Time‐Varying Risk–Return Trade‐off in the Stock Market

We uncover a strong comovement of the stock market risk–return trade‐off with the consumption–wealth ratio (CAY). The finding reflects time‐varying investment opportunities rather than countercyclical aggregate relative risk aversion. Specifically, the partial risk–return trade‐off is positive and constant when we control for CAY as a proxy for investment opportunities. Moreover, conditional market variance scaled by CAY is negatively priced in the cross‐section of stock returns. Our results are consistent with a limited stock market participation model, in which shareholders require an illiquidity premium that increases with CAY, in addition to the risk premium that is proportional to conditional market variance.     

Differential risk premiums and the UIP puzzle

We respecify the uncovered interest rate parity (UIP) conditions by inverting the market price of the risk (Sharpe ratio) formula. Our empirical model provides new insight indicating that violations to the UIP stem from the existence of a risk premium in the exchange rates and from observed market return differentials being a noisy statistic of the markets’ expected return differentials in our respecified model. Using an integrated macro‐micro structure framework for expected market return differentials improves our model fit and the validity of UIP.     

Isolating the disaster risk premium with equity options

The US equity risk premium is approximated with a mean unhedged equity return. I utilize out-of-the-money put options to obtain a hedged equity return, which allows me to quantify the disaster risk premium as the difference between the means of unhedged and hedged equity returns. I demonstrate that a substantial fraction of the U.S. equity risk premium over the period from 1996 to 2016 is attributed to disasters defined as stock price depreciations below a pre-specified strike price. Employing alternative hedging schemes increases the contribution of disasters to the equity risk premium.     

Understanding Housing Market Volatility

The Campbell–Shiller present value formula implies a factor structure for the price–rent ratio of housing market. Using a dynamic factor model, we decompose the price–rent ratios of 23 major housing markets into a national factor and independent local factors, and we link these factors to the economic fundamentals of the housing markets. We find that a large fraction of housing market volatility is local and that the national factor has become more important than local factors in driving housing market volatility since 1999, consistent with the findings in Del Negro and Otrok (2007). The local volatilities mostly are due to time variations of idiosyncratic housing market risk premia, not local growth. At the aggregate level, the growth and interest rate factors jointly account for less than half of the total variation in the price–rent ratio. The rest is due to the aggregate housing market risk premium and a pricing error. We find evidence that the pricing error is related to money illusion, especially at the onset of the recent housing market bubble. The rapid rise in housing prices prior to the 2008 financial crisis was accompanied by both a large increase in the pricing error and a large decrease in the housing market risk premium.     

A Generalized Earnings‐Based Stock Valuation Model with Learning

We present a stock valuation model in an incomplete‐information environment in which the unobservable mean of earnings growth rate (MEGR) is learned and price is updated continuously. We calibrate our model to a market portfolio to empirically evaluate its performance. Of the 8.84% total risk premium we estimate, the earnings growth premium is 4.57%, the short‐rate risk contributes 3.38%, and the learning‐induced risk premium on the unknown MEGR is 0.89% (a nontrivial 10% of the total risk premium). This result highlights the significant learning effect on valuation, implying an additional risk premium in an incomplete‐information environment.     

Computing the market price of volatility risk in the energy commodity markets

In this paper, we demonstrate the need for a negative market price of volatility risk to recover the difference between Black–Scholes [Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654]/Black [Black, F., 1976. Studies of stock price volatility changes. In: Proceedings of the 1976 Meetings of the Business and Economics Statistics Section, American Statistical Association, pp. 177–181] implied volatility and realized-term volatility. Initially, using quasi-Monte Carlo simulation, we demonstrate numerically that a negative market price of volatility risk is the key risk premium in explaining the disparity between risk-neutral and statistical volatility in both equity and commodity-energy markets. This is robust to multiple specifications that also incorporate jumps. Next, using futures and options data from natural gas, heating oil and crude oil contracts over a 10 year period, we estimate the volatility risk premium and demonstrate that the premium is negative and significant for all three commodities. Additionally, there appear distinct seasonality patterns for natural gas and heating oil, where winter/withdrawal months have higher volatility risk premiums. Computing such a negative market price of volatility risk highlights the importance of volatility risk in understanding priced volatility in these financial markets.     

Is Volatility Risk for the British Pound Priced in U.S. Options Markets?

This paper estimates the premium for volatility risk for European currency options written on British pounds. The average annualized premium for volatility risk is neither statistically different from zero nor invariant to the option's moneyness. However, the risk premium is positively and nonproportionaly related to the level of volatility, except for out‐of‐the‐money options. Finding a zero premium for volatility risk does not undermine the assumption of a zero‐price volatility risk in many extant stochastic‐volatility option pricing models and the option pricing formulas in those models.     

The price of variance risk

Between 1996 and 2014, it was costless on average to hedge news about future variance at horizons ranging from 1 quarter to 14 years. Only unexpected, transitory realized variance was significantly priced. These results present a challenge to many structural models of the variance risk premium, such as the intertemporal CAPM and recent models with Epstein–Zin preferences and long-run risks. The results are also difficult to reconcile with macro models in which volatility affects investment decisions. At the same time, the data allows us to distinguish between different disaster models; a model in which the stock market has a time-varying exposure to disasters and investors have power utility fits the major features of the variance term structure.     

The world ex ante risk premium: an empirical investigation

A number of recent papers have focused on testing the linearity restrictions implied by international asset pricing models. The tests, however, have not addressed an additional restriction implied by the models; namely, that the risk premium on the world portfolio is positive. This study provides a direct assessment of this restriction. The evidence indicates that the ex ante world market risk premium can be negative. The results are robust to market proxies that are hedged and unhedged with respect to currency risk. Subperiod analysis indicates that the rejection of the positive risk premium restriction is driven by the first half of the sample period.     

News sentiment and sovereign credit risk

We explore the impact of media content on sovereign credit risk. Our measure of media tone is extracted from the Thomson Reuters News Analytics database. As a proxy for sovereign credit risk we consider credit default swap (CDS) spreads, which are decomposed into their risk premium and default risk components. We find that media tone explains and predicts CDS returns and is a mixture of noise and information. Its effect on risk premium induces a temporary change in investors’ appetite for credit risk exposure, whereas its impact on the default component leads to reassessments of the fundamentals of sovereign economies.     

Financialization and speculators risk premia in commodity futures markets

J.M. Keynes coined the term normal backwardation, a situation where a futures price for a particular expiry month is less than the expected spot price for that month. He argued hedgers pay speculators a risk premium, giving rise to normal backwardation. We study the behavior of commodity futures before and since financialization of the markets, which started about 20 years ago. We find the poor returns to managed futures in recent years are likely due to the impact of financialization and the associated outside money suppressing the futures risk premium.     

Time-varying rare disaster risk and stock returns

This study provides empirical support for theoretical models that allow for time-varying rare disaster risk. Using a database of 447 international political crises during the period 1918-2006, we create a crisis index that shows substantial variation over time. Changes in this crisis index, our proxy for changes in perceived disaster probability, have a large impact on both the mean and volatility of world stock market returns. Crisis risk is positively correlated with the earnings-price ratio and the dividend yield. Cross-sectional tests also show that crisis risk is priced: Industries that are more crisis risk sensitive yield higher returns.     

Expected returns and expected dividend growth

We investigate a consumption-based present-value relation that is a function of future dividend growth and find that changing forecasts of dividend growth are an important feature of the post-war U.S. stock market, despite the failure of the dividend–price ratio to uncover such variation. In addition, dividend forecasts are found to covary with changing forecasts of excess stock returns over business cycle frequencies. This covariation is important because positively correlated fluctuations in expected dividend growth and expected returns have offsetting effects on the log dividend–price ratio. The market risk premium and expected dividend growth thus vary considerably more than is apparent using the log divided–price ratio alone as a predictive variable.     

On the test of the correction mechanism for mis-pricing between assets using a statistical yield spread model

This paper investigates the existence of a correction mechanism for mis-pricing between Japanese stock and bond. By this correction mechanism we mean that when deviations occur from the equilibrium levels of the expected return differentials between stock and bond — the risk premium differentials, the market will tend to correct the mis-pricing and bring the expected return differentials back to the equilibrium levels. We assume that the yield spread between the predicted earnings price ratio of stock and the yield to maturity of bond reflects the risk premium between stock and bond, and estimate the equilibrium risk premium differentials and mis-prices between stock and bond by modelling their behaviors with a statistical yield spread model (SYS). Empirical results strongly indicate the existence of the mis-pricing correction mechanism, suggesting the inefficiency of securities markets.     

Future Realized Return,Firm‐specific Risk and the Implied Expected Return

In this paper, I propose a novel approach to derive a firm‐specific measure of expected return. It builds on recent accounting‐based valuation models developed by Clubb (2013) and Ashton and Wang (2013). The measure is intrinsically linked to commonly used financial ratios, including book‐to‐market, (forward) earnings yield, and dividend‐to‐price, as well as growth and past returns. The empirical evidence shows that it is significantly positively associated with future realized stock returns and also significantly correlated with commonly used risk characteristics in a theoretically predictable manner. The results are likely to be of interest to practitioners and managers in making capital allocation decisions and to academics in need of proxies for firms’ discount rates and expected returns.     

Extreme downside risk and expected stock returns

We propose a measure for extreme downside risk (EDR) to investigate whether bearing such a risk is rewarded by higher expected stock returns. By constructing an EDR proxy with the left tail index in the classical generalized extreme value distribution, we document a significantly positive EDR premium in cross-section of stock returns even after controlling for market, size, value, momentum, and liquidity effects. The EDR premium is more prominent among glamor stocks and when high market returns are expected. High-EDR stocks are generally characterized by high idiosyncratic risk, large downside beta, lower coskewness and cokurtosis, and high bankruptcy risk. The EDR premium persists after these characteristics are controlled for. Although Value at Risk (VaR) plays a significant role in explaining the EDR premium, it cannot completely subsume the EDR effect.     

THE INVESTMENT OPPORTUNITY SET AND ITS PROXY VARIABLES

We use a real options approach to evaluate the performance of several proxy variables for a firm's investment opportunity set. The results show that, on a relative scale, the market‐to‐book assets ratio has the highest information content with respect to investment opportunities. Although both the market‐to‐book equity and the earnings–price ratios are related to investment opportunities, they do not contain information that is not already contained in the market‐to‐book assets ratio. Consistent with this finding, a common factor constructed from several proxy variables does not improve the performance of the market‐to‐book assets ratio.     

Recovering the market risk premium from higher-order moment risks

We propose a consistent approach for the estimation of the market risk premium. As a first step, we define the broadest possible set of ex ante estimators from the viewpoint of a power utility optimiser holding the market portfolio. We then employ an evaluation framework to optimise the parametrisation of the methodology. We show that this theoretical framework can still produce reasonable market risk premium estimates, even when the representative agent is not a power utility optimiser. Our results show that the inclusion of higher-order moment risk premia improves the accuracy of the method.     

Habit formation,the cross section of stock returns and the cash-flow risk puzzle

Non-linear external habit persistence models, which feature prominently in the recent “equity premium” asset pricing and macroeconomics literature, generate counterfactual predictions in the cross-section of stock returns. In particular, we show that in the absence of cross-sectional heterogeneity in firms’ cash-flow risk, these models produce a “growth premium,” that is, stocks with high price-to-fundamental ratios command a higher premium than stocks with low price-to-fundamental ratios. This implication is at odds with the well-established empirical observation of a “value premium” in the cross-section of stock returns. Substantial heterogeneity in firms’ cash-flow risk yields both a value premium as well as most of the stylized facts about the cross-section of stock returns, but it generates a “cash-flow risk puzzle”: Quantitatively, value stocks have to have “too much” cash-flow risk compared to the data to generate empirically plausible value premiums.     

Pricing of time-varying liquidity risk in Finnish stock market: new evidence

Using two recently developed illiquidity measures, we estimate a conditional version of liquidity-adjusted capital asset pricing model (LCAPM), which allows for a time-varying decomposition of the total illiquidity premium into a level component and three risk components. The total estimated annualized illiquidity premium for the Finnish equities during 1997–2015 is 1.13–1.90% depending on the illiquidity measure. Of the three systematic liquidity risk components, risk arising from hedging of wealth shocks is the most important followed by commonality in liquidity risk, whereas flight to liquidity risk is not significantly priced in the Finnish stock market. Our results show that the liquidity risk is time varying, therefore the models estimating the risk-return relationship should address the issue of conditionality.