Leseprobe

## Table of Contents

1. Introduction

2. Motivation and Hypotheses Development

3. Data and Methodology

4. Results

5. Conclusion

6. Bibliography

7. Appendix

## 1. Introduction

Modern technologies made public and private information directly accessible around the world. With new faster systems for transactions, securities should have the ability to reflect all Information without delay. But inconsistent with the efficient market hypothesis in the last decades were found an increasing number of anomalies from which eleven can be described as well know (eg. Stambaugh et al. 2012).

Daily close-to-close returns can be decomposed in their overnight and intraday components. Recent empirical studies suggest that these returns behave distinctively different in their predictive power, risk premia and beta. Hendershott et al. (2020) analysed the relationship between the returns and beta showing that the weakly relation between beta and returns is driven entirely by returns during the trading day. They determined that the security market line is negative when using daytime returns. They described this phenomenon as a result of speculative behaviours of marginal day traders buying high-beta stocks when the market opens and clear their positions at the end of the trading day. However, beta is positively related to overnight returns on the daily data i.e., the CAPM model hold overnight. Another key difference between overnight and intraday returns which has been long pointed out is the much higher intraday return volatility per unit of time than overnight. French and Roll (1986) could show that this excess trading volatility is not driven by public information instead it is driven by private information and mispricing. Often intraday returns are assumed being negligible or constant over the trading day. In contrast to this assumption Bogousslavsky (2020) shows that asset pricing anomalies occur intraday in many ways. According to his paper mispricing strategies including e.g., gross profitability, idiosyncratic volatility, and net stock perform good at the first hours of a day but worse at the end of the day substantiating the theory of intraday price pressure induced by capital-constrained arbitrageurs who close their positions at the end of the day. Baradehi et al. (2022) show that Momentum strategies based on intraday returns perform good at longer horizons while the strategies based on overnight returns don’t. Lou et al. (2015) found out that the abnormal returns on momentum strategies occur mostly overnight (intraday) in the time period between 1993-2013 (1926-1962). In contrast, average intraday momentum profits are economically and statistically insignificant. He attributes this to the change of investor clienteles. Size and value premiums instead accrue intraday.

## 2. Motivation and Hypotheses Development

For explaining the different behaviour of stock returns, we first start with the basic idea of a multiple factor model where exists multiple priced risk factors whose covariance matrix varies between the day and night. In case of different behaviour of intraday and overnight returns there are existing different types of risk factors e.g., which can predict the expected stock return. To explain relation between returns and beta we determine that the risk-return relationship is positive only during specific times, for example in January (Tinic and West, 1984), during months of low inflation (Cohen et al., 2005) or days with news about economic trends like inflation or unemployment. By looking at returns of the CDAX decomposed into its intraday and overnight returns we see a distinctively different behaviour. In Figure I the cumulative CDAX overnight returns seem to slowly but steadily increase while the complementary intraday part seems to fluctuate stationary around zero with higher variance.

This maybe even slightly decreasing trend in intraday returns could lead to the assumption that the risk premium for some factors is negative intraday. This would violate the assumption of a multi-factor model being applicable in intraday trading. In this case we would likely require a model with heterogeneous agents and time-varying constraints (Hendershott et al., 2020). We will therefore construct our first Hypothesis:

*Intraday returns in the German Equity Market will receive a negative risk premium by applying multi-factor models.*

Despite the papers mentioned above, there is not much evidence for the appearance of the momentum intraday and overnight anomalies in the German equity market. Most of the papers focus on the US-market. Therefore, there could be a reversal or statistically insignificant trend in Germany. So, this paper attempts to test some of the findings. For our hypothesis development on momentum returns we rely on the assumptions made by Baradehi et al. that overnight returns reflect news rather than investors trading, but we notice that intraday returns may also be strongly affected by news for example in the preceding of the NYSE-Opening (e.g., Dimpfl, Thomas, 2009). The impact by other countries stock prices when the German market is closed could drive the behaviour of the German stock market reversal to the results made by US-Data. We take up the idea of Baradehi et al. that the predictive power of intraday return that is not observed for overnight return can be attributed to investors trading. Therefore, reversal and momentum effects could be differently strong predicted by intraday than overnight signals in dependence on how strong momentum is driven, whether by underestimation of the public or by private signals. We also mention the assumption of Baradehi et al. that Momentum based on intraday returns could also be present if investors sufficiently underweight the precision of others signals. We construct our second Hypothesis:

*Momentum and Reversal in the German Equity Market behave differently intraday than overnight and can be predicted by using intraday signals rather than close-close returns.*

In the first step of my analysis, I provide some descriptive statics of daily overnight and intraday returns in the German equity market. Followed by this, we will discuss evidence for differences in the return-/beta relation and make an answer to our first Hypothesis. Then we will go over to the momentum analysis and show their predictive power for momentum and reversal strategies based on overnight and intraday return signals and take a quick look on where it happens (intraday vs. overnight) like Baradehi et al. (2022) and Lou et al. (2015).

## 3. Data and Methodology

This work examines daily returns of German equities or portfolios composed of them, spitted into their intraday and overnight components. The study covers the period from January 2005 to July 2022 (T = 210 months). All daily open and close prices, Market Value as the share price multiplied by the number of ordinary shares in issue and Market to Book come from the data provider Thomson Reuters Datastream/Worldscope. Datastreams open and close prices are only adjusted for capital changes, but not for dividends. Therefore, I use the dividend payments at the Ex-Dividend date from Compustat at WRDS receiving via a list of Datasreams ISIN. I received the stock specific data for all German stocks listed on the Xetra Stock Exchange, excluding financial service providers such as banks and insurance companies because of them being different valued by the market than industrial companies. To address issues with the data quality of individual stock returns, I take advantage of the filters proposed by Ince & Porter (2006) and adapt them for our model. First observations were deleted from the beginning/end of the sample period until the first/last appearance of a nonzero return. Then I repeated this procedure by deleting Firms with Market Prices below 1,5 Euro. In the last step I excluded all Firms with a missing opening Price percentage above 5 Percent of their Datapoints. From the 1017 firms including in the sample, 482 remained. Overnight returns were calculated by where is a dummy Variable taking the value of the dividend payoff of the firm at the ex-dividend date . For further analysis I calculated a value weighted portfolio of the firms included in the sample. The adjusted of 0.94 with the CDAX daily returns imply, that our portfolio being good at representing the German equity market. Afterwards I calculated daily, monthly overnight, intraday and close to close risk factors and in the sense of Fama and French (1993). I therefore assigned each stock to one of the six double sorted portfolios separated by the Median of the Market Value at first July of the respective year and the Book to Market Value 30, 70 percentiles according to last fiscal-year end. I then estimated the value weighted returns of these six portfolios and calculated the factors with the following formula.

Low correlation of 0.44 can between our and a public dataset of Bruckner et al. provided by HU Berlin could be explained by our specific filters described above. Table II shows some descriptive statistics of the returns decomposed into overnight and intraday components over the last 17 years. We can see the average intraday return is positive in 15 out of 17 years, whereas the intraday return is positive in seven. After preparing the data CAPM-Beta is generated for all firms which are traded for at last 230 trading days in the corresponding one-year horizons beginning on 01.07.2005. Afterwards I calculated the market and portfolios excess return by the difference of the value weighted market portfolio, single stock respectively and the risk-free rate. The risk-free rate is given by the 1-Month Euro Interbank Offered Rate scaled down time-continuously to daily, intraday and overnight horizons^{1}. By regression of the individual returns on market excess return, we obtain the market risk beta coefficient. For calculating the Fama French beta exposures and the risk factors and are added to our regression model. Corresponding overnight and intraday factors were calculated by regression on the overnight/intraday factors and returns respectively. After extracting the coefficients, we regress the intraday-/overnight-/close-close excess return with a Fama-MacBath regression on the coefficients using standard errors allowing for ten lags of autocorrelation following Hendershott et al. (2020). With the two-step procedure of T time fixed cross-sectional regressions and averaging the coefficients over time, we obtain the risk premiums ( in the following form:

We use individual stocks for performing the regression instead of partitioning the stocks into portfolios, arguing that it could cause the information contained in individual stock betas to become opaque and tend to shrink (Ang et al., 2020). I will do an analysis on beta sorted portfolios afterwards. We will also check if the results differ while using the close-close coefficients instead of the individual ones. In further analysis we create beta sorted quintile portfolios using close-close CAPM-Beta and report their monthly overnight and intraday excess returns. I check if the results are consistent in high-/low Book to Market and high-/low Market Value portfolios. In a last step I simulate the results of a zero-cost betting on/against Beta strategy in which we buy (sell) stocks with high (low) beta at the end of the trading day and invert this procedure at the next morning stock opening.

After the analysis on the beta coefficients, I create return signals for predicting the momentum effects according to Baradehi et al. by summing log intraday, overnight and close-close returns over all trading days in each horizon, e.g., one month, to construct intraday and overnight signals.

These log return signals are denoted by , and where is the Horizon in the set . Beforehand I apply an additional stronger filter excluding all firms with missing opening data above 3 % of the sample. From the 482 Firms 423 firms remain in the sample. For a stock being included in the sample, I require return observations over the corresponding time horizon After applying these Filters we assign each stock each month according to its log return signals based on the breakpoints of the signals to their corresponding intraday overnight and close-close quintile groups. We then calculate for each month and each quintile portfolio an equally weighted monthly portfolio return . The time-series of equally weighted month portfolio returns, in excess of risk-free rates, are then regressed on the market excess-return, and correcting for autocorrelation with 3 lags using the Newey West approach for estimating the corresponding three-factor alpha i.e., intercept. In a last step, we take a quick look back at the 12-month momentum-strategy and try to see where momentum happens intraday or overnight by looking at their decomposed returns.

## 4. Results

In this section, we study how beta affects the intraday and overnight return in a cross-sectional analysis. And later observe the prediction of Momentum by intraday and overnight signals.

**Table V Fama-MacBath Regression on CAPM-Beta**

Table V reports results from the equal weighted cross sectional Fama-MacBeth regression of daily returns (in percent) on betas. Returns are measured during the day, from open-to-close, and during the night, from close-to-open. t-statistics are reported in parentheses. Standard errors are based on Newey-West corrections, allowing for ten lags of serial correlation.

Abbildung in dieser Leseprobe nicht enthalten

The results of the equal weighted cross-sectional Fama-MacBath regressions show the slope of the security market line computed from the daytime returns in Table V is -0,197 %, implying that for every increase in beta by 1, the expected intraday return decreases by 0,197 according to the classical Capial Asset Pricing Model (CAPM) with statistical significance. In contrast the regression of the overnight returns delivers the exactly complementary results with a coefficient of 0,202 % while the coefficient on close-close returns is insignificant positive but low. The results are comparable to Table 1 of Hendershott et al. (2020). By looking at the regressions including Fama-French factors (Table VI Panel B) we see that the coefficients on are significant positive (negative) for intraday (overnight) returns which could lead us to the assumption that large firms outperform small firms at night where it is the opposite intraday. We will look more at this assumption later. The respectively close-close coefficients are positive but within lower significance than their overnight correspondents. By looking at the regression on close-close coefficients instead of individual ones (Table VI Panel C) we obtain no remarkable different results for Beta, only for the coefficients we earn less significant results, which can be explained by a systematically difference between the risk exposures on that factor intraday than overnight. The coefficient is positive in any case, but also within low significance. In Table VII Panel A we see that the monthly excess return of the portfolios based on beta is steadily decreasing from low to high beta portfolios intraday. The effect overnight is reversal. Buying the highest quintiles beta stocks and selling portfolios with low beta generates a monthly average return of 5.31% overnight and - 5.08 % intraday. In Panel B and C, we can see that our results are consistent in high/low Market Value and Book to Market subsamples. The overnight return is higher among low and medium beta stocks for higher Market Value, whereas the intraday return is smaller. We can also see the tendency that high Book to Market stocks have been likely to outperform low stocks at the day, but we can see no real pattern for the behaviour overnight. Both observations are in line with the results of Boguslavsky (2020) who showed that for example the Book to Market anomaly occurs in intraday trading. Some of the anomalies occur only in specific times of the trading day. By simulating the “zero-cost” betting on/against beta strategy, we obtain monthly average returns. In Panel D we see the monthly average return ignoring any kind of transaction and shorting cost results in average 11.5 % with peaking monthly returns of over 100 % noticing that the most of these abnormal high returns take place in the period between 2006 and 2010. In the other years, we see lower but mostly positive returns per month. By correcting for lending and transactions costs, we would likely get more interesting results.

Now we will move on to analyse the prediction of momentum intraday vs. overnight. Table VIII and Figure II show the results of momentum strategies based on intraday, overnight and close-close log-return signals. We see that the strategy which goes long in past winners and sell past losers earns a positive alpha over all time horizons, whereas the strategies based upon overnight signals earns a negative alpha.

**[...]**

^{1} As an alternative I could have used overnight/intraday risk-free rates for a more accurate representation. Further study of the appropriate risk-free rate may be important.

- Arbeit zitieren
- Samuel Köppel (Autor:in), Intraday and Overnight Returns in the German Equity Market, München, GRIN Verlag, https://www.grin.com/document/1274380

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