The long-run equity risk premium

Based on a survey of US Chief Financial Officers (CFOs), we present expectations of the equity risk premium measured over a 10-year horizon relative to a 10-year US Treasury bond. This multi-year survey has been conducted each quarter from June 2000 to June 2005. Each quarter the survey also provides measures of cross-sectional disagreement about the risk premium, skewness, and a measure of individual uncertainty. The individual uncertainty is deduced from the 80% confidence interval that each respondent provides for his or her risk premium assessment. We also present evidence on the determinants of the long-run risk premium. Our analysis suggests there is a positive correlation between the ex ante risk premium and real interest rates as reflected in Treasury Inflation Indexed Notes.     

The Variation of Economic Risk Premiums in Real Estate Returns

We examine the predictable components of returns on stocks, bonds, and real estate investment trusts (REITs). We employ a multiple-beta asset pricing model and find that there are varying degrees of predictability among stocks, bonds, and REITs. Furthermore, we find that most of the predictability of returns is associated with the economic variables employed in the asset pricing model. The stock market risk premium is highly important in capturing the predictable variation in stock portfolios, and the bond market risk premiums (term and risk structure of interest rates) are important in capturing the predictable variation in bond portfolios. For REITs, however, both the stock and bond market risk premiums capture the predictable variation in returns. REITs have comparable return predictability to stock portfolios. We conclude that there is an important economic risk premium for REITs that are not captured by traditional multiple-beta asset pricing models.     

Rare disaster risk and the expected equity risk premium

Consistent with the predictions of rare disaster models, we find that a proxy for the time‐varying probability of rare disasters helps to explain fluctuations in expectations of the equity risk premium. Our proxy for disaster risk is a recently developed measure of global political instability, and the expected market risk premium is from Value Line analysts' expected stock returns. Consistent with long‐run risk models, uncertainty about expected GDP growth and expected consumption growth is also significantly positively related to the expected market risk premium. We obtain similar results when we use the earnings–price ratio and the dividend–price ratio as proxies for the expected market risk premium.     

Consumption growth predictability and asset prices

We derive and test a consumption-based intertemporal asset pricing model in which an asset earns a risk premium if it performs poorly when expected future consumption growth deteriorates. The predictability of consumption growth combined with the recursive preference delivers news about future consumption growth an additional risk factor, in addition to news about current consumption growth. We model the consumption growth dynamics using a vector autoregressive (VAR) structure with a set of instrumental variables commonly used for forecasting future economic growth. Our VAR estimation provides strong empirical support for future consumption growth predictability. The cross-sectional test shows that the model explains reasonably well the dispersion in average excess returns of 25 portfolios sorted on size and book-to-market, as well as 25 portfolios sorted on size and long-term return reversal. Growth stocks and long-term winners underperform value stocks and long-term losers, respectively, because growth stocks and long-term winners hedge adverse changes in the future consumption growth opportunities.     

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.     

Inflation Uncertainty, Real-Interest-Rate Uncertainty, and the Liquidity Premium on Government Bonds

This paper shows that the components of uncertainty about nominal interest rates, real-rate uncertainty and inflation uncertainty, have different effects on the liquidity premium. An increase in inflation uncertainty should increase the equilibrium liquidity premium because investors reduce the effect of inflation uncertainty on the riskiness of their portfolios by holding more short-term bonds. In contrast, an investor can reduce the effects of uncertainty about future ex-ante real rates on portfolio return by matching more closely the maturity dates of the bonds held with the date on which the portfolio is to be liquidated for consumption purposes. Thus, the effect of an increase in real-rate uncertainty on the equilibrium liquidity premium is ambiguous, depending on the relative magnitudes of long-term and short-term saving and the proportions of short-term and long-term bonds issued by the government.     

A consumption-based model of the term structure of interest rates

This paper proposes a consumption-based model that accounts for many features of the nominal term structure of interest rates. The driving force behind the model is a time-varying price of risk generated by external habit. Nominal bonds depend on past consumption growth through habit and on expected inflation. When calibrated to data on consumption, inflation, and the aggregate market, the model produces realistic means and volatilities of bond yields and accounts for the expectations puzzle. The model also captures the high equity premium and excess stock market volatility.     

Technology prospects and the cross-section of stock returns

In an economy with time-varying investment opportunities, the changes in technology prospects affect aggregate consumption and individual firm's future dividends, and lead to systematic technology risk. We construct a technology factor to track the changes in technology prospects measured by U.S. patent shocks, and find that this factor explains the growth of aggregate consumption, helps to price important stock portfolios, and carries significant risk premium. Our empirical results suggest the existence of technology risk in the cross-section of stock returns.     

Monetary Policy Uncertainty and the Response of the Yield Curve to Policy Shocks

This paper studies the nonlinear response of the term structure of interest rates to monetary policy shocks and presents a new stylized fact. We show that uncertainty about monetary policy changes the way the term structure responds to monetary policy. A policy tightening leads to a significantly smaller increase in long-term bond yields if policy uncertainty is high at the time of the shock. We also look at the decomposition of bond yields into expectations about future policy and the term premium. The weaker response of yields is driven by the fall in term premia, which fall more strongly if uncertainty about policy is high. Conditional on a monetary policy shock, higher uncertainty about monetary policy tends to make securities with longer maturities relatively more attractive to investors. As a consequence, investors demand even lower term premia. These findings are robust to the measurement of monetary policy uncertainty, the definition of the monetary policy shock, and to changing the model specification.     

News and the cross-section of expected corporate bond returns

We study the cross-section of expected corporate bond returns using an inter-temporal CAPM (ICAPM) with three-factors: innovations in future excess bond returns, future real interest rates and future expected inflation. Our test assets are a broad range of corporate bond market index portfolios. We find that two factors – innovations about future inflation and innovations about future real interest rates – explain the cross-section of expected corporate bond returns in our sample. Our model provides an alternative to the ad hoc risk factor models used, for example, in evaluating the performance of bond mutual funds.     

Inflation and the stock market: Understanding the “Fed Model”

The so-called Fed model postulates that the dividend or earnings yield on stocks should equal the yield on nominal Treasury bonds, or at least that the two should be highly correlated. In US data there is indeed a strikingly high time series correlation between the yield on nominal bonds and the dividend yield on equities. This positive correlation is often attributed to the fact that both bond and equity yields comove strongly and positively with expected inflation. Contrary to some of the extant literature, we show that this effect is consistent with modern asset pricing theory incorporating uncertainty about real growth prospects and habit-based risk aversion. In the US, high expected inflation has tended to coincide with periods of heightened uncertainty about real economic growth and unusually high risk aversion, both of which rationally raise equity yields.     

Examining the bond premium puzzle with a DSGE model

The basic inability of standard theoretical models to generate a sufficiently large and variable nominal bond risk premium has been termed the “bond premium puzzle.” We show that the term premium on long-term bonds in the canonical dynamic stochastic general equilibrium (DSGE) model used in macroeconomics is far too small and stable relative to the data. We find that introducing long-memory habits in consumption as well as labor market frictions can help fit the term premium, but only by seriously distorting the DSGE model's ability to fit other macroeconomic variables, such as the real wage; therefore, the bond premium puzzle remains.     

The comovement of US and German bond markets

We use a vector-autoregression, with parameter estimates corrected for small-sample bias, to decompose US and German unexpected bond returns into three ‘news’ components: news about future inflation, news about future real interest rates, and news about future excess bond returns (term premia). We then cross-country correlate these news components to see which component is responsible for the high degree of comovement of US and German bond markets. For the period 1975-2003 we find that inflation news is the main driving force behind this comovement. When news is coming to the US market that future US inflation will increase, there is a tendency that German inflation will also increase. This is regarded bad news for the bond market in both countries whereby bond prices are bid down leading to immediate negative return innovations and changing expectations of future excess bond returns. Thus, comovement in expected future inflation is the main reason for bond market comovement.     

Consumption Volatility Risk

We show that time variation in macroeconomic uncertainty affects asset prices. Consumption volatility is a negatively priced source of risk for a wide variety of test portfolios. At the firm level, exposure to consumption volatility risk predicts future returns, generating a spread across quintile portfolios in excess of 7% annually. This premium is explained by cross‐sectional differences in the sensitivity of dividend volatility to consumption volatility. Stocks with volatile cash flows in uncertain aggregate times require higher expected returns.     

Mortgage timing

We study how the term structure of interest rates relates to mortgage choice at both household and aggregate levels. A simple utility framework of mortgage choice points to the long-term bond risk premium as distinct from the yield spread and the long yield as a theoretical determinant of mortgage choice: when the bond risk premium is high, fixed-rate mortgage payments are high, making adjustable-rate mortgages more attractive. We confirm empirically that the bulk of the time variation in both aggregate and loan-level mortgage choice can be explained by time variation in the bond risk premium, whether bond risk premia are measured using forecasters’ data, a vector autoregressive (VAR) term structure model, or a simple household decision rule based on adaptive expectations. The household decision rule moves in lock-step with mortgage choice, lending credibility to a theory of strategic mortgage timing by households.     

Do subjective expectations explain asset pricing puzzles?

The structural uncertainty model with Bayesian learning, advanced by Weitzman (AER 2007), provides a framework for gauging the effect of structural uncertainty on asset prices and risk premiums. This paper provides an operational version of this approach that incorporates realistic priors about consumption growth volatility, while guaranteeing finite asset pricing quantities. In contrast to the extant literature, the resulting asset pricing model with subjective expectations yields well-defined expected utility, finite moment generating function of the predictive distribution of consumption growth, and tractable expressions for equity premium and risk-free return. Our quantitative analysis reveals that explaining the historical equity premium and risk-free return, in the context of subjective expectations, requires implausible levels of structural uncertainty. Furthermore, these implausible prior beliefs result in consumption disaster probabilities that virtually coincide with those implied by more realistic priors. At the same time, the two sets of prior beliefs have diametrically opposite asset pricing implications.     

交易所国债期限风险溢价的实证研究

本文考察了上海证券交易所国债期限风险溢价的时间变化特征及决定因素。实证结果显示，债券剩余期限越长，平均风险溢价越高；通过对不同期限债券组合的风险溢价序列建立回归模型，发现长短期利差及风险溢价的前期值对中长期债券期限风险溢价的时变性具有明显的解释能力。     

Valuation Risk and Asset Pricing

Standard representative‐agent models fail to account for the weak correlation between stock returns and measurable fundamentals, such as consumption and output growth. This failing, which underlies virtually all modern asset pricing puzzles, arises because these models load all uncertainty onto the supply side of the economy. We propose a simple theory of asset pricing in which demand shocks play a central role. These shocks give rise to valuation risk that allows the model to account for key asset pricing moments, such as the equity premium, the bond term premium, and the weak correlation between stock returns and fundamentals.     

What do asset prices have to say about risk appetite and uncertainty?

Building on intuition from the dynamic asset pricing literature, we uncover unobserved risk aversion and fundamental uncertainty from the observed time series of the variance premium and the credit spread while controlling for the conditional variance of stock returns, expectations about the macroeconomic outlook, and interest rates. We apply this methodology to monthly data from both Germany and the US. We find that the variance premium contains a substantial amount of information about risk aversion whereas the credit spread has a lot to say about uncertainty. We link our risk aversion and uncertainty estimates to practitioner and “academic” risk aversion indices, sentiment indices, financial stress indices, business cycle indicators and liquidity measures.     

Structural breaks, parameter uncertainty, and term structure puzzles

We show that uncertainty about parameters of the short rate model can account for the rejections of the expectations hypothesis for the term structure of interest rates. We assume that agents employ Bayes rule to learn parameter values in the context of a model that is subject to stochastic structural breaks. We show that parameter uncertainty also implies that the verdict on the expectations hypothesis varies systematically with the term of the long bond and the particular test employed, in the same way that is found in empirical tests.