Two proposals are made that may facilitate the creation of derivative market instruments, such as futures contracts, cash-settled based on economic indices. The first proposal concerns index number construction: indices based on infrequent measurements of nonstandardized items may control for quality change by using a hedonic repeated measures method, an index number construction method that follows individual assets or subjects through time and also takes account of measured quality variables. The second proposal is to establish markets for perpetual claims on cash flows matching indices of dividends or rents. Such markets may help us to measure the prices of the assets generating these dividends or rents even when the underlying asset prices are difficult or impossible to observe directly. A perpetual futures contract is proposed that would cash settle every day in terms of both the change in the futures price and the dividend or rent index for that day.

Two proposals are made that may facilitate the creation of derivative market instruments, such as futures contracts, cash settled based on economic indices. The first proposal concerns index number construction: indices based on infrequent measurements of nonstandardized items may control for quality change by using a hedonic repeated measures method, an index number construction method that follows individual assets or subjects through time and also takes account of measured quality variables. The second proposal is to establish markets for perpetual claims on cash flows matching indices of dividends or rents. Such markets may help us to measure the prices of the assets generating these dividends or rents even when the underlying asset prices are difficult or impossible to observe directly. A perpetual futures contract is proposed that would cash settle every day in terms of both the change in the futures price and the dividend or rent index for that day.

Two proposals are made that may facilitate the creation of derivative market instruments, such as futures contracts, cash settled based on economic indices. The first proposal concerns index number construction: indices based on infrequent measurements of nonstandardized items may control for quality change by using a hedonic repeated measures method, an index number construction method that follows individual assets or subjects through time and also takes account of measured quality variables. The second proposal is to establish markets for perpetual claims on cash flows matching indices of dividends or rents. Such markets may help us to measure the prices of the assets generating these dividends or rents even when the underlying asset prices are difficult or impossible to observe directly. A perpetual futures contract is proposed that would cash settle every day in terms of both the change in the futures price and the dividend or rent index for that day.

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.

Long historical averages of real earnings help forecast present values of future real dividends. With aggregate U.S. stock market data (1871–1986), a vector‐autoregressive forecast of the present value of future dividends is, for each year, roughly a weighted average of moving‐average earnings and current real price, with between two thirds and three fourths of the weight on the earnings measure. We develop the implications of this for the present‐value model of stock prices and for recent results that long‐horizon stock returns are highly forecastable.