Gabriel A. Hawawini, Intertemporal Cross-Dependence in Securities Daily Returns and the Short-Run Intervaling Effect on Systematic Risk, The Journal of Financial and Quantitative Analysis, Vol. 15, No. 1 (Mar., 1980), pp. 139-149

The purpose of this paper is to demonstrate mathematically that the skewness of securities' returns--the ratio of the third moment to the standard deviation cubed--is sensitive to the length of the differencing interval over which returns are measured. Empirical observations of this so-called intervaling effect on skewness have been reported in at least three articles in this Journal. There have been no attempts, however, to examine this effect analytically. The empirical evidence presented in the literature is often contradictory and remains unexplained because of a lack of an analytical insight into the causes of the intervaling effect.

Gabriel A. Hawawini, Ashok Vora, Evidence of Intertemporal Systematic Risks in the Daily Price Movements of NYSE and AMEX Common Stocks, The Journal of Financial and Quantitative Analysis, Vol. 15, No. 2 (Jun., 1980), pp. 331-339

In this comment to a paper by Levhari and Levy published in this journal on February 1977 we provide evidence that shows that their conclusion does not hold if one applies the model to a large sample of common stocks.

This paper traces the historical developments of the efforts to find simple and accurate methods of approximating an annuity's implicit yield and a bond's yield to maturity. It is shown that the little known history of yield approximations is nevertheless very rich, with contributions dating as far back as the late seventeenth century. It is also shown that the standard textbook approximation formula for the bond's yield to maturity is the least accurate of a large family of formulas, some of which were suggested as early as 1855.

We report evidence of seasonality in the Fama and MacBeth estimate of the CAPM-based risk premium in four stock exchanges: the NYSE and the London, Paris, and Brussels exchanges.Specifically, we found that, in Belgium and France, risk premia are positive in January and negative the rest of the year.There is no January seasonal in the U.K. risk premium.Instead, we observed in this country a positive April seasonal and a negative average risk premium over the rest of the year.In the U.S., the pattern of risk-premium seasonality coincides with the pattern of stock-return seasonality.Both are positive and significant only in January.We also found that the January risk premium in the U.S. is significantly larger than those observed in the European markets.Interestingly, the reported patterns of risk-premium seasonality in European equity markets do not fully coincide with the observed patterns of stock-return seasonality in these markets.For example, in the U.K., average stock returns arc significant and positive in January and April, whereas the market risk premium is significantly positive only in April.A possible interpretation of this phenomenon is presented in the paper.THE SEASONAL BEHAVIOR of stock market returns has been documented in several studies.Rozeff and Kinney [24], Keim [16], and Roll [23] report that U.S. stock market returns are, on average, higher in January than during the remaining eleven months of the year.This January seasonal is not restricted to U.S. common stocks.Gultekin and Gultekin [9] and others have observed the same phenomenon in most stock exchanges around the world. 1 More to the point, however, is the fact that the U.S. January seasonal is not confined to stock market returns.Recent contributions by Tinic and West [28,29] indicate the presence of a January seasonal in the coefficients of the estimated relationship between average portfolio returns and systematic risk.Their results reveal, "The positive relationship between return and risk is unique to January.The risk premiums during the remaining eleven months are not significantly different from zero" ([28], p. 561). 2 The purpose of this paper is to examine the relationship between average returns and risk in the United States, the United Kingdom, France, and Belgium and to find out whether the estimated coefficients of the risk-return relationship exhibit a January seasonal similar to that observed in the U.S. equity market.The examination of stock price behavior in markets other than the United States is of interest for at least three reasons.First, it provides additional evidence in support of or against the validity of security-pricing models such as the two-parameter capital asset pricing model (CAPM).3 Second, it allows us to compare the pattern of risk-premium seasonality across national stock markets.Third, looking at non-U.S.data may help us in understanding why the market risk premium exhibits seasonalities.In particular, we seek to find out whether risk-premium seasonality is linked to return seasonality.If this were the case, then, any potential explanation of return seasonality could also be a possible explanation of risk-premium seasonality.For example, if return seasonality could be explained by the so-called tax-loss selling hypothesis, 4 which predicts that stock returns will be higher in the first month of the fiscal year, then the tax-loss selling hypothesis could have something to do with riskpremium seasonality.Consider the following empirical result reported in Section II.In January, and only in January, average stock returns and the market risk premium are positive in the United States.They are not significantly different from zero during the rest of the year.Now, based on the U.S. evidence, we may be tempted to link the January seasonal in stock returns to the January seasonal in the risk premium.But a look at the evidence from other countries reveals that these two phenomena may not be related.Indeed, in the United Kingdom, France, and Belgium, the evidence is not consistent with the linkage hypothesis.Specifically, we present below evidence indicating that, in Belgium and France, the CAPM-based risk