The continuously compounded (CC) interest rate on a one-month Treasury bill observed at the end of month t–1 is the sum of a CC expected real return and a CC expected inflation rate, Rt–1 = Et–1(rt) + Et–1(It). Two approaches are used to split Rt–1 between its two components. In the first, models for rt produce estimates of Et–1(rt), which are used to infer Et–1(It) as Rt–1 – Et–1(rt). The second approach models It to produce estimates of Et–1(It) and infer Et–1(rt) as Rt–1 – Et–1(It). By design, the estimates of Et–1(rt) and Et–1(It) from both approaches have the properties implied by rational bill prices. Received October 10, 2018; Editorial decision December 31, 2018 By Editor Jeffrey Pontiff

To what extent does TF, the target Federal funds rate set by the Fed, influence other rates? There is lots of variation in rates unrelated to TF, and any effects of TF on rates dissipate quickly for longer maturities. For short rates, all the tests have interpretations in terms of: (i) a Fed that has the power to control rates and uses it, and (ii) a Fed that has little power over rates or chooses not to exercise its power. In the end, there is no conclusive evidence (here or elsewhere) on the role of the Fed versus market forces in the long-term path of interest rates.

Time (hourly payoffs) and salary (the payoff does not vary with hours) account for the bulk of the payoffs on labor contracts. This article argues that the choice between time and salary centers on the presence (time) or absence (salary) of information about flows of effort or output per unit time. Without information about the flow of hourly effort or output, payoffs for time give the worker an incentive to supply hours without effort. Time can then become uninformative about output. In this situation, if the contract includes a fixed payoff, it is likely to be a salary rather than a payoff for time.

Suppose the ICAPM governs asset prices and there is a total of S state variables that might be of hedging concern to investors. Can we determine which state variables are, in fact, of hedging concern? What does it mean to say that these state variables are priced, that is, that they give rise to special risk premiums in expected returns? The goal of this paper is to formulate this problem clearly and show when it can and cannot be solved. Ignoring estimation problems, it is possible to find the set of priced state variables when the state variables are identified (named). When we know the number of state variables, but not their names, confident conclusions about even the number of them that produce special risk premiums are probably impossible, unless the number is zero, so the ICAPM collapses to the CAPM.

The concept of multifactor portfolio efficiency plays a role in Merton's intertemporal CAPM (the ICAPM), like that of mean-variance efficiency in the Sharpe-Lintner CAPM. In the CAPM, the relation between the expected return on a security and its risk is just the condition on security weights that holds in any mean-variance-efficient portfolio, applied to the market portfolio M. The risk-return relation of the ICAPM is likewise just the application to M of the condition on security weights that produces ICAPM multifactor-efficient portfolios. The main testable implication of the CAPM is that equilibrium security prices require that M is mean-variance-efficient. The main testable implication of the ICAPM is that securities must be priced so that M is multifactor-efficient. As in the CAPM, building the ICAPM on multifactor efficiency exposes its simplicity and allows easy economic insights.

Market efficiency survives the challenge from the literature on long-term return anomalies. Consistent with the market efficiency hypothesis that the anomalies are chance results, apparent overreaction to information is about as common as underreaction, and post-event continuation of pre-event abnormal returns is about as frequent as post-event reversal. Most important, consistent with the market efficiency prediction that apparent anomalies can be due to methodology, most long-term return anomalies tend to disappear with reasonable changes in technique.

There are time-varying term and default premiums in the expected returns on money market securities. Default premiums decline with maturity and tend to be higher during recessions. Term premiums tend to increase with maturity during good times, but humps and inversions in the term structure of expected returns are common during recessions. Treasury bills produce positive average term premiums for the overall sample, but average term premiums for private-issuer securities are close to 0.0. A general conclusion is that variation in forward rates is primarily variation in current epected returns rather than in forecasts of changes in interest rates.

This paper presents a regression approach to measuring the information in forward interest rates about time varying premiums and future spot interest rates. Like earlier work, the regressions identify variation in the expected premiums on longer-maturity Treasury bills. The more novel evidence concerns the forecasts of future spot rates in forward rates. The regressions provide evidence that the one-month forward rate has power to predict the spot rate one month ahead. During periods preceding 1974, forward rates have reliable forecast power for one-month spot rates up to five months in the future.

This paper examines expected returns on U.S. Treasury bills and on U.S. Government bond portfolios. Expected bill returns are estimated from forward rates and from sample average returns. Both estimation methods indicate that expected returns on bills tend to peak at eight or nine months and never increase monotonically out to twelve months. Reliable inferences are limited to Treasury bills and thus to maturities up to a year. The variability of longer-term bond returns preempts precise conclusions about their expected returns.