Knowledge that Transforms

Weekly data for foreign currency futures prices are examined for evidence of risk premiums. Covariance risks are measured with respect to the excess returns from benchmark portfolios for consumption and wealth. When the parameters representing the prices of the covariance risks are held constant, no risk premiums are detected. However, when these prices are allowed to vary with the conditional expected returns and variances of the benchmark portfolios, possibly reflecting changing investment opportunities, strong evidence of risk premiums is obtained.

We undertake a comprehensive investigation of price and volume co-movement using daily New York Stock Exchange data from 1928 to 1987. We adjust the data to take into account well-known calendar effects and long-run trends. To describe the process, we use a seminonparametric estimate of the joint density of current price change and volume conditional on past price changes and volume. Four empirical regularities are found: (i) positive correlation between conditional volatility and volume; (ii) large price movements are followed by high volume; (iii) conditioning on lagged volume substantially attenuates the “leverage” effect; and (iv) after conditioning on lagged volume, there is a positive risk-return relation.