The comovements in real stock prices between the U.K. and the U.S. appear to be too large to be accounted for in terms of the comovements of real dividends between the countries even after consideration of the possibility of information pooling. When consideration is made of the comovements of real interest rates between the countries, there is weaker evidence of excess comovement of price.

The comovements in real stock prices between the U.K. and the U.S. appear to be too large to be accounted for in terms of the comovements of real dividends between the countries even after consideration of the possibility of information pooling. When consideration is made of the comovements of real interest rates between the countries, there is weaker evidence of excess comovement of price.

My initial motivation for considering volatility measures in the efficient markets models was to clarify the basic smoothing properties of the models to allow an understanding of the assumptions which are implicit in the notion of market efficiency. The efficient markets models, which are described in section II below , relate a price today to the expected present value of a path of future variables. Since present values are long weighted moving averages, it would seem that price data should be very stable and smooth. These impressions can be formalized in terms of inequalities describing certain variances (section III). The results ought to be of interest whether or not the data satisfy these inequalities, and the procedures ought not to be regarded as just "another test" of market efficiency. Our confidence of our understanding of empirical phenomena is enhanced when we learn how such an obvious property of data as its "smoothness" relates to the model, and to alternative models (section IV below).On further examination of the volatility inequalities, it became clear that the inequalities may also suggest formal tests of market efficiency that have distinct advantages over conventional tests. These advantages take the form of greater power in certain circumstances of robustness to data errors such as misalignment and of simplicity and understandability. An interpretation of volatility tests versus regression tests in terms of the likelihood principle is offered in section V.

Models which represent long-term interest rates as long averages of expected short-term interest rates imply, because of the smoothing implicit in the averaging, that long rates should not be too volatile. The volatility of actual long-term interest rates, as measured by the variance of short-term holding yields on long-term bonds, appears to exceed limits imposed by the models. Such excess volatility implies a kind of forecastability for long rates. Long rates show a slight tendency to fall when they are high relative to short rates rather than rise as predicted by expectations models.

Models which represent long-term interest rates as long averages of expected short-term interest rates imply, because of the smoothing implicit in the averaging, that long rates should not be too volatile. The volatility of actual long-term interest rates, as measured by the variance of short-term holding yields on long-term bonds, appears to exceed limits imposed by the models. Such excess volatility implies a kind of forecastability for long rates. Long rates show a slight tendency to fall when they are high relative to short rates rather than rise as predicted by expectations models.

A model of the tax structure of interest rates is developed and simple approximate expressions relating yield to coupon are derived. The effect on these simple expressions of alternative assumptions about holding period length, expectations of future interest rates, and other factors, is evaluated. It is shown that with recent U.S. yield averages the new-seasoned yield spread varies with the new-seasoned coupon spread as the theory prescribes. It is concluded that new issue yield averages should provide a more reliable measure of the cost of debt capital than is provided by seasoned yield averages.

This paper examines postwar U.S. term structure data and finds that for almost any combination of maturities between one month and ten years, a high yield spread between a longer-term and a shorter-term interest rate forecasts rising shorter-term interest rates over the long term, but a declining yield on the longer-term bond over the short term. This pattern is inconsistent with the expectations theory of the term structure, but is consistent, with a model in which the spread is proportional to the value implied by the expectations theory.