Random Walk of Stock Prices: A Test of the Variance-Time Function

Young, William E.

doi:10.2307/1909580

Cited by 18 publications

(8 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…18. Young [28] also found that the percent of significant p rose with T. This can be interpreted as evidence that, for some stocks, negative higher order autocorrelation is present in unit period (monthly) returns. To see this, note that his ratios (see our footnote 14) are pairwise comparisons between unit and longer period variance, and the only autocorrelation pattern that influences the ratios is that of the unit period returns (see our eq.…”

Section: Discussionmentioning

confidence: 87%

The Time-Variance Relationship: Evidence on Autocorrelation in Common Stock Returns

Schwartz¹,

Whitcomb²

1977

The Journal of Finance

View full text Add to dashboard Cite

IT IS WELL ESTABLISHED THAT, under stationarity and intertemporal independence, the variance of returns has a precise functional relationship with,the differencing interval. However, in the voluminous literature on the properties of returns distributions, relatively scant attention has been paid to the time-variance relationship as a test of intertemporal returns independence, although, as far back as 1949, Holbrook Working [27] suggested such an application. The only exceptions appear to be Mandelbrot and Wallis [16] who mention the time-variance relationship as a tool for investigating long cycle dependence with variable periodicity, and Poole {21] and Young [28] who use it in empirical tests (using flexible exchange rates, and common stock returns, respectively). The time-variance relationship may be an especially robust tool for random walk analysis since, like spectral analysis, it does not require a priori specification of precise autocorrelation schemes. Furthermore the relationship can be used to gain insight into a variety of issues such as: the impact of specialist trading on stock price volatility (see Barnea [3] and Schwartz and Whitcomb [24]); the variance of net present value under dependent cash flow streams (where the time-variance relationship provides an alternative to the Markovian model of Bussey and Stevens [5]); and the finding by Altman, Jacquillat and Levasseur [2] and Pogue and Solnik [20] that the market model R2 falls as the differencing interval is shortened.In Section I, we allow for a general autoregressive structure, and thereby determine the effect of autocorrelation patterns on the time-variance relationship for both total returns and market model residuals. We also show that autocorrelation accounts for the observed lower market model R2 for shorter differencing intervals. Section II reports the results of our tests for autocorrelation on a sample of NYSE stocks. Section II contains our concluding remarks. The effects of nonstationarity and a special case multiple order autocorrelation scheme are considered in, respectively, Appendices A and B. I. THE TIME-VARIANCE RELATIONSHIPConsider a differencing interval of T years, broken into shorter intervals n years long. Then, the T year interval contains T/ n (integer) short periods, t = 1,..., T/n. Let the random variable r, be the (log) return, expressed as a rate per n over the tth short period, r, = log,[(P, + D,)/P, ,J. Return per annum over the T year differenc-

show abstract

Section: Discussionmentioning

confidence: 87%

The Time-Variance Relationship: Evidence on Autocorrelation in Common Stock Returns

Schwartz¹,

Whitcomb²

1977

The Journal of Finance

View full text Add to dashboard Cite

show abstract

“…Young [28] also found that the percent of significant ρ rose with T . This can be interpreted as evidence that , for some stocks, negative higher order autocorrelation is present in unit period (monthly) returns.…”

mentioning

confidence: 93%

“…However, in the voluminous literature on the properties of returns distributions, relatively scant attention has been paid to the time‐variance relationship as a test of intertemporal returns independence, although, as far back as 1949, Holbrook Working [27] suggested such an application. The only exceptions appear to be Mandelbrot and Wallis [16] who mention the time‐variance relationship as a tool for investigating long cycle dependence with variable periodicity, and Poole [21] and Young [28] who use it in empirical tests (using flexible exchange rates, and common stock returns, respectively).…”

mentioning

confidence: 99%

See 1 more Smart Citation

The Time‐variance Relationship: Evidence on Autocorrelation in Common Stock Returns

Schwartz¹,

Whitcomb²

1977

The Journal of Finance

View full text Add to dashboard Cite

“…Many researchers have noted that for differencing internals longer than a few days, stock returns and return residuals are predominantly negatively auto‐correlated, e.g. , Cootner [5], Fama [6], Fama and MacBeth [8], Young [11], and more recently Schwartz and Whitcomb [10]. Cootner argues that negative auto‐correlation is caused by market participants with different levels of expertise, causing stock prices to vary within “reflecting barriers,” around intrinsic values, with reversals occurring at the barriers.…”

mentioning

confidence: 99%

Earnings Announcements and Auto‐correlation: An Empirical Test

Brown

1979

J of Financial Research

View full text Add to dashboard Cite

Many researchers have noted that for differencing internals longer than a few days, stock returns and return residuals are predominantly negatively auto-correlated, e.g., Cootner [5], Fama [6], Fama and MacBeth [8], Young [11], and more recently Schwartz and Whitcomb [10]. Cootner argues that negative auto-correlation is caused by market participants with different levels of expertise, causing stock prices to vary within "reflecting barriers," around intrinsic values, with reversals occurring at the barriers. Schwartz and Whitcomb found that "the impact of market makers and delayed portfolio rebalancing seem to provide the strongest explanations of the (negative) correlation patterns we have observed." The other authors cited above did not consider explanations for the observed auto-correlation. This paper develops arguments and tests empirically the proposition that the observed auto-correlation of monthly stock return residuals is associated with the adjustment of stock prices to earnings announcements. An analysis of covariance is used to test for the statistical association between auto-correlation and earnings announcement variables.The major findings of the paper are that the level of auto-correlation of monthly stock residuals is related to the EPS variables and that the relationship indicated by the empirical test is approximately that suggested by the theoretical development. The major conclusion is that there is an association between earnings announcements and the level of auto-correlation.The arguments and models developed in this paper extend prior work by the author, and a brief summary of that work and some further evidence, useful for the present work, are given in Section I. Next, a methodology is developed to relate EPS information and auto-correlation. Finally, the results of the test are interpreted and conclusions are presented. I. Earnings Announcements and Stock Price ReversalsIn a previous article, Brown [4] examined the adjustment of stock prices of a sample of securities chosen because they exhibited unusually high or low Earnings Per Share (EPS). The selection criterion for inclusion in the sample was (1) at least a 20 percent change in annual EPS from the previous year and (2) fourth quarter EPS different from what could have been predicted on the basis of the first three quarters of results.' The author examined the adjustment on a daily basis using the cumulative average residual paradigm developed by Fama, et al. [7]. The original paper presented only the results for the days subsequent to the EPS announcement in the Wall Street Journal. Figure I presents those results modified slightly to include the cumulative returns for the 20 days prior to the EPS announcement.*Associate Professor of Finance, Florida State University.I As an example, consider a firm which earned $1 (25 cent per quarter) the previous year, and has earned $1.50 (50 cent per quarter) for the first three quarters of the current year. In order to be included in the sample it would have to earn at least 51 cent in th...

show abstract

Random Walk of Stock Prices: A Test of the Variance-Time Function

Cited by 18 publications

References 7 publications

The Time-Variance Relationship: Evidence on Autocorrelation in Common Stock Returns

The Time-Variance Relationship: Evidence on Autocorrelation in Common Stock Returns

The Time‐variance Relationship: Evidence on Autocorrelation in Common Stock Returns

Earnings Announcements and Auto‐correlation: An Empirical Test

Contact Info

Product

Resources

About