Inflation and the formation of expectations

This paper develops a model of expectations which generates paths that are consistent with observations that an acceleration of the monetary growth rate initially raises and eventually lowers real holdings of cash balances. It introduces a two-part expectations hypothesis where individuals are assumed to form expectations about the entire path of the price level and about the short-term inflation rate. Interaction between regressive and extrapolative elements induces a transitory rise in money holdings during the initial phase of inflation as expectations are that the process will reverse itself. Subsequently, as expectations catch up, the decline in desired holdings induces an overshooting of the inflation rate.     

Inequality risk premia

Using a long time-series of U.S. income inequality, I find that the market pays higher prices for assets that hedge against increased inequality. This is consistent with the prediction of an incomplete-markets model incorporating preferences over both comparative and noncomparative consumption “goods” when the weight on the former is large. The model implies that the time-series properties of the premium can be used to identify the substitutability of these two sources of utility. There is evidence that the magnitude of the (negative) inequality risk premium is countercyclical, suggesting that agents care more about status when they are worse off.     

Political uncertainty and risk premia

We develop a general equilibrium model of government policy choice in which stock prices respond to political news. The model implies that political uncertainty commands a risk premium whose magnitude is larger in weaker economic conditions. Political uncertainty reduces the value of the implicit put protection that the government provides to the market. It also makes stocks more volatile and more correlated, especially when the economy is weak. We find empirical evidence consistent with these predictions.     

Mean-variance cointegration and the expectations hypothesis

The present paper sheds further light on a well-known (alleged) violation of the expectations hypothesis of the term structure (EHT): the frequent finding of unit roots in interest rate spreads. We show that the EHT implies (i) that the nonstationarity stems from the holding premium, which is hence (ii) cointegrated with the spread. In a stochastic discount factor framework, we model the premium as being driven by the integrated variance of excess returns. Introducing the concept of mean-variance cointegration, we actually find cointegration relations between the conditional first and second moment of US bond data.     

Countercyclical currency risk premia

We describe a novel currency investment strategy, the ‘dollar carry trade,’ which delivers large excess returns, uncorrelated with the returns on well-known carry trade strategies. Using a no-arbitrage model of exchange rates we show that these excess returns compensate U.S. investors for taking on aggregate risk by shorting the dollar in bad times, when the U.S. price of risk is high. The countercyclical variation in risk premia leads to strong return predictability: the average forward discount and U.S. industrial production growth rates forecast up to 25% of the dollar return variation at the one-year horizon. The estimated model implies that the variation in the exposure of U.S. investors to worldwide risk is the key driver of predictability.     

Bond risk premia and realized jump risk

We find that augmenting a regression of excess bond returns on the term structure of forward rates with an estimate of the mean realized jump size almost doubles the R² of the forecasting regression. The return predictability from augmenting with the jump mean easily dominates that offered by augmenting with options-implied volatility and realized volatility from high-frequency data. In out-of-sample forecasting exercises, inclusion of the jump mean can reduce the root mean square prediction error by up to 40%. The incremental return predictability captured by the realized jump mean largely accounts for the countercyclical movements in bond risk premia. This result is consistent with the setting of an incomplete market in which the conditional distribution of excess bond returns is affected by a jump risk factor that does not lie in the span of the term structure of yields.     

Long-term foreign exchange risk premia and inflation risk

As highlighted by recent literature, long-term foreign exchange risk premia (FRP) of a currency pair tend to covary negatively with short-term real interest rate differentials (RIRD) of the pair. We fit an affine term structure model for 9 major currencies against the US dollar and estimate two components of this covariance: the real risk premia (RRP) component and the inflation risk premia differential (IRPD) component. We find that the IRPD component is significantly negative for all currency pairs in our sample. We propose a macro-finance model to understand the types of shocks that generate such covariance.     

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.     

Exchange rate and inflation risk premia in the EMU

This paper tests the effects of exchange rate and inflation risk factors on asset pricing in the European Union (EU) stock markets. This investigation was motivated by the results of Vassalou [J. Int. Money Finance, 2000, 19, 433–470] showing that both exchange rate and foreign inflation are generally priced in equity returns, and it studies the opportunity of evaluating the causality between these sources of risk after the elimination of the EU currency risks because of the adoption of the single currency. Our results show that both exchange rate and inflation risks are significantly priced in the pre- and post-euro periods. Moreover, the sizes of exchange rate and inflation risk premiums are economically significant in the pre- and post-euro periods. Futhermore, the UK and excluding-UK inflation risk premiums explain, in part, our evidence concerning a large EUR/GBP exchange rate risk premium and the existence of an economically significant domestic non-diversifiable risk after euro adoption. Hence overlooking inflation risk factors can produce an under/overestimation of the currency premiums and a miscalculation of the degree of integration of stock markets.     

International evidence on bond risk premia

This paper revisits the study of time-varying excess bond returns in international bond markets. Using newly available yield curve data from 10 different countries with independent monetary policy, I test the robustness of Cochrane and Piazzesi (2005). For most countries in my sample, I find more modest predictive power for forward rates than originally found by Cochrane and Piazzesi (2005) for the US. Their single-factor model captures well the predictability in international data, and this factor also tends to have a tent-shape in most countries of my sample. CP factors are more idiosyncratic across countries than yields or forward rates. Finally, I show that the recent financial crisis has significantly affected the predictability of excess bond returns.     

Asset pricing,time-varying risk premia and interest rate risk

This paper investigates the role of interest rate risk in explaining security price changes. We develop and test a two-factor linear beta pricing model of security returns in which the factors are the excess returns on the long-term, riskless bond and the equal-weighted equity market index. We find that time-variation in the interest rate and market risk premia influence expected security returns. Furthermore, conditional interest rate volatility affects security returns, particularly during periods of substantial interest rate movements.     

Extracting inflation expectations and inflation risk premia from the term structure: A joint model of the UK nominal and real yield curves

This paper analyses the UK interest rate term structure over the period since October 1992, when the United Kingdom adopted an explicit inflation target, using an affine term structure model estimated using both government bond yields and survey data. The model imposes no-arbitrage restrictions across nominal and real yields, which enables interest rates to be decomposed into expected real policy rates, expected inflation, real term premia and inflation risk premia. The model is used to shed light on major developments over the period, including the impact of Bank of England independence and the low real bond yield ‘conundrum’.     

Time-varying state variable risk premia in the ICAPM

We find that the relation between state variables, such as the t-bill rate and term spread, and consumption growth is time-varying. In the cross-section of U.S. stocks, risk premia for exposure to state variables vary over time accordingly. When a state variable predicts consumption strongly relative to its own history, its annualized risk premium increases by 6% (0.4 in Sharpe ratio). This effect implies that risk premia can switch signs and are increasing in the conditional variance of the state variable. These common drivers of time-varying risk premia are consistent with the Intertemporal CAPM. Benchmark factors contain the same conditional expected return effects as state variable risk premia.     

Time-varying risk premia and the cross section of stock returns

This paper develops and estimates a heteroskedastic variant of Campbell’s [Campbell, J., 1993. Intertemporal asset pricing without consumption data. American Economic Review 83, 487–512] ICAPM, in which risk factors include a stock market return and variables forecasting stock market returns or variance. Our main innovation is the use of a new set of predictive variables, which not only have superior forecasting abilities for stock returns and variance, but also are theoretically motivated. In contrast with the early authors, we find that Campbell’s ICAPM performs significantly better than the CAPM. That is, the additional factors account for a substantial portion of the two CAPM-related anomalies, namely, the value premium and the momentum profit.     

Option-implied volatility factors and the cross-section of market risk premia

The main goal of this paper is to study the cross-sectional pricing of market volatility. The paper proposes that the market return, diffusion volatility, and jump volatility are fundamental factors that change the investors’ investment opportunity set. Based on estimates of diffusion and jump volatility factors using an enriched dataset including S&P 500 index returns, index options, and VIX, the paper finds negative market prices for volatility factors in the cross-section of stock returns. The findings are consistent with risk-based interpretations of value and size premia and indicate that the value effect is mainly related to the persistent diffusion volatility factor, whereas the size effect is associated with both the diffusion volatility factor and the jump volatility factor. The paper also finds that the use of market index data alone may yield counter-intuitive results.     

Determinants of stock market volatility and risk premia

Summary. We show the dynamics of diverse beliefs is the primary propagation mechanism of volatility in asset markets. Hence, we treat the characteristics of the market beliefs as a primary, primitive, explanation of market volatility. We study an economy with stock and riskless bond markets and formulate a financial equilibrium model with diverse and time varying beliefs. Agents states of belief play a key role in the market, requiring an endogenous expansion of the state space. To forecast prices agents must forecast market states of belief which are beliefs of others hence our equilibrium embodies the Keynes Beauty Contest. A market state of belief is a vector which uniquely identifies the distribution of conditional probabilities of agents. Restricting beliefs to satisfy the rationality principle of Rational Belief (see Kurz, 1994, 1997) our economy replicates well the empirical record of the (i) moments of the price/dividend ratio, risky stock return, riskless interest rate and the equity premium; (ii) Sharpe ratio and the correlation between risky returns and consumption growth; (iii) predictability of stock returns and price/dividend ratio as expressed by: (I) Variance Ratio statistic for long lags, (II) autocorrelation of these variables, and (III) mean reversion of the risky returns and the predictive power of the price/dividend ratio. Also, our model explains the presence of stochastic volatility in asset prices and returns. Two properties of beliefs drive market volatility: (i) rationalizable over confidence implying belief densities with fat tails, and (ii) rationalizable asymmetry in frequencies of bull or bear states.This research was supported by a grant of the Smith Richardson Foundation to the Stanford Institute for Economic Policy Research (SIEPR). We thank Kenneth Judd for constant advice which was crucial at several points in the development of this work. We also thank Kenneth Arrow, Min Fan, Michael Magill, Carsten Nielsen, Manuel Santos, Nicholas Yannelis, Ho-Mou Wu and Woody Brock for comments on earlier drafts. The RBE model developed in this paper and the associated programs used to compute it are available to the public on Mordecai Kurzs web page at http://www.stanford.edu/ mordecai.This revised version was published online in January 2005 with corrections to the Cover date.     

Varying risk premia in international bond markets

Cochrane and Piazzesi [Cochrane, J.H., Piazzesi, M., 2005. Bond risk premia. American Economic Review 95, 138–160] use forward rates to forecast future bond returns. We extend their approach by applying their model to international bond markets. Our results indicate that the unrestricted Cochrane and Piazzesi (2005) model has a reasonable forecasting power for future bond returns. The restricted model, however, does not perform as well on an international level. Furthermore, we cannot confirm the systematic tent shape of the estimated parameters found by Cochrane and Piazzesi (2005). The forecasting models are used to implement various trading strategies. These strategies exhibit high information ratios when implemented in individual countries or on an international level and outperform alternative approaches. We introduce an alternative specification to forecast future bond returns and achieve superior risk-adjusted returns in our trading strategy. Bayesian model averaging is used to enhance the performance of the proposed trading strategy.