Academic finance has had a remarkable impact on many financial services. Yet long-term investors have received curiously little guidance from academic financial economists. Mean-variance analysis, developed almost fifty years ago, has provided a basic paradigm for portfolio choice. This approach usefully emphasizes the ability of diversification to reduce risk, but it ignores several critically important factors. Most notably, the analysis is static; it assumes that investors care only about risks to wealth one period ahead. However, many investors—-both individuals and institutions such as charitable foundations or universities—-seek to finance a stream of consumption over a long lifetime. In addition, mean-variance analysis treats financial wealth in isolation from income. Long-term investors typically receive a stream of income and use it, along with financial wealth, to support their consumption. At the theoretical level, it is well understood that the solution to a long-term portfolio choice problem can be very different from the solution to a short-term problem. Long-term investors care about intertemporal shocks to investment opportunities and labor income as well as shocks to wealth itself, and they may use financial assets to hedge their intertemporal risks. This should be important in practice because there is a great deal of empirical evidence that investment opportunities—-both interest rates and risk premia on bonds and stocks—-vary through time. Yet this insight has had little influence on investment practice because it is hard to solve for optimal portfolios in intertemporal models. This book seeks to develop the intertemporal approach into an empirical paradigm that can compete with the standard mean-variance analysis. The book shows that long-term inflation-indexed bonds are the riskless asset for long-term investors, it explains the conditions under which stocks are safer assets for long-term than for short-term investors, and it shows how labor income influences portfolio choice. These results shed new light on the rules of thumb used by financial planners. The book explains recent advances in both analytical and numerical methods, and shows how they can be used to understand the portfolio choice problems of long-term investors.

We show that inflation risk is priced in stock returns and that inflation risk premia in the cross-section and the aggregate market vary over time, even changing sign as in the early 2000s. This time variation is due to both price and quantities of inflation risk changing over time. Using a consumption-based asset pricing model, we argue that inflation risk is priced because inflation predicts real consumption growth. The historical changes in this predictability and in stocks' inflation betas can account for the size, variability, predictability and sign reversals in inflation risk premia.

We investigate the determinants of moment risk premia (MRP) and their relationship with stock returns. Stocks with high beta, idiosyncratic volatility and maximum return are associated with a high variance risk premium (VRP). The skew risk premium (SRP) is mainly driven by return reversals, the maximum return and idiosyncratic skewness, while the kurtosis risk premium (KRP) is associated with all firm characteristics. We find that both the VRP and SRP are negatively related to stock returns, while the KRP has no relation with stock returns. However, the negative relation between the SRP and stock returns is robust to the inclusion of firm-level variables, while the VRP is not.

Merton (1987) predicts that idiosyncratic risk can be priced. I develop a simple equilibrium model of capital markets with information costs in which the idiosyncratic risk premium depends on the average level of idiosyncratic volatility. This dependence suggests that the idiosyncratic risk premium varies over time. I find that in U.S. markets, the covariance between stock-level idiosyncratic volatility and the idiosyncratic risk premium explains future stock returns. Stocks in the highest quintile of the covariance between the volatility and risk premium earn an average 3-factor alpha of 70 bps per month higher than those in the lowest quintile.

It is well known that in the postwar period stockreturns have tended to be low when the short term nominal interest rate is high. In this paper I show that more generally the state of the term structure of interest rates predicts stock returns. Risk premia on stocks appear to move closely together with those on 20-year Treasury bonds, while risk premia on Treasury bills move somewhat independently. Average returns on 20-year bonds have been very low relative to average returns on stocks. I use these observations to test some simple asset pricing models. First I consider latent variable models in which betas are constant and risk premia vary with expected returns on a small number of unobservable hedge portfolios. The data strongly reject a single-latent-variable model. The last part of the paper examines the relationship between conditional means and variances of returns on bills, bonds and stocks. Bill returns tend to be high when their conditional variance is high, but there is a perverse negative relationship between stock returns and their conditional variance. A model is estimated which assumes that asset returns are determined by their time-varying betas with a fixed-weight "benchmark" portfolio of bills, bonds and stocks, whose return is proportional to its conditional variance. This portfolio is estimated to place almost all its weight on bills, indicating that uncertainty about nominal interest rates is important in pricing both short- and long-term assets

We develop an econometric methodology to infer the path of risk premia from a large unbalanced panel of individual stock returns. We estimate the time-varying risk premia implied by conditional linear asset pricing models where the conditioning includes both instruments common to all assets and asset specific instruments. The estimator uses simple weighted two-pass cross-sectional regressions, and we show its consistency and asymptotic normality under increasing cross-sectional and time series dimensions. We address consistent estimation of the asymptotic variance by hard thresholding, and testing for asset pricing restrictions induced by the no-arbitrage assumption. We derive the restrictions given by a continuum of assets in a multi-period economy under an approximate factor structure robust to asset repackaging. The empirical analysis on returns for about ten thousands US stocks from July 1964 to December 2009 shows that risk premia are large and volatile in crisis periods. They exhibit large positive and negative strays from time-invariant estimates, follow the macroeconomic cycles, and do not match risk premia estimates on standard sets of portfolios. The asset pricing restrictions are rejected for a conditional four-factor model capturing market, size, value and momentum effects.