This paper is concerned with the valuation of multiperiod cash flows in a world where prices are determined according to the Sharpe-Lintner-Black model of capital market equilibrium. We find that the current market value of any future net cash flow is the current expected value of the flow discounted at risk-adjusted discount rates for each of the periods until the flow is realized. The discount rates are known and non-stochastic, but the rates for the different periods preceding the realization of a cash flow need not to be the same, and the rates relevant for a given period can differ across cash flows. The risk adjustments in the discount rates arise because of uncertainties about reassessments through time of the expected value of a flow and the relationships between these reassessments and the corresponding reassessments of the expected cash flows of all firms.

When adjusted for variation through time in expected premiums, the forward rates of interest that are implicit in Treasury Bill prices contain assessments of expected future spot rates of interest that are about as good as those that can be obtained from the information in past spot rates. Moreover, in setting bill prices and forward rates, the market reacts appropriately to the negative autocorrelation in monthly changes in the spot rate and to changes through time in the degree of this autocorrelation. This evidence is consistent with the market efficiency proposition that in setting bill prices, the market correctly uses the information in past spot rates.

The evidence in Fama and Bliss (1987) that forward interest rates forecast future spot interest rates for horizons beyond a year repeats in the out-of-sample 1986--2004 period. But the inference that this forecast power is due to mean reversion of the spot rate toward a constant expected value no longer seems valid. Instead, the predictability of the spot rate captured by forward rates seems to be due to mean reversion toward a time-varying expected value that is subject to a sequence of apparently permanent shocks that are on balance positive to mid-1981 and on balance negative thereafter.

The evidence in Fama and Bliss (1987) that forward interest rates forecast future spot interest rates for horizons beyond a year repeats in the out-of-sample 1986-2004 period. But the inference that this forecast power is due to mean reversion of the spot rate toward a constant expected value no longer seems valid. Instead, the predictability of the spot rate captured by forward rates seems to be due to mean reversion toward a time-varying expected value that is subject to a sequence of apparently permanent shocks that are on balance positive to mid-1981 and on balance negative thereafter.

Value premiums, which we define as value portfolio returns in excess of market portfolio returns, are on average much lower in the second half of the July 1963–June 2019 period. But the high volatility of monthly premiums prevents us from rejecting the hypothesis that expected premiums are the same in both halves of the sample. Regressions that forecast value premiums with book-to-market ratios in excess of market (BM–BMM) produce more reliable evidence of second-half declines in expected value premiums, but only if we assume the regression coefficients are constant during the sample period. Received: January 21, 2020; editorial decision: July 21, 2020; Editor: Jeffrey Pontiff.

We use bootstrap simulations to examine the properties of long-horizon U.S. stock market returns. We document the rate at which continuously compounded market returns converge toward normal distributions as we extend the horizon from 1 month to 30 years, and the rate at which dollar payoffs converge toward lognormal. We also verify that, though largely irrelevant at short horizons, uncertainty about the expected market return has a substantial impact on uncertainty about long-horizon payoffs.

The Nobel Foundation asks that the Nobel lecture cover the work for which the Prize is awarded. The announcement of this year's Prize cites empirical work in asset pricing. I interpret this to include work on efficient capital markets and work on developing and testing asset pricing models—the two pillars, or perhaps more descriptive, the Siamese twins of asset pricing. I start with efficient markets and then move on to asset pricing models.