi-variances

Considering the asymmetric volatility response to positive and negative shocks, this paper investigates VIX term structure forecasting by incorporating the realized upside and downside semi-variances based on high-frequency data, named good volatility and bad volatility, into the discrete-time GARCH-type model. We derive the risk-neutral model specification and calculate the analytical expression of VIX term structure, then estimate parameters by the maximum likelihood method. The MoP strategy (momentum of predictability, Wang et al., 2018) is extended for VIX term structure forecasting. Our empirical results show that incorporating high frequency data and considering the asymmetric shocks of realized variance are necessary to get much more accurate forecasting. The application of MoP strategy demonstrates the superior forecasting ability of integrating the advantages of multiple individual models. The evaluation of economic significance further confirms the superiority of our newly proposed model and the combination of multiple individual models, and results are robust under the alternative realized measure.     

Correlations between stock returns and bond returns: income and substitution effects

We attempt to better understand the varying correlations between stock and bond returns across countries and over sample periods using international data. The observation is that there are two forces that affect the correlation between stock and bond returns. The force that drives a positive correlation is identified as the income effect. The force that drives a negative correlation is identified as the substitution effect. In combination, the two effects help determine the actual correlation between stock and bond returns. We contribute to the literature by proposing an empirical method, the structural vector autoregression (VAR) identification method, to identify the two—income and substitution—effects and to measure the relative importance of the two effects that determine the actual net relation between the two asset returns. We further provide some evidence that the income and substitution effects are related to, among other things, the size of the financial market, the growth and volatility (risk) of the economy, and the business cycle over time. In addition, the framework of the income and substitution effects helps us better understand the automatic stabilizing effects of the dynamic optimal asset allocation during business cycles.     

Dividend yields and stock returns: Implications of abnormal January returns

This study examines the empirical relation between stock returns and (long-run) dividend yields. The findings show that much of the phenomenon is due to a nonlinear relation between dividend yields and returns in January. Regression coefficients on dividend yields, which some models predict should be non-zero due to differential taxation of dividends and capital gains, exhibit a significant January seasonal, even when controlling for size. This finding is significant since there are no provisions in the after-tax asset pricing models that predict the tax differential is more important in January than in other months.     

Asymmetric effects of federal funds target rate changes on S&P100 stock returns,volatilities and correlations

We study the effects of FOMC announcements of federal funds target rate decisions on individual stock returns, volatilities and correlations at the intraday level. For all three characteristics we find that the stock market responds differently to positive and negative target rate surprises. First, the average response to positive surprises (that is, bad news for stocks) is larger. Second, in case of bad news the mere occurrence of a surprise matters most, whereas for good news its magnitude is more important. These new insights are possible due to the use of high-frequency intraday data.