Investor risk aversion and the weekend effect: the basics.

Young, Michael T.

ABSTRACT

This paper provides an explanation of the continued persistence of the weekend effect. Using the 23 non-holiday Wednesday closings of 1968 as a benchmark, it is postulated that negative Monday returns can be explained by risk averse investors reacting to the arrival of new information.

INTRODUCTION

It is well documented that stock returns, on average, are statistically lower on Monday. Yet there is little consensus on the explanations for this phenomenon. This paper pursues two objectives. First, to provide additional theoretical insight into the empirical persistence of the weekend effect, and secondly, using the non-holiday Wednesday closings of 1968, examine the underlying liquidity and information dissemination processes and thereby isolate factors driving the weekend effect. Of particular interest is the employment of pre-1986 daily liquidity and information data from the Center of Research in Security Prices (CRSP).

During the second half of 1968, the NYSE and the AMEX were closed on twenty-three Wednesdays due to a backlog of paperwork. These closings offer a unique opportunity to analyze the anomalous behavior of the market surrounding non-trading hours. By using cross-sectional data this study observes several determinants of information flow and market liquidity related to individual security prices.

An opportunity to test the effect of information flow on anomalous returns is provided by the systematic discontinuities in trading surrounding the 1968 Wednesday closings. The twenty-three closed Wednesdays were non-trading, regular business days with full information flow in the market, whereas weekends represent non-trading, non-business days with reduced information flow.

LITERATURE

Differences in information processing are usually explained using three different hypotheses, (French & Roll, 1986). First, public information is more likely to arrive during normal business hours. Second, private information affects prices throughout the trading day. Third, noise caused by trading may induce pricing errors. In light of these three hypotheses, the 1968 Wednesday closings represent normal business days when no information, public or private, can be absorbed into the market. While weekends are non-trading days with information absorption into the market not being possible, they are also non-business days with less information flow available for absorption. Weekends are non-trading, non-business days, whereas the twenty-three closed Wednesdays are non-trading, regular business days. Also, interestingly, for the 1968 closed Wednesdays, there is no trading noise to induce pricing errors.

The major component of liquidity reflected in market data, and addressed in this study is daily volume. (Karpov, 1987) provides a comprehensive review of the work related to the price/volume relationship through 1986. Most studies find a positive correlation between price change and volume. Other studies look at the NYSE intraday bid-ask spread as a measure of volatility. (Keim & Stambaugh, 1984) hypothesize, test, and reject the hypothesis that market makers transacting at the bid (ask) price with disproportionate frequency at the market close on certain days of the week could induce low (high) returns on those days. They indicate that bid-ask effects can be discounted as an important contributor to high pre-holiday returns. However, holidays, while representing non-trading days, often represent non-business days. Holidays, being non-business days, do not have the same information flows as do the non-trading, regular business closed Wednesdays of 1968. (Stoll & Whaley, 1990) propose that wider spreads reflect the specialists' ability to profit from their privileged knowledge. (Brock & Kleidon, 1992) test specialists' monopoly power to control inelastic demand during times of wider spread. (Madhavan, 1992) explains wider spreads with variation in the cost of adverse selection. (Lee, Mucklow & Ready, 1993) document the relationship between the intraday width of bid-ask spreads for NYSE stocks and reported earnings, which reflects information flow occurring only on business days. Further evidence of a day-of-the-week effect for bid-ask spreads is provided by (Chordia, Roll & Subrahmanyam, 2001). These authors find that, for a sample of NYSE stocks, liquidity declines on Friday and spreads increase "dramatically" during down markets but decline only slightly during up markets.

A conclusive body of literature demonstrates that seasonal return patterns for equity securities vary by firm size. (Rogalski, 1984) finds significant differences in post-holiday return by weekday and firm size. (French, 1980) uses a time-diffusion process as an explanation for higher than expected returns for post-holiday trading days for every weekday except Tuesday. (Roll, 1983) finds high returns accruing to small firms on the trading day prior to New Year's Day. (Lakonishok & Smidt, 1984) note that "prices also rise in all (size) deciles (of market capitalization) on the last trading day before Christmas." (Merrill, 1965) finds a disproportionate frequency of Dow Jones Industrial Average advances on days preceding holidays during the 1897 to 1965 period. (Keim & Stambaugh, 1984) indicate that the weekend effects generate significant premiums that accrue to small firms on Fridays.

Some research incorporates the 1968 Wednesday closings and/or the weekend effect in volume and volatility studies. (French & Roll, 1986) and others show that returns are more volatile during exchange trading hours than during non-trading hours. In addition, French and Roll argue that private information dissemination is the principle factor behind high trading-time variances. (Jain & Joh, 1988) report that average volume across the days of the week (and for each hour) are significantly different. Average daily trading volume is lowest on Monday, increases from Monday to Wednesday, and then declines on Thursday and Friday. (Ross, 1989) argues that "in an arbitrage-free economy, the volatility of prices is directly related to the rate of flow of information to the market." (Pettengill, 1989) tests whether the weekend effect is a closed market effect by examining the difference between the mean returns on the trading days prior to exchange holidays and on ordinary days. He finds no significant difference between Wednesday closings and regular trading days. However, Pentengill's study excludes the trading days immediately adjacent to the twenty-three 1968 closed Wednesdays. (Houston & Ryngaert, 1992) look at volume and volatility patterns for weeks with Wednesday closings. They report that Wednesday closings did not affect weekly volume or weekly volatility. However, they argue that volume and variance are shifted between periods within the weeks with reduced trading hours. This is consistent with reduced trading, temporarily and simultaneously, reducing the transmission of private information into traded market prices. They further indicate that trading volume is redistributed rather evenly among Monday, Tuesday, and Friday with the largest increase in trading volume on Thursday following Wednesday closings. Trading volatility is also redistributed to the remaining four days with the largest increase on Fridays and smallest on Mondays. (Steeley, 2001) finds that a day-ofthe-week effect exists for market returns in the UK and is related to the arrival time and nature of new information. Finally, (Berument & Halil, 2001) report that the variance of the S&P 500 index is a function of the week day. They find that variance is highest on Friday and lowest on Wednesday and propose that Friday's high variance is the result of increased levels of macroeconomic news releases on Thursday and Friday. Although some of these works include an examination of the 1968 Wednesday closings, none provide a tested explanatory link between non-trading, regular business day influences and liquidity and information flow. This can be attributed in part to the, heretofore, unavailable necessary data.

PREMISE

Stock returns on Monday are lower than other days. Why? There is no clear consensus. With a cursory review, there appears to be no consistent and logical reason for Monday to be any different than other days except for the fact that the market is closed over the weekend. However, market closure in and of itself should make no difference. The premise here is that if the market is closed, and there is no new information arriving, then the price should not change. If there is new information while the market is closed, then the market should react in the following ways:

1) Good News: The spread should increase slightly as analysts try to determine the new "correct" price. If nothing else, the Ask price should increase. The volume should also go up as traders try to react to the information. Return should increase as investors react to the news.

2) Bad News: The market reaction should be the same as above but in the opposite direction for the spread. Volume should go up as investors try to dump the stock. Finally, returns should decrease for obvious reasons.

3) Ambiguous Information: The spread should increase substantially while analysts try to assess the impact on firm price. Volume should increase substantially as some traders believe the information to be good and others believe it to be bad and try to make a profit by trading accordingly. If investors are risk neutral, the price will remain unchanged provided the information is truly ambiguous as the number of traders who believe the price will increase and those that believe that it will decrease should be the same. However, if participants in the market are risk averse, they will be more inclined to attempt to protect themselves from loss rather than attempt to profit on the information thus causing a decrease, or at a minimum no change, in price.

The preceding premise is dependent on the stock being actively traded. If the stock is held in a portfolio primarily as a "buy-and-hold" security, the market reactions will be somewhat mitigated. This is often the case for large firms. In addition, the larger the firm, the larger the number of analysts who follow the stock, thereby increasing the likelihood of the market reaching a consensus on the "correct" new price prior to the market opening, thus reducing the premise effects. This will not necessarily hold true for securities of smaller firms, indicating that small and large firms should be viewed differently in light of return, liquidity, and information flows.

Even with a conservative assumption that there are equal amounts of good, bad, and ambiguous information coming to the market after closure on Friday and over the weekend, one should see a low return, increased volatility, and increased liquidity (volume) on Monday. As indicated earlier, a preponderance of past research supports this conclusion.

Therefore, if the arrival of information is the driving factor for Monday returns, then there should be the same effects on Thursday after a Wednesday close. In fact, the "closed-Wednesday-Thursday effect" should be more pronounced since there is information dissemination of a full, active business day.

DATA AND METHODOLOGY

The hypothesis is that differences in daily returns can be explained by liquidity and information flow. Inferences are made using daily firm-specific data drawn from the Center of Research in Security Prices (CRSP) files. This approach is particularly appealing in that daily liquidity and information data from periods prior to 1986, not available from CRSP before July 1995, and therefore not available to most previous researchers, are used to provide empirical insight into the persistence of the weekend effect.

To this end, this research investigates firm-specific daily returns, firm-specific trading liquidity, and firm-specific trading information flow for firms whose stock was continuously traded on the NYSE and/or the AMEX from the beginning of 1968 to the middle of 1969. The ability to attribute differences in volume and volatility to firm-specific rather than institutional factors is enhanced by the inclusion, not only of the NYSE firms, but of AMEX firms as well.

The applied methodology addresses the return-liquidity-information issue with a two approach process. In Approach I, ordinary least squares (OLS) analysis is performed for the test-period, consisting of the twenty-three weeks with closed Wednesdays in 1968, and addresses return, dispersion, and volume differences between days of the week with particular attention given to Thursdays that follow closed Wednesdays. More complicated, alternative approaches for daily returns is offered by (Scholes & Williams, 1977) and (Dimson, 1979) that reduce the bias in the estimated b's, however, according to (Peterson, 1989), they do not provide a clear-cut benefit over OLS procedures. (Ingram & Ingram, 1993) indicate that joint generalized least squares (JGLS) methods have advantages over OLS procedure if there is significant cross-correlation. In this study cross-correlation is not found to be significant. Approach II addresses differences between days of the week for return, dispersion, and volume measures tested over two time periods:

1) Before-Closings: the pre-test period (January 1968 through June 1968)

2) During-Closings: the test-period (the twenty-three weeks with closed Wednesdays in 1968); and across two firm groups:

1) Small Firms: Decile 1, the lowest capitalized firms, and

2) Large Firms: Decile 10, the highest capitalized firms.

A traditional restrictive model approach is used that differentiates firm-specific daily returns, liquidity influences, and information flow influences by the day of the week for the test-period. This approach differentiates firm-specific daily returns by the day of the week and isolates the impact of liquidity and information influences. The following traditional restricted models for the four-day trading week are applied to the firm-specific daily data for the twenty-three weeks with Wednesday closings:

where,

Rt = b0 + b1D1t + b2D2t + b3D4t + ,t, (1)

It = b0 + b1D1t + b2D2t + b3D4t + ,t, (2)

Lt = b0 + b1D1t + b2D2t + b3D4t + ,t, (3)

Rt = the daily return,

It = information flow (volatility measure) for the security, quantified by firm-specific relative range:

= daily high less the daily low / [(daily high plus the daily low)/2]

Lt = liquidity (volume measure) for the security, quantified by firm-specific relative volume:

= the daily number of shares traded / the total number of shares outstanding

D1t = {1 if Monday, 0 otherwise}

D2t = {1 if Tuesday, 0 otherwise}

D4t = {1 if Thursday, 0 otherwise}

[member of]i = disturbance term.

Previous research and a priori expectations indicate that in equation 1, b1 and b3 should be negative and the latter should have greater magnitude. If the hypothesis presented is correct, these lower returns on Monday and Thursday (after a Wednesday close) are a function of the arrival of new information. Therefore, in equations 2 and 3, b1 and b3 should be positive. Also, if a regular business day produces more information than appears on the weekend, the latter should have greater magnitude.

For the purpose of detecting the impact of liquidity and information flow on security returns, the usual, straight-forward method for testing the equality of means from two samples is employed. Typical t-test methodology is used to compare:

1) Daily information flow differences between the Before-Closings Period and the DuringClosings Period for:

a) Small and Large Firms together,

b) Small Firms, and

c) Large Firms;

2) Daily liquidity differences between the Before-Closings Period and the During-Closings Period for:

a) Small and Large Firms together,

b) Small Firms only, and

c) Large Firms.

The usual t statistic for testing the equality of means is employed for the two sample comparisons:

t = ([bar.[x.sub.1]] - [bar.[x.sub.2]] / [square root of [s.sup.2](1/[n.sub.1] + 1/[n.sub.2]),

where, s2 is the pooled variance

[s.sup.2] = [([n.sub.1] - 1) [s.sub.1.sup.2] + ([n.sub.2] - 1) [s.sup.2.sub.2]] / [n.sub.1] + [n.sub.2] - 2

and, where s12 and s22 are the sample variances of the two groups. The usual assumption of equal population variances for this t statistic in comparisons is satisfied.

Of particular interest is the intriguing polar contrast of decile sampling techniques. By examining the highest and lowest capitalized firms, decile sampling provides a polar analysis of the existence of influential effects on liquidity and information predicated on firm size. Rather than using a firm size continuum, a more rigorous examination is made by comparing the extreme poles of firm size, namely the Small Firms and Large Firms groups.

In general, the information arrival should be the same in both the before-closings and during-closings periods for all days except Thursday. Also liquidity should be higher on all days with Thursday getting the lion's share of the increases. This corresponds to the work done by (Houston & Ryngaert, 1992).

RESULTS

The first step in the analysis is to ascertain the pattern of returns, information arrival, and liquidity within the week. Parameter estimates from equation 1 appear in Table 1. As predicted, Thursday's returns are significantly less than Friday's for all three groupings. Also, the returns for the large firm portfolio on Monday and Tuesday are less than Friday's return, but the decrease is only one fourth that observed on Thursday. Of more interest, however, are the liquidity (equation 2) and information flow (equation 3) results in Tables 2 and 3 respectively. Liquidity is significantly greater on Thursday than any other day. In conjunction with this, information flow is greatest for all three portfolios on Thursday and for the combined and small firm portfolios on Monday. The magnitude, as predicted, is greatest on Thursday.

Having identified the fact that returns are lower on Monday and Thursday, that information flow is larger on these days, and that liquidity is greater on Thursday, the next step is to determine if there is a change in these variables as a result of the Wednesday closings. The t-test results for a change in information flow for the three portfolios appear in Tables 4, 5, and 6. Information flow is numerically larger on all days except Thursday for all three portfolios during the before-closings period. This difference is statistically significant only for the combined portfolio and the large firm portfolio, however. In contrast, the information flow is significantly greater during the after-closings period on Thursday for all three portfolios. This result at first was rather surprising. However, assuming that there is no increase in information on any day during a Wednesday-closings week except Thursday and observing that liquidity across all days has either remained constant or increased, this result makes perfect sense. Holding all else constant, an increase in liquidity should cause the relative range (information flow) to decline. This simply puts the Thursday increases in stark contrast and shows that the open business day generates a large amount of information that must be analyzed and absorbed into the market.

A comparison of liquidity between periods shows an increase across all days for the combined portfolio (Table 7) and the small firm portfolio (Table 8) with the largest increases occurring on Thursday. Relative daily trading volume for the combined portfolio increases by 16.2% on Monday, 16.7% on Tuesday, and 23.1% on Friday. Thursday's increase is a staggering 36.0%. As can be seen below, the small firms in the portfolio are driving these increases. The net result is an overall weekly volume that is relatively unchanged. These numbers are consistent with those of (Houston & Ryngaert, 1992). Thursday's increase is probably due to the markets' reaction to Wednesday's information as well as a general redistribution in trading patterns as investors make up for lost time.

The small firm portfolio reflects a similar pattern of increases. Volume on Monday and Tuesday increases by 19.9% and 20.4% respectively. Friday sees an increase of 27.6% and Thursday nearly doubles that of Monday and Tuesday at 38.7%. It appears that for small firms, which are followed by fewer analysts, it takes two days to sort out the meaning of any information which arrived on Wednesday.

The large firm portfolio (Table 9) has no change in liquidity on any day except Thursday which has a 25.0% increase. In fact, the relative volume decreased on Monday, Tuesday, and Friday, but these changes are not statistically significant. For those who believe in an efficient market this is good news. The more closely watched larger firms react very quickly to any new information.

SIGNIFICANT IMPLICATIONS

While previous studies fail to provide a consensus explanation for negative Monday returns, this study synthesizes a coherent explanation of "anomalous" Monday negative returns. The intent is to show that negative Monday returns are not anomalous, and can be explained logically based upon the degree of liquidity and information flow.

The most important result is that on Thursday following a Wednesday market closing, returns are significantly lower while information flow and liquidity are significantly larger. This indicates that when there is an increase in information coming to the market, traders, being risk averse, lower the price of securities until they can process the information and/or observe the markets' reaction. It is reasonable to assume, therefore, that this reaction is not limited only to days following a normal business day with the market closed, but also on Mondays which follow information arrival over the weekend.

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Michael T. Young, Minnesota State University--Mankato

Table 1: OLS Results For Testing Differences in Daily Returns

Independent Variable Combined Small-Firm Large-Firm

Intercept (Friday) 0.001967 ** 0.003212 ** 0.000839 **
 (0.0001) (0.0001) (0.0003)
b1 (Monday) -0.000142 0.000416 -0.000648 *
 (0.7330) (0.5999) (0.0493)
b2 (Tuesday) -0.000801 -0.000964 -0.000654 *
 (0.0537) (0.2240) (0.0473)
b3 (Thursday) -0.002073 ** -0.001558 * -0.002541 **
(0.0001) (0.0496) (0.0001)

* significant at the 5% level

** significant at the 1% level

Parameter estimates for model: Rt = b0 + b1D1t + b2D2t + b3D4t + t,
applied to the firm-specific daily data for the twenty-three weeks in
1968 with Wednesday closings. Where, Rt is the average daily return.
The Combined portfolio consists of all firms whose stock was
continuously traded on the NYSE and/or AMEX from the beginning of 1968
through the middle of 1969. The Small-Firm and Large-Firm portfolios
consist of the smallest and largest capitalization decile respectively.

Table 2: OLS Results For Testing Differences in Daily Liquidity

Independent Variable Combined Small-Firms Large-Firms

Intercept (Friday) 0.003083 ** 0.005557 ** 0.000844 **
 (0.0001) (0.0001) (0.0001)
b1 (Monday) -0.000066 -0.000087 -0.00005
 (0.5920) (0.7259) (0.1101)
b2 (Tuesday) -0.000023 -0.000029 -0.000018
 (0.8525) (0.9071) (0.5588)
b3 (Thursday) 0.000472 ** 0.000715 ** 0.000251 **
(0.0001) (0.0040) (0.0010)

* significant at the 5% level

** significant at the 1% level

Parameter estimates for model: Lt = b0 + b1D1t + b2D2t + b3D4t + t,
applied to the firm-specific daily data for the twenty-three weeks in
1968 with Wednesday closings. Where, Lt is firm-specific daily
relative volume. The Combined portfolio consists of all firms whose
stock was continuously traded on the NYSE and/or AMEX from the
beginning of 1968 through the middle of 1969. The Small-Firm and
Large-Firm portfolios consist of the smallest and largest
capitalization decile respectively.

Table 3: OLS Results For Testing Differences in Daily Information Flow

Independent Variable Combined Small- Firms Large-Firms

Intercept (Friday) 0.026336 ** 0.035244 ** 0.018270 **
(0.0001) (0.0001) (0.0001)
b1 (Monday) 0.001225 ** 0.002082 ** 0.00044
 (0.0002) (0.0005) (0.0552)
b2 (Tuesday) 0.000318 0.000657 0.000008
 (0.3409) (0.2691) (0.9698)
b3 (Thursday) 0.003333 ** 0.003898 ** 0.002817 **
 (0.0001) (0.0001) (0.0001)

* significant at the 5% level

** significant at the 1% level

Parameter estimates for model: It = b0 + b1D1t + b2D2t + b3D4t + t,
applied to the firm-specific daily data for the twenty-three weeks in
1968 with Wednesday closings. Where, It is firm-specific daily
relative trading range. The Combined portfolio consists of all firms
whose stock was continuously traded on the NYSE and/or AMEX
from the beginning of 1968 through the middle of 1969. The Small-Firm
and Large-Firm portfolios consist of the smallest and largest
capitalization decile respectively.

Table 4: T-Test Comparing Daily Information Flow Before and During
Wednesday Closings: Combined Portfolio

Day of the Week Monday Tuesday Thursday Friday

Mean Before Closings 0.02859637 0.02746306 0.02839674 0.02728663
Mean After Closings 0.02756052 0.02665362 0.029559 0.02215075
Prob > [absolute
 value of T] 0.0025 0.0137 0.0003 0.0037

Information flow is measured as the firm-specific daily relative
trading range. The Combined portfolio consists of all firms whose
stock was continuously traded on the NYSE and/or AMEX from the
beginning of 1968 through the middle of 1969.

Table 5: T-Test Comparing Daily Information Flow Before and During
Wednesday Closings: Small-Firm

Day of the Week Monday Tuesday Thursday Friday

Mean Before Closings 0.03736189 0.03616932 0.03703348 0.03586639
Mean After Closings 0.03732636 0.03590122 0.03914173 0.03524393
Prob > [absolute
 value of T] 0.9544 0.6526 0.0009 0.2942

Information flow is measured as the firm-specific daily relative
trading range. The small-firm portfolio consists of the smallest
capitalization decile of all firms whose stock was continuously traded
on the NYSE and/or AMEX from the beginning of 1968 through the middle
of 1969.

Table 6: T-Test Comparing Daily Information Flow Before and During
Wednesday Closings: Large-Firm

Day of the Week Monday Tuesday Thursday Friday

Mean Before Closings 0.02061107 0.01953222 0.0205235 0.01947363
Mean After Closings 0.01871067 0.0182789 0.02108688 0.01827019
Prob > [absolute
 value of T] 0.0000 0.0000 0.0248 0.0000

Information flow is measured as the firm-specific daily relative
trading range. The large-firm portfolio consists of the largest
capitalization decile of all firms whose stock was continuously traded
on the NYSE and/or AMEX from the beginning of 1968 through the middle
of 1969.

Table 7: T-Test Comparing Daily Liquidity Before and During Wednesday
Closings: Combined Portfolio

Day of the Week Monday Tuesday Thursday Friday

Mean Before Closings 0.00259552 0.00262157 0.00261368 0.00250412
Mean After Closings 0.00301673 0.00306026 0.00355552 0.00308338
Prob > [absolute
 value of T] 0.0000 0.0000 0.0001 0.0001

Liquidity is measured as the firm-specific relative daily volume. The
Combined portfolio consists of all firms whose stock was continuously
traded on the NYSE and/or AMEX from the beginning of 1968 through the
middle of 1969.

Table 8: T-Test Comparing Daily Liquidity Before and During Wednesday
Closings: Small-Firm

Day of the Week Monday Tuesday Thursday Friday

Mean Before Closings 0.00456254 0.00459088 0.00452039 0.00435591
Mean After Closings 0.00547016 0.00552826 0.00627191 0.00555727
Prob > [absolute
 value of T] 0.0000 0.0000 0.0001 0.0001

Liquidity is measured as the firm-specific relative daily volume. The
small-firm portfolio consists of the smallest capitalization decile of
all firms whose stock was continuously traded on the NYSE and/or AMEX
from the beginning of 1968 through the middle of 1969.

Table 9: T-Test Comparing Daily Liquidity Before and During Wednesday
Closings: Large-Firm

Day of the Week Monday Tuesday Thursday Friday

Mean Before Closings 0.00080359 0.00082766 0.00087552 0.00081783
Mean After Closings 0.00079342 0.00082521 0.00109452 0.00084355
Prob > [absolute
 value of T] 0.702 0.9288 0.0001 0.3514

Liquidity is measured as the firm-specific relative daily volume. The
large-firm portfolio consists of the largest capitalization decile of
all firms whose stock was continuously traded on the NYSE and/or AMEX
from the beginning of 1968 through the middle of 1969.