Stock returns and the term structure

In monthly U.S. data for 1959–1979 and 1979–1983, the state of the term structure of interest rates predicts excess stock returns, as well as excess returns on bills and bonds. This paper documents this fact and uses it to examine some simple asset pricing models. In 1959–1979, the data strongly reject a single-latent-variable specification of predictable excess returns. There is considerable evidence that conditional variances of excess returns change through time, but the relationship between conditional mean and conditional variance is reliably positive only at the short end of the term structure.     

THE EXPECTATIONS HYPOTHESIS OF THE TERM STRUCTURE IN EUROCURRENCY MARKETS

This paper uses daily eurocurrency deposit rates for six currencies to extend previous research on the expectations hypothesis of the term structure. The reported results confirm earlier findings that the behavior of long term interest rates is perverse. For example, it is shown that in the case of five-year eurocurrency deposits denominated in US dollars, German marks and Swiss francs, the coefficient relating the excess holding period return to the yield spread between long and short term securities exceeds one, implying that long term rates tend to move in a direction opposite to the prediction of the expectations hypothesis. This study also employs a variety of techniques to examine the temporal stability of the coefficient in both the long and short maturity regressions used in testing the expectations hypothesis. While we do find instability, the nature of the parameter variation is markedly different from that found in foreign exchange markets when similar tests are employed.     

Estimation of a rational expectations model of the term structure

This paper shows how to represent a vector autoregression (VAR) in terms of the eigenvalues and eigenvectors of its companion matrix. This representation is used to impose the exact restrictions implied by the expectations hypothesis on the VAR for short and long term interest rates and to calculate the restricted maximum likelihood estimates. The first difference representation for short and long rates used by Sargent (1979) is shown to be inconsistent with the expectations hypothesis, but a VAR with two unit roots is constructed that satisfies the exact restrictions and leads to similar restricted estimates.     

Testing the expectations hypothesis when interest rates are near integrated

Nominal interest rates are unlikely to be generated by unit-root processes. Using data on short and long interest rates from eight developed and six emerging economies, we test the expectations hypothesis using cointegration methods under the assumption that interest rates are near integrated. If the null hypothesis of no cointegration is rejected, we then test whether the estimated cointegrating vector is consistent with that suggested by the expectations hypothesis. The results show support for cointegration in 10 of the 14 countries we consider, and the cointegrating vector is similar across countries. However, the parameters differ from those suggested by theory. We relate our findings to existing literature on the failure of the expectations hypothesis and to the role of term premia.     

New Hope for the Expectations Hypothesis of the Term Structure of Interest Rates

Survey data on interest rate expectations permit separate testing of the two alternative hypotheses in traditional term structure tests: that the expectations hypothesis fails, and that expected future interest rates are ex post inefficient forecasts. We find that the source of the spread's poor predictions of future interest rates varies with maturity. At short maturities the expectations hypothesis fails. At long maturities, however, changes in the yield curve reflect changes in expected future rates one-for-one, an implication of the expectations hypothesis. This result confirms earlier findings that long rates underreact to short rates, but now it cannot be attributed to term premia.     

Domestic variance and international comovement bonds tests of interest rates

This article demonstrates that long rates exhibit both domestic excess variance and international excess comovement compared to fundamental yields derived from short rates under the rational expectations theory of term structure. The results are consistent for all countries sampled: the US, UK, Canada, Germany, and Japan. Probing deeper, long rates are found to “overreact” to domestic expected future inflation and/or short real rates both of which are the underlying components of the short nominal rate according to the Fisher hypothesis. Since inflation rates as well as short real rates are highly correlated between countries, the excess volatility in long rates translates into excess covariance (“co-overreact”) internationally.     

Three aspects of the Swiss term structure: an empirical survey

The term structure is an important transmitter of, and indicator for, monetary policy. This paper studies the Swiss term structure using monthly data from 1989 to 2005. We study the impact of the new monetary policy strategy that the Swiss National Bank (SNB) adopted at the beginning of 2000 on three aspects of the term structure. First, we test the expectations hypothesis and find it confirmed at the short end of the yield curve. At the long end, time-varying term premia seem present. Second, we ask whether the yield curve contains information regarding future inflation and economic activity. We find that a steepening of the yield curve predicted an increase in economic activity in the short term before the change in policy strategy, but not thereafter. Third, we study the contemporaneous reaction of the term structure to macroeconomic conditions and conclude that the SNB’s commitment to stabilizing inflation may have become more credible after the change in the monetary policy strategy.      

Further analysis of the expectations hypothesis using very short-term rates

Longstaff [Longstaff, F., 2000. The term structure of very short-term rates: new evidence for the expectations hypothesis. Journal of Financial Economics 58, 397–415] finds support for the expectations hypothesis at the very short end of the repurchase agreement (repo) term structure while other studies find calendar-time-based regularities cause rejection of the expectations hypothesis. Using Longstaff’s methods on a sample of repo rates that pre-dates Longstaff’s sample, we reject the expectations hypothesis for every maturity. The pre-Longstaff-sample repo data comes from a time period where the behavior of short-term interest rates is similar to the long-run average behavior of short-term interest rates. Our results imply that expectations hold when rates are less volatile and/or that we may be entering a period of lower volatility.     

RESPONSE OF FINANCIAL MARKETS TO ANNOUNCEMENTS OF THE AUSTRALIAN CURRENT ACCOUNT BALANCE

This paper documents the response of exchange rates, interest rates and stock prices to monthly announcements of the Australian current account balance. Survey data on market participants' expectations and forecasts generated from ARIMA time series models are used to identify the unexpected component of the announcements. The study also controls for day-of-the-week effects that have been documented in the Australian equity market The results support the efficient market hypothesis and show a significant depreciation of the Australian dollar in foreign exchange markets and a significant rise in both short- and long-term interest rates to announcements of larger than expected current account deficits. The study was, however, unable to find evidence of a significant stock price response to the current account announcements.     

Structural breaks, parameter uncertainty, and term structure puzzles

We show that uncertainty about parameters of the short rate model can account for the rejections of the expectations hypothesis for the term structure of interest rates. We assume that agents employ Bayes rule to learn parameter values in the context of a model that is subject to stochastic structural breaks. We show that parameter uncertainty also implies that the verdict on the expectations hypothesis varies systematically with the term of the long bond and the particular test employed, in the same way that is found in empirical tests.     

Excess long real rate volatility

Variance and comovement bounds tests are performed on riskless real interest rates for the USA, Canada, UK, Germany, and Japan. Each country’s long real rate exhibits excess volatility relative to its fundamental long real rate derived under the rational expectations theory of real term structure. Internationally, each country’s long real rate relative to the USA exhibits excess comovement relative to their corresponding fundamental long real rates. The excess volatility clouds the arbitrage-induced link between long and short real rates. This noise hinders the monetary transmission mechanism and the ability of central bankers to influence long real rates by managing short real rates.     

Testing the Expectations Hypothesis on the Term Structure of Volatilities in Foreign Exchange Options

This article tests the expectations hypothesis in the term structure of volatilities in foreign exchange options. In particular, it addresses whether long-dated volatility quotes are consistent with expected future short-dated volatility quotes, assuming rational expectations. For options observed daily from December 1, 1989 to August 31, 1992 on dollar exchange rates against the pound, mark, yen, and Swiss franc, we are unable to reject the expectations hypothesis in the great majority of cases. The current spread between long- and short-dated volatility rates proves to be a significant predictor of the direction of future short-dated rates.     

THE INFORMATION CONTENT AND USEFULNESS OF THE TERM STRUCTURE OF THE NEW ZEALAND BANK BILL MARKET

This paper applies the rationality concept and expectations hypothesis to test the information efficiency of the term structure of the New Zealand bank bill market. Weekly data is collected from June 1986 to November 1988. The sample period is partitioned into two subperiods by the sharemarket crash in October 1987. The empirical results suggest the presence of a time varying risk premium. This is reflected by the significantly positive volatility measure in the first subperiod and the significant interest rate level variable in both subperiods. The forecast errors correlate significantly with the growth in money supply and overseas interest rate variables. Factors other than market information inefficiency could be responsible for the significant correlation; namely the impact of the sharemarket crash on market perceptions about inflation expectations and the non-simultaneous data problem in calculating the differential costs of borrowing. Despite the rejection of the joint hypothesis, forward rates are found to have information about future spot rates beyond that contained in past spot rates, and are able to predict interest rates at least 30 days ahead.     

THE TESTING OF AUSTRALIAN STOCK MARKET INDICES FOR MEAN-VARIANCE EFFICIENCY

Three different market indices are tested for mean-variance efficiency using monthly data for leading Australian securities, and following the methodologies suggested in Roll (1979). The balance of the evidence is against index efficiency and against the two-parameter asset pricing theory. However, this could be influenced by imperfections in the tests, inadequate data, and sampling errors in the betas.     

Pricing the risks of default

This paper decomposes default risk into timing and recovery risks. The two default components are explicitly priced as if they were traded in the futures market. We develop estimation strategies evaluating recovery risks and then construct implicit prices of contingent securities reflecting purely the timing risk. The models are estimated on monthly data for rates on certificates of deposit offered by institutions in the Savings and Loan Industry, during the 1987–1991 period. Empirical results support market expectations of lower likelihoods of default after 1989.     

DIRECT TESTS OF THE DIVERGENCE OF OPINION HYPOTHESIS IN THE MARKET FOR RACETRACK BETTING

The “divergence of opinion” hypothesis suggests predictable pricing effects in markets where assumptions of homogeneous investor expectations and unrestricted short selling do not hold. Direct tests of the hypothesis in traditional financial markets do not exist apparently because of the severity of several requirements, including that measurement of divergent ex-ante expectations be unambiguously paired with associated ex-post results. This and remaining conditions are met in direct tests of the hypothesis in a pricing arena where divergence of opinion influences are likely to be present: racetrack betting. Results provide no statistically significant support for the divergence of opinion hypothesis.     

Martingales and efficient forecasts of effective mortgage rates

Economic theory and empirical evidence indicate that the optimal near-term forecast of a long-term rate is (approximately) today's rate; the no-change model should provide excellent near-term forecasts of a long-term rate. This article estimates the longest forecast horizon over which no-change predictions of each of three mortgage-related interest rates pass a series of quality tests. The empirical results reject the optimality of no-change predictions of the one-year Treasury bill rate for all forecast horizons. Since October 1979, the tests support the hypothesis that no-change predictions of the 30-year conventional home mortgage and GNMA rates are optimal for forecast horizons of up to three-quarters-ahead.     

The Relation between Stock Prices and Inflationary Expectations: The International Evidence

This paper provides empirical evidence on the relation between stock returns and inflationary expectations for nine countries over the period 1971–80. The Fisherian assumption that real returns are independent of inflationary expectations is soundly rejected for each major stock market of the world. Using interest rates as a proxy for expected inflation, our data provide consistent support for the Geske and Roll model whose basic hypothesis is that stock price movements signal (negative) revisions in inflationary expectations. Finally, a weak real interest rate effect was found for some of these countries.     

Equity Risk Premium

Abstract

The equity risk premium (ERP) is an essential building block of the market value of risk. In theory, the collective action of all investors results in an equilibrium expectation for the return on the market portfolio excess of the risk-free return, the ERP. The ability of the valuation actuary to choose a sensible value for the ERP, whether as a required input to capital asset pricing model valuation, or any of its descendants, is as important as choosing risk-free rates and risk relatives (betas) to the ERP for the asset at hand.

The historical realized ERP for the stock market appears to be at odds with pricing theory parameters for risk aversion. Since 1985, there has been a constant stream of research, each of which reviews theories of estimating market returns, examines historical data periods, or both. Those ERP value estimates vary widely from about ?1% to about 9%, based on a geometric or arithmetic averaging, short or long horizons, short- or long-run expectations, unconditional or conditional distributions, domestic or international data, data periods, and real or nominal returns.

This paper examines the principal strains of the recent research on the ERP and catalogues the empirical values of the ERP implied by that research. In addition, the paper supplies several time series analyses of the standard Ibbotson Associates 1926–2002 ERP data using short Treasuries for the risk-free rate. Recommendations for ERP values to use in common actuarial valuation problems also are offered.