Luis M. Viceira

Who Should Buy Long-Term Bonds?

According to conventional wisdom, long-term bonds are appropriate for long-term investors who value stability of income. We develop a model of optimal consumption and portfolio choice for infinitely-lived investors facing stochastic interest rates, solve it using an approximate analytical method, and evaluate the conventional wisdom. We show that the demand for long-term bonds has both a myopic component and an intertemporal hedging component. As risk aversion increases, the myopic component shrinks to zero but the hedging component does not. An infinitely risk-averse investor who is infinitely unwilling to substitute consumption intertemporally should hold a portfolio of long-term indexed bonds that is equivalent to an indexed perpetuity. This portfolio finances a riskless consumption stream and in this sense provides a stable income. We calibrate our model to postwar US data and compare consumption and portfolio rules with and without bond indexation, portfolio constraints, and the possibility of investment in equities. We find that when indexed bonds are not available, inflation risk leads investors to shorten their bond portfolios and increase their precautionary savings. This has serious welfare costs for conservative investors, who are much better off when they have the opportunity to buy indexed bonds. We also find that the ratio of bonds to equities in the optimal portfolio increases with the coefficient of relative risk aversion, which is consistent with conventional portfolio advice but inconsistent with the mutual fund theorem of static portfolio analysis. Our results illustrate the general point that static portfolio choice models should not be used to study the dynamic problems facing long-term investors.

Spectral GMM Estimation of Continuous-Time Processes

This paper derives a methodology for the exact estimation of continuous-time stochastic models based on the characteristic function. The estimation method does not require discretization of the process, and it is easy to apply. The method is essentially generalized method of moments on the complex plane. Hence it shares the optimality and distribution properties of GMM estimators. Moreover, we show that there are instruments that make the estimator asymptotically efficient. We illustrate the method with some applications to relevant estimation problems in continuous-time finance. We estimate a model of stochastic volatility, a jump-diffusion model with constant volatility and a model that nests both the stochastic volatility model and the jump-diffusion model. We find that negative jumps are important to explain skewness and asymmetry in excess kurtosis of the stock return distribution, while stochastic volatility is important to capture the overall level of this kurtosis. Positive jumps are not statistically significant once we allow for stochastic volatility in the model. We also estimate a non-affine model of stochastic volatility and we find that the power of the diffusion coefficient appears to be between one and two, rather than the value of one-half that leads to the standard affine stochatic volatility model. Finally, we offer an explanation for the observation that the estimate of persistence in stochatic volatility increases dramatically as the frequency of the observed data falls based on a multiple factor stochastic volatility model.

The Term Structure of the Risk–Return Trade-Off

Expected excess returns on bonds and stocks, real interest rates, and risk shift over time in predictable ways. Furthermore, these shifts tend to persist for long periods. Changes in investment opportunities can alter the risk–return trade-off of bonds, stocks, and cash across investment horizons, thus creating a “term structure” of the risk–return trade-off. This term structure can be extracted from a parsimonious model of return dynamics, as is illustrated with data from the U.S. stock and bond markets. Recent research in empirical finance has documented that expected excess returns on bonds and stocks, real interest rates, and risk shift over time in predictable ways. Furthermore, these shifts tend to persist over long periods of time. One important implication of time variation in expected returns is that investors, particularly aggressive investors, may want to engage in market-timing (or tactical asset allocation), based on the predictions of their return forecasting model, in order to maximize short-term return. There is considerable uncertainty, however, about the degree of asset return predictability, which makes it hard to identify the optimal market-timing strategy. A second, less obvious implication of asset return predictability is that risk—defined as the conditional variances and covariances per period of asset returns—may be significantly different for different investment horizons, thus creating a “term structure of the risk–return trade-off.” This article characterizes this trade-off and explores its implications for the asset allocation decisions of long-horizon investors. We present an empirical model that captures the complex dynamics of expected returns and risk but is simple to apply. Specifically, we model interest rates and returns as a vector autoregressive (VAR) model. We show how to extract the term structure of risk using this parsimonious model of return dynamics, and we illustrate our approach with the use of quarterly data from the U.S. stock, T-bond, and T-bill markets for the period since World War II. In our empirical application, we use variables that have been identified as return predictors by past empirical research, such as the short-term interest rate, the dividend–price ratio, and the yield spread between long-term and short-term bonds. These variables enable us to capture horizon effects on stock market risk, inflation risk, and real interest rate risk. Among our findings are the following: Mean reversion in stock returns decreases the volatility per period of real stock returns at long horizons, whereas reinvestment risk increases the volatility per period of real T-bill returns. Inflation risk increases the volatility per period of the real return on long-term nominal bonds held to maturity. Stocks and bonds exhibit relatively low positive correlation at both ends of the term structure of risk, but they are highly positively correlated at intermediate investment horizons. Inflation is negatively correlated with the real returns on bonds and stocks at short horizons but positively correlated at long horizons. These patterns have important implications for the efficient mean–variance frontiers that investors face at different horizons and suggest that asset allocation recommendations based on short-term risk and return may not be adequate for long-horizon investors. For example, the composition of the global minimum variance (GMV) portfolio changes dramatically for different horizons. We calculated the GMV portfolio when predictor variables are at their unconditional means—that is, when market conditions are average—and found that at short horizons, the GMV portfolio consists almost exclusively of T-bills but at long horizons, reinvestment risk makes T-bills risky. Thus, long-term investors can achieve lower risk with a portfolio that consists predominantly of long-term bonds and stocks. We also found that the composition of the tangency portfolio of bonds and stocks (calculated under the counterfactual assumption that a riskless long-term asset exists with a return equal to the average T-bill return) becomes increasingly biased toward stocks as the horizon increases. The reason is the increasing positive correlation between stocks and bonds at intermediate investment horizons and the decrease of the volatility per period of stock returns at long horizons. To concentrate on horizon effects, we bypass several other considerations that may be important in practice—for example, changes in volatility through time—and, ignoring the possibility that investors care about other properties of the return distribution, we consider only the first two moments of returns. In addition, our results depend on the particular model of asset returns that we estimated. We treated the parameters of our VAR(1) model as known, whereas these parameters are highly uncertain, and investors should take this uncertainty into account in their portfolio decisions. Fortunately, our main conclusions hold up well when the model is estimated over subsamples or is extended to allow higher-order lags. The technical details of this study are provided in “Long-Horizon Mean–Variance Analysis: User Guide,” which is available in the supplemental material.

Bond risk, bond return volatility, and the term structure of interest rates

This paper explores the time variation in the bond risk, as measured by the covariation of bond returns with stock returns and consumption growth, and in the volatility of bond returns. A robust stylized fact in empirical finance is that the spread between the yields on long- and short-term bonds forecasts future excess returns on bonds at varying horizons positively; in addition, the short-term nominal interest rate forecasts both the stock return volatility and the exchange rate volatility positively. This paper presents evidence that movements in both the short-term nominal interest rate and the yield spread are positively related to changes in the subsequent realized bond risk and bond return volatility. The yield spread appears to proxy for business conditions, while the short rate appears to proxy for inflation and economic uncertainty. A decomposition of bond betas into a real cash flow risk component and a discount rate risk component shows that yield spreads have offsetting effects in each component. A widening yield spread is correlated with a reduced cash-flow (or inflationary) risk for bonds, but it is also correlated with a larger discount rate risk for bonds. The short rate only forecasts the discount rate component of the bond beta.

Stock Market Mean Reversion and the Optimal Equity Allocation of a Long-Lived Investor

This paper solves numerically the intertemporal consumption and portfolio choice problem of an infinitely-lived investor who faces a time-varying equity premium. The solutions we obtain are very similar to the approximate analytical solutions of Campbell and Viceira (1999), except at the upper extreme of the state space where both the numerical consumption and portfolio rules flatten out. We also consider a constrained version of the problem in which the investor faces borrowing and short-sales restrictions. These constraints bind when the equity premium moves away from its mean in either direction, and are particularly severe for risk-tolerant investors. The constraints have substantial effects on optimal consumption, but much more modest effects on optimal portfolio choice in the region of the state space where they are not binding.

Return Predictability in the Treasury Market: Real Rates, Inflation, and Liquidity

This paper decomposes inflation-indexed and nominal government bond excess return predictability into liquidity, real interest rate risk and inflation risk. We estimate a systematic liquidity premium in Treasury Inflation Protected Securities (TIPS) yields relative to nominal yields. The liquidity premium is around 30 bps during normal times but larger during the early years of TIPS and during the financial crisis 2008-2009. We find that time-varying liquidity premia in TIPS and time-varying inflation risk premia in nominal bonds generate return predictability. We find no evidence that shocks to relative issuance generate bond return predictability in the US or UK. Since their first issuance in 1997, inflation-indexed bonds in the U.S. have gained wide acceptance among investors and they now constitute a significant fraction of the stock of U.S. Treasury debt. Yet many academics and Treasury market pundits argue that these bonds, known as Treasury Inflation Protected Securities (TIPS), have a smaller and less liquid market than their nominal counterparts, U.S. Treasury notes and bonds.2 This paper conducts an empirical investigation of the sources and magnitude of illiquidity in the TIPS market. Conditional on a measure of the liquidity discount on TIPS relative to nominal Treasury bonds, it asks to what extent liquidity risk and to what extent time-varying inflation risk and time-varying real interest rate risk generate excess return predictability in government bonds. Understanding the liquidity differential between TIPS and Treasury bonds is important for several reasons. First, it is well-known that the Expectations Hypothesis of the term structure of interest rates does not hold for U.S. nominal government bonds (Campbell and Shiller 1991, Fama and Bliss 1987, Cochrane and Piazzesi 2005). Equivalently, excess returns on U.S. nominal government bonds are predictable. Explanations of return predictability in government bond returns emphasize either a time-varying real interest rate risk premium, or a time-varying inflation risk premium, or a combination of those two (Wachter 2006, Campbell, Sunderam, and Viceira 2010). Pflueger and Viceira (2011) have highlighted that inflation-indexed bonds can be very helpful in disentangling inflation risk and real interest rate risk as the fundamental sources of government bond return predictability. But such an exercise requires identifying price and return differentials between the two bond markets 2For evidence of relatively lower liquidity in TIPS see D’Amico, Kim, and Wei (2008), Campbell, Shiller, and Viceira (2009), Fleckenstein, Longstaff, and Lustig (2010), Fleming and Krishnan (2009), Dudley, Roush, and Steinberg Ezer (2009), Gurkaynak, Sack, and Wright (2010), and Haubrich, Pennacchi, and Ritchken (2011).Estimating the liquidity differential between inflation-indexed and nominal bond yields, we separately test for time-varying real rate risk premia, inflation risk premia, and liquidity premia in U.S. and U.K. bond markets. We find strong, model independent evidence that real rate risk premia and inflation risk premia contribute to nominal bond excess return predictability to quantitatively similar degrees. The estimated liquidity premium between U.S. inflation-indexed and nominal yields is systematic, ranges from 30 bps in 2005 to over 150 bps during 2008-2009, and contributes to return predictability in inflation-indexed bonds. We find no evidence that bond supply shocks generate return predictability.

The Euro as a Reserve Currency for Global Investors

In this article, we explore the demand for the euro for risk management purposes, and the evidence of stock market integration in the euro area. We define a reserve currency as one that investors demand either because it helps them hedge real interest risk and inflation risk, or because it helps them reduce the volatility of their portfolio of stocks and bonds because its return is negatively correlated with the returns on those assets. This article re-examines the role of the euro as a reserve currency in the sense of Campbell, Viceira and White (2003), updating their evidence, and reviews the evidence of Campbell, Serfaty-de Medeiros and Viceira (2010) in detail. Consistent with the intuition that an integrated capital market is one in which there is a common discount factor pricing securities, we also investigate whether stocks in the euro area have moved from a regime in which national stock markets were priced with discount rates that were predominantly country specific, to a regime in which national stock markets are predominantly priced by a euro area-wide common discount rate. We adopt the beta decomposition approach of Campbell and Vuolteenaho (2004) and Campbell, Polk and Vuolteenaho (2010) to test for capital market integration, and find robust evidence of increased capital market integration in the euro zone, and consequently improved risk sharing among euro zone economies.