Robert B. Litterman

Bio: Robert B. Litterman is an academic researcher from Goldman Sachs. The author has contributed to research in topics: Capital asset pricing model & Bayesian vector autoregression. The author has an hindex of 24, co-authored 50 publications receiving 7497 citations. Previous affiliations of Robert B. Litterman include Federal Reserve Bank of Minneapolis & Federal Reserve System.

Forecasting and conditional projection using realistic prior distributions

Abstract: This paper develops a forecasting procedure based on a Bayesian method for estimating vector autoregressions. The procedure is applied t o 10 macroeconomic variables and is shown to improve out-of-sample forecasts relative to univariate equations. Although cross-variable responses are damped by the prior, considerable interaction among the variables is shown to be captured by the estimates We provide unconditional forecasts as of 1982:12 and 1983:3. We also describe how a model such as this can be used to make conditional projections and to analyze policy alternatives. As an example, we analyze a Congressional Budget Office forecast made in 1982: 12 Although no automatic causal interpretations arise from models like ours, they provide a detailed characterization of the dynamic statistical interdependence of a set of economic variables, information that may help in evaluating causal hypotheses without containing any such hypotheses.

Forecasting With Bayesian Vector Autoregressions-Five Years of Experience

Abstract: The results obtained in five years of forecasting with Bayesian vector autoregressions (BVAR's) demonstrate that this inexpensive, reproducible statistical technique is as accurate, on average, as those used by the best known commercial forecasting services. This article considers the problem of economic forecasting, the justification for the Bayesian approach, its implementation, and the performance of one small BVAR model over the past five years.

Asset Allocation: Combining Investor Views with Market Equilibrium

Abstract: nvestors create global bond portfolios for a variety of reasons: to diversify interest rate risk, to manage yield, to control exposure to foreign currencies, and to enlarge the universe of possible trading opportunities. This article describes a new approach to international asset allocation of fured-income securities. We show how to construct portfolios by choosing the optimal weights to invest in assets in each country and the optimal degree of hedging of currency exposure, given the investor's views for interest rates and exchange rates. While our approach brings several new features to the traditional asset allocation problem, its most innovative contribution is to allow investors to compare their outlook for currencies and interest rates with expected returns generated by an International Capital Asset Pricing Model (ICAPM) equilibrium. The simple idea that expected returns ought to be consistent with market equilibrium, except to the extent that the investor explicitly states otherwise, turns out to be of critical importance in making practical use of the model. In particular, it allows investors to specifj views in a much more flexible way than otherwise would be permitted. For example, rather than requiring investors to specify views about absolute returns on every asset, our approach allows investors to specifj as many or as few views as they wish views with different degrees of confidence and views about relative returns on different assets. This use of the expected returns associated with asset market equilibrium as a reference point for investors is a unique feature of the model. Much of our article focuses on this aspect of our approach.' Another advantage to our approach is that it jointly determines the optimal allocations of bonds into differI

Explorations Into Factors Explaining Money Market Returns

Abstract: In this article, we measure and interpret the common "factors" that describe money market returns. Results are presented for both three- and four-factor models. We find that the three-factor model explains, on average, 86 percent of the total variation in most money market returns while the four-factor model explains, on average, 90 percent of this variation. Using mimicking portfolios, we provide an interpretation of the systematic risks represented by these factors. IN THIS ARTICLE, WE attempt to measure and interpret the common "factors" that describe money market returns. The factor approach we employ assumes that the covariance matrix of a set of random variables, in this case excess returns, can be decomposed into common or systematic components and idiosyncratic or nonsystematic components. This decomposition into systematic and nonsystematic components is based on an assumption of a linear relationship between the returns of each security and a set of "common" factors. This is the assumption of linear return-generating models, which form an integral part of the structure of many asset pricing theories-for example, arbitrage pricing theory (APT) as developed by Ross (1976). The interpretation is that the common factors represent sources of systematic or nondiversifiable risk and the idiosyncratic component of returns represents diversifiable risks.' Our focus here is not on testing a particular asset pricing model per se but on developing empirical evidence for the existence of stylized facts regarding money market returns. The stylized facts take the form of the existence, measurement, and interpretation of the common factors that are found in money markets. Our attempt to measure and interpret these sources of systematic risk may eventually lead to the construction of observable eco

Optimization of conditional value-at-risk

Abstract: A new approach to optimizing or hedging a portfolio of nancial instruments to reduce risk is presented and tested on applications. It focuses on minimizing Conditional Value-at-Risk (CVaR) rather than minimizing Value-at-Risk (VaR), but portfolios with low CVaR necessarily have low VaR as well. CVaR, also called Mean Excess Loss, Mean Shortfall, or Tail VaR, is anyway considered to be a more consistent measure of risk than VaR. Central to the new approach is a technique for portfolio optimization which calculates VaR and optimizes CVaR simultaneously. This technique is suitable for use by investment companies, brokerage rms, mutual funds, and any business that evaluates risks. It can be combined with analytical or scenario-based methods to optimize portfolios with large numbers of instruments, in which case the calculations often come down to linear programming or nonsmooth programming. The methodology can be applied also to the optimization of percentiles in contexts outside of nance.

Economic Forces and the Stock Market

Abstract: This paper tests whether innovations in macroeconomic variables are risks that are rewarded in the stock market. Financial theory suggests that the following macroeconomic variables should systematically affect stock market returns: the spread between long and short interest rates, expected and unexpected inflation, industrial production, and the spread between high- and low-grade bonds. We find that these sources of risk are significantly priced. Furthermore, neither the market portfolio nor aggregate consumption are priced separately. We also find that oil price risk is not separately rewarded in the stock market.

Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach

Abstract: Using a Bayesian likelihood approach, we estimate a dynamic stochastic general equilibrium model for the US economy using seven macro-economic time series. The model incorporates many types of real and nominal frictions and seven types of structural shocks. We show that this model is able to compete with Bayesian Vector Autoregression models in out-of-sample prediction. We investigate the relative empirical importance of the various frictions. Finally, using the estimated model we address a number of key issues in business cycle analysis: What are the sources of business cycle fluctuations? Can the model explain the cross-correlation between output and inflation? What are the effects of productivity on hours worked? What are the sources of the "Great Moderation"?

Shocks and frictions in US business cycles: A Bayesian DSGE approach

Abstract: We estimate a dynamic stochastic general equilibrium (DSGE) model for the US economy. The model incorporates many types of real and nominal frictions: sticky nominal price and wage setting, habit formation in consumption, investment adjustment costs, variable capital utilisation and fixed costs in production. It also contains many types of shocks including productivity, labour supply, investment, preference, cost-push and monetary policy shocks. Using Bayesian estimation techniques, the relative importance of the various frictions and shocks in explaining the US business cycle are empirically investigated. We also show that this model is able to outperform standard VAR and BVAR models in out-of-sample prediction.