Beta Estimation and Thin Trading : Evidence from Bahrain Bourse

This study is provides some guidelines indicating how to estimate beta (systematic risk) for companies listed on the Bahrain Bourse. Several estimation techniques were used to estimate beta. The methodology suggested by Fama and MacBeth (1973) for testing the CAPM based on cross-section analysis is used. Several problems are identified which require attention when estimating beta of companies listed on the Bahrain Stock Exchange. These are the intervals of rate return, the length of the estimation period, the best procedure to control for thin trading, the market index that should be used to estimate beta and the stability of beta estimates over time. The present study uses rates of return for different intervals (daily, weekly and monthly) for the period between January 2007 and December 2011 for 39 companies to test a number of hypotheses. The results of various tests show the following: 1) the estimated betas are insensitive to the length of period used; 2) the impact of return intervals on estimated betas is not significant ; 3) betas estimated using the All-Share Index and the MCSI are not significantly different from each other; 4) the estimated betas based on weekly data do not depend on the day of the week chosen to calculate the rate of returns; and 5) the impact of thin trading on beta depends on the method used to account for thin trading.


Introduction
The capital asset pricing model (CAPM) predicts that an asset's expected and required rates of return are linear functions of its systematic (non-diversified) risk, measured by beta.This is because beta is the only measure of risk that explains the cross sectional variation of asset rates of return.Beta measures the risk associated with a particular asset in relation to the overall market.Since it was developed by Sharpe (1964), Lintner (1965) and Black (1972) (SLB hereafter), CAPM underwent extensive investigations to determine its validity and the usefulness for determining the rates of return of securities and portfolios.Those investigations yielded mixed results.The results of a number of empirical studies, such as Reinganum (1981), Lakonishok and Shapiro (1986), Fama and French (1992), Jagadeesh (1992), Yang and Donghui (2007), Nikolaos (2009) and Zubairi and Farooq (2011), provide that the relationship between beta and expected rate of return is not always significant.Fama and French (2004) state that empirical work since the late 1970s has challenged the validity of the prediction made by CAPM.Specifically, evidence mounts that much of the variation in expected return is unrelated to market beta.However, Vosilov and Bergström (2010) report that beta is a proper predictor of rate of return.Despite the mixed research results, practitioners continue to use the model for portfolio construction, investment decisions and measuring asset rates of return and cost of capital.A survey of a thousand financial directors of American firms which is made on a regular basis by Duke University and CFO Magazine shows that in 2008 and 2009 nearly 75% of respondents used CAPM in the construction of asset valuations (Graham & Harvey, 2009).
The present paper contributes to the literature on the subject as it represents a primary investigation in at least two respects.While there is substantial evidence about this relationship for developed countries, there is little evidence for developing economies with relatively immature stock markets and potentially unique transmission mechanism mediating real activities and monetary policies.
One of the most important assumptions when making beta estimates is that the security is traded frequently.This assumption cannot be assumed in Bahrain, as it has what must be described as an emerging stock exchange which characterized by non-synchronous trading or thin trading.That is to say, not every security is traded every day.Estimating beta using the index model (Equation, 1) in the presence of non-synchronous trading leads to biased estimates of beta.To overcome this problem, several estimation procedures have been developed, but there is no consensus about which procedure leads to unbiased beta estimates.Hence, the issue that should be resolved is: (3) What is the best estimation procedure to control for non-synchronous trading on the Bahrain Bourse?
Evidence relating to the procedures for controlling for thin trading are not conclusive (Dimson & March, 1983;Berglund et al., 1989;Bartholdy & Riding, 1994;Louma et al., 1994).Bartholdy and Riding (1994) use a monthly return interval with an estimation period of five years in New Zealand and report no significant difference between the various control methods.
Estimation of beta requires information about the market index.However, there is no clear definition of this index.The Capital Asset Pricing Model specifies the index as a value weighted market index containing all risky assets.The only market index available for the Bahrain Bourse is the All-Share Index.It contains 39 value weighted stocks.This index has several problems, including the fact that a large number of companies included in the index are thinly traded and a few companies dominate the index.These problems might indicate that the Bahrain Index does not represent the overall market.Therefore, the use of this index might not be appropriate for estimating beta.An alternative might be a price index (Dow Jones method) consisting of stocks trading on most trading days.This leads to next issue that should be addressed which is: (4) Which index should be used to estimate beta?
Another important assumption about beta estimates is that it is stationary, or constant over time.Violation of this assumption will limit the use of beta estimates as a measure of systematic risk.Blume (1971) found that beta estimates do not appear to be constant over time.His results show that the value of beta estimated using the market model is related to the previous period.He suggested a correction procedure which is based on a crosssection regression from one period to the next.The estimated regression equation is then used to adjust the betas for the next period.The results of Vasikcek (1973) lend further support to those reported by Blume (1971), However, he suggested another correction procedure.As the estimation of the index is crucial to the estimation of beta, the issue that should be considered is: (5) Are betas constant over time?Therefore, the estimation methodology used to estimate betas should address the above mentioned five problems.

Data and Methodology
The data used in addressing the five problems identified in the previous section is collected from various issues of local newspapers over the period between January 1990 andDecember 2003 (inclusive).For a stock to qualify for inclusion in the sample it is required to have prices available for fourteen years from 2007 through 2011.A total of 35 companies were included.
The optimal return interval (issue number (1) above) is addressed using three return frequencies: for each stock daily, weekly and monthly returns adjusted for splits, dividends and rights issues were calculated.For the issue of the optimal length of the estimation period (issue number (2) above) three different estimation periods are used.These involve monthly returns from January 2007 to June 2009, five years of monthly returns from January 2007 to December 2011, and three years of monthly returns from January 2008 to December 2011.For each period betas were estimated using daily, weekly and monthly rates of return.The market proxy used is the Bahrain Bourse All-Share Index.
Issue number (3) is concerned with the optimal procedure to control for thin trading.The following estimation techniques are used: The abbreviations used are as defined for Equation (1).Scholes-Williams (1977).Scholes and Williams (1977) addressed the issue of thin trading and then recommended the following correction method: (2) Where β -1 : OLS beta with the return on the market index lagged one period.
β 0 : OLS beta with the contemporaneous return of the market index.
β +1 : OLS beta with the return on the market index leading one period.ρ: First order autocorrelation coefficient of the return on the market.

Beta Based on Rates of Return Adjusted for Thin Trading
Bahrain Bourse is characterized by non-synchronous and infrequent trading of many stocks.Many studies have pointed out that thin (or infrequent) trading can generate spurious serial correlation in stock return and seriously bias the outcomes of empirical tests for market efficiency (Lo & MacKinlay, 1990;Stoll & Whaley, 1990;Miller et al., 1994).To deal with this problem, the methodology proposed by Miller et al. (1994) is employed.These authors suggested an adjustment based on the estimation of a moving average model which reflects the number of non-trading days.However, due to difficulties in determining the non-trading days, Miller et al. (1994) show that an AR(1) model can be used instead.Specifically, the model can be stated in the following equations: (3) Then, using the residuals from Equation (3), adjusted returns are computed as follows: (4)

Where
is the adjusted return for thin trading at time t.All tests are conducted with both observed and corrected data.

The Length of Estimation Period
It has been argued that an estimation period of four to five years is an appropriate trade-off between the number of observations and the stability of the beta estimate when dealing with monthly data (Brailsford et al., 1997).However, for the sample used in this research, 39 companies have consistent data over six years, and therefore, subsequent analysis adopts a six-year estimation period and the analysis uses the logarithm of monthly returns (log monthly returns).
The three different estimation periods, involving log monthly returns from January 2007 to June 2009, from January 2007 to December 2011 (five years), and from January 2008 to December 2011 (three years), are used.For each period betas are estimated using daily, weekly and monthly rates of return.The market proxy used is the Bahrain Bourse All-Share Index.
Tables 1, 2 and 4 show regular bets betas, betas adjusted for thin trading and Scholes-Williams betas from the three different estimation periods for monthly rates of return.It can be seen from the tables that the differences in beta estimation are small.Analysis of variance is used to test the null hypothesis that states beta is stable over time.The results indicate that F-statistics are 1.237, 0.33 and 0.724, for regular betas, betas adjusted for thin trading and Scholes-Williams betas, respectively.The F-statistics indicate that the null hypothesis cannot be rejected at a five per cent level of significance.These results further support the use of beta by practitioners in estimating the cost of capital, capital budgeting and valuing companies, among other decisions.

Rate of Return Intervals
Practitioners use different return intervals for estimating betas.It is not customary to use daily rates of return.
There is a consensus among practitioners to use weekly or monthly figures.To test the effect of rate of return interval on the estimates, betas of the sample companies are estimated using daily, weekly and monthly rates of return.These estimates were made for the whole period, and the All-Share Index is used as the market proxy.
Table 3 presents the estimated betas (regular betas, betas that are based on the rates of return adjusted for thin trading and Scholes-Williams betas) using monthly rates of return.Analysis of variance is used to test the sensitivity of estimated betas to rate of return intervals.The F-statistics obtained are 0.564, 0.287 and 0.236 for regular betas, betas adjusted that are based on rates of return adjusted for thin trading and Scholes-Williams betas, respectively.These statistics are not significant at the five per cent level, which indicates that the null hypothesis (H 0 : Beta daily = Beta weekly = Beta monthly ) cannot be rejected.These results are true regardless of the procedure used to estimate betas.

Thin Trading Effect
Table 4 shows the estimates for three types of beta, namely regular beta, beta based on returns after adjusting them for thin trading of the 39 companies and the difference between the mean betas for the whole period (that is 2007-2011).It is evident from the table that there is not much difference between the betas obtained from the three procedures used.The estimated betas of the sample are all positive, with exception of four companies that have negative betas.Alahli United Banks (AUB) has the highest beta, while Bahrain Middle East Bank had the lowest positive estimated beta.Furthermore, the most frequently traded stocks have upward biased OLS beta estimates, and this is consistent with the findings of Dimson (1979).
The Table 2 shows the significance level for the two-sample t-test run for the three different returns.The tests at the five per cent significance level indicate high p-values, and, therefore, the null hypothesis (H 0 : Beta regular = Beta SW = Beta adjusted for thin trading) cannot be rejected.The results show that for most companies, the estimated regular betas are higher than those of thin trading betas, while betas sw are higher than the regular and thin trading betas.The results show that H 0 cannot be rejected for the mean difference between the estimated regular betas and those estimated after adjusting returns for thin trading.However, the null hypotheses of no significant differences between the regular beta and beta SW and between thin trading beta and beta SW are rejected at the per cent significance level.These results indicate that the variations in beta estimates are substantial.

The Effect of Using Different Market Proxies on Estimated Betas
For all methods of estimating betas using the market model, the independent variable is market rate of return.However, the magnitude of the independent variable depends on the market proxies.Two market proxies are used to measure the impact of the independent variable on the estimated betas.These are the Bahrain All-Share Index calculated by Bahrain Bourse and the Bahrain Index calculated by Morgan Stanley (MSCI).To test the null hypotheses, beta was estimated for the sample companies using the whole sample period and the Bahrain Index (MCSI) as the independent variable.The results are compared with those reported in Table 5.The estimated betas of the sample companies using MSCI as the market proxy are shown in Table 2.The results are based on the daily rates of return.A t-test was used to test the sensitivity of estimated betas to the market proxy used in the market model.The estimated betas were compared using the three procedures, namely regular betas, betas that are based on rates of return adjusted for thin trading and Scholes-Williams.The results provide evidence in support of the null hypothesis which states that the betas estimated using the All-Share Index and MSCI are not significantly different from each other at the five per cent significance level.However, the results may not be generalized because only two market proxies are used in the analysis.

The Effect of Seasonality
A considerable body of research provides evidence suggesting that beta is not the only factor that affects the pricing of returns on securities, but that there are also seasonal and firm size effects.It has been noted that seasonality is an explanatory factor of risk-adjusted returns.Brailsford et al. (1997) provide examples of large returns in January and low returns on Mondays and Tuesdays.
To remove the seasonality effect, it is customary to include dummy variables in the ordinary least squares (OLS) regression.Draper and Paudyal (1995) found that UK stock betas have day of the week or day of the month effects when using weekly or monthly observation, respectively.They also noted that the variation in the estimates is often statistically significant and that estimates from weekly returns calculated on Monday or at the end of the month were significantly different from those derived for other days of the week or selected days of the month.The results reported by Asamoah and Quartey-Papafio (2011) lend further support to the findings of Draper and Paudyal (1995).They found that estimated betas are sensitive to the day-of-the-week effect.To test the seasonality effect, betas were estimated for the sample companies using weekly rates of return with the purpose of testing the following null hypothesis: Beta Sunday = Beta Monday = Beta Tuesday = Beta Wednesday = Beta Tursday The estimated betas using weekly rate of returns are shown in Tables 6 to 10. Analysis of variance (ANOVA) is used to test the null hypothesis that estimated betas are not affected by the-day-of-the-effect, while a t-test is used to test the null hypothesis that there is no significant difference between each pair of days of the week.The results of these tests are reported in Table 6 to 10.The evidence shown indicates that the null hypotheses cannot be rejected at the five per cent level of significance.

Conclusion
Ever since the seminal work by Markowitz (1959) beta has occupied center stage in both risk management and risk measurement.The parameter beta is used in finance in the form of the market model to estimate systematic risk, which risk determines the rate of return of individual stocks and portfolios.Although such betas are assumed to be time invariant, considerable evidence shows that beta risk is not constant over time.This violates one of the important assumptions on which its use depends.Beta estimation has traditionally been obtained by running a single regression model in which the rate of return of a company's stock as the dependent variable and the market rate of return is the independent variable.The beta of a stock is important in a variety of contexts, such as the determination of the cost of capital, project evaluation, a company's valuation in asset pricing theory and hedging using index derivatives.
The aim of the present study is to consider the effects of various issues on the estimated betas of companies listed on the Bahrain Bourse.Those issues are 1) the length of the estimated period, 2) the effect of the period of returns (daily, weekly and monthly) 3) the effect of the market proxy, 4) the effect of thin trading and 5) the effect of seasonality represented by the day of the week effect.
The results show that, 1) using three different time periods to estimate betas, that those estimates are not sensitive to the length of period used; 2) the betas estimated using daily, monthly or weekly returns are not significantly different; 3) betas estimated using the All-Share Index and MCSI are not significantly different from each other; 4) estimated betas are not sensitive to the day-of-the-week effect.Finally, stocks listed on the Bahrain Bourse are thinly traded and hence the impact of this characteristic on estimated betas was examined.It is found that the impact of thin trading on beta depends on the method used to account for thin trading.

Table 1 .
Comparison of estimated betas (regular beta, thin-trading, sholes-williams) with all-share Index for Bahrain bourse as market proxy (using daily rate of return) for the period from January 2007 to June 2009 Note.*** Significant at 0.001, **Significant at 0.05, *Significant at 0.10.

Table 2 .
Comparison of estimated betas (Regular beta, Thin-trading, Sholes-Williams) with all-share index for Bahrain Bourse as market proxy (using daily rate of return) for the period from July 2009 to December 2011

Table 3 .
Comparison of estimated betas (Regular beta, Thin-trading, Sholes-Williams) with all-share index for Bahrain Bourse as market proxy (using monthly rate of return)

Table 4 .
Comparison of estimated betas (Regular beta, Thin-trading, Sholes-Williams) with Bahrain Bourse all shares-index as market proxy (using daily rate of return)

Table 5 .
Comparison of estimated betas (Regular beta, Thin-trading, Sholes-Williams) with MSCI index for Bahrain Bourse as market proxy (using daily rate of return) Note.*** Significant at 0.001, **Significant at 0.05, *Significant at 0.10.

Table 6 .
Comparison of estimated betas (Regular beta, Thin-trading, Sholes-Williams) with All-Share Index for Bahrain Bourse as market proxy (using weekly rate of return) and weekly rate of return-Sunday

Table 7 .
Comparison of estimated betas (Regular beta, Thin-trading, Sholes-Williams) with all-share index for Bahrain Bourse as market proxy (using weekly rate of return) and weekly rate of return-Monday

Table 8 .
Comparison of estimated betas (Regular beta, Thin-trading, Sholes-Williams) with all-share index for Bahrain Bourse as market proxy (using weekly rate of return) and weekly rate of return-Tuesday *** Significant at 0.001, **Significant at 0.05, *Significant at 0.10.

Table 9 .
Comparison of estimated betas (Regular beta, Thin-trading, Sholes-Williams) with All-Share Index for Bahrain Bourse as market proxy (using weekly rate of return) and weekly rate of return-Wednesday

Table 10 .
Comparison of estimated betas (Regular beta, Thin-trading, Sholes-Williams) with all-share index for Bahrain Bourse as market proxy (using weekly rate of return) and weekly rate of return-Thursday Note.*** Significant at 0.001, **Significant at 0.05, *Significant at 0.10.