The Role of Size and Book-to-Market Ratio as Proxies for ...
the size and book-to-market EFFECTS AND THEIR ROLE AS RISK
PROXIES in the istanbul stock exchange
Mine H. Aksu
Sabanci University, Istanbul, Turkey
Turkan Onder
Marmara University, Istanbul, Turkey
* We would like to thank the session participants at the EFMA 2000 (Athens) meeting for their comments and suggestions, Dr. George Frankfurter for his useful criticisms and invaluable suggestions, Dr. Hakan Orbay for the risk- free return data, and Olga Bilir of Koc University and Tayfun Keskin of Sabanci University for their competent research assistantships.
Correspondence to: Mine H. Aksu, Graduate School of Business, Sabanci University, Orhanli, 81474 Tuzla, Istanbul, Turkey. Phone: +90 (216)483-9678; Fax: +90 (216)483-9699
e-mail: maksu@sabanciuniv.edu
the size and book-to-market EFFECTS AND THEIR ROLE AS RISK
PROXIES in the istanbul stock exchange
Abstract
In this paper, we explore the relationship of size and book-to-market ratio with stok returns and with firm-specific and macro-economic fundamentals in the Istanbul Stock Exchange (ISE). We apply two different asset pricing models, the one factor CAPM and the three-factor Fama and French model, to individual security returns and to size/book-to-market sorted portfolios. We find both size and book-to-market effects to be significant, but the former has a higher explanatory power. We also evaluate the firm-specific risk and return characteristics of our extreme portfolios in different states of the Turkish economy and look at the relationship between the Fama and French factors and macro-economic indicators. Our results reveal some new empirical regularities in the ISE and support the Fama and French findings to justify models for additional risk factors in returns.
132 words
Key words: beta, size, book-to-market ratio, emerging markets, asset-pricing, Istanbul Stock Exchange.
JEL classification: G12, G14, G15
1. Introduction
This paper examines the size and book-to-market effects on stock returns and their rational risk explanation in the emerging market of the Istanbul Stock Exchange (ISE). A large body of literature has documented predictable patterns in stock returns that challenge the validity of the EMH/ CAPM (Efficient Markets Hypothesis/Capital Asset pricing Model) paradigm. These studies have found that, alongside market beta, average stock returns in the U.S. are related to earnings/price (E/P) (Basu, 1983), leverage (Bhandari, 1988), past sales growth (Lakonishok et al., 1994), size [market value of equity (ME)] (Banz, 1981), and book-to-market equity (BE/ME) (Rosenberg et al., 1985). Among these variables, size and BE/ME have been found to be the most significant in explaining the cross-section of average returns and to subsume the roles of most other variables, including market beta (Fama and French 1993, 1996; Kothari and Shanken, 1997; Pontiff and Schall, 1998).[i] Given this predictive power, researchers have reported evidence from the US and other developed markets that small capitalization, high BE/ME “value” stocks earn higher returns than high priced “glamour” stocks. For example, Fama and French (henceforth FF) (1998) report significant value effects in the major Europen, Australian and the Far East markets; Arshanapalli et al.(1998) find size and value effects in 18 global markets; and Elfakhani, et al.(1998) report a significant size and a BE/ME effect but no market- beta effect in Canada.
The primary purpose of this paper is to examine whether there is a size and BE/ME effect on returns in the ISE. To the extent that emerging markets (EMs) are not integrated with developed markets, they provide independent out-of-sample tests to study such anomalous return patterns and the economics driving them. However, most studies on EM returns have used multi-country samples dominated by larger EMs (see for example, FF, 1998 and Arshanapalli et al., 1998). Such large-scale studies have the advantage of using large sample sizes. However, they yield mixed results as a result of the sample countries’ differences in terms of the size, liberalization, and efficiency of their markets and institutions, political and economic risk exposure, average market capitalization, investor characteristics, and reporting environments.[ii] Thus the study of solely the ISE data is for the sake of holding constant these country-specific characteristics that are expected to affect the returns and the risk factors. Although the ISE is one of the fastest growing emerging markets, little is known about its empirical regularities.[iii] This paper attempts to fill a part of this gap.
The second related issue investigated in the paper is the ongoing controversy about the economic rationale behind these return anomalies. Following the earlier Chan and Chen(1991) and FF(1992, 1993) studies, a number of papers have argued that, in line with rational asset pricing, size and BE/ME proxy for additional non-diversifiable risk factors, such as that of relative financial distress. Consistent with the “fundamental risk” explanation, FF(1993) developed a popular three-factor asset pricing model which relates the expected return on a portfolio in excess of the risk-free rate to two other common risk factors alongside the excess return on a market portfolio: a return premium related to small size (SMB) and a return premium related to high book-to-market ratio (HML). The model predicts that firms with smaller market capitalization (high book-to-market) will tend to have positive slopes on the size (book-to-market) premium and hence have higher average returns as compensation for bearing the extra risk. Pro and contra empirical evidence on developed markets has started to abound. Using data on 10 and 18 developed markets, respectively, Liew and Vassalou(2000) and Kelly (2003) find that HML and SMB contain information that capture, respectively, future growth in the economy and both future growth and unexpected inflation. Doukas et al.(2003) report higher analysts’ earnings forecast errors, their proxy for the risk of investor ambiguity, in smaller and high BE/MVE firms. Petkova and Zhang (2003) document that value (and small) stocks are riskier than growth (and big) stocks in bad times when expected risk premium is high. However, Peevey et al.(1993) has found that distressed firms do not have higher returns than healthy firms. Knez and Ready(1997) and Downs and Ingram(2000) document that the risk premium on size disappears when the return outliers, are eliminated.
Another challenge to the risk-based explanation for these two anomalies has come from a behavioral line of financial research based on psychological biases of investors which suggests that these anomalies are the result of market irrationality leading to over or under-reaction to long-term or short-term past information (see, for example, DeBondt and Thaler, 1985; Lakonishok et al., 1994; Richards, 1997). In support of the mispricing story, Daniel and Titman(1997) and Daniel et al.(2001) posit that there is a stronger relation between expected returns and the book-to-market characteristic than between expected returns and the loadings in the FF three-factor model, both in the U.S. and in Japan. The anomalous-signed negative book-to-market effect observed in German stocks during the 1881-1913 period also support their mispricing results (Bossaerts and Fohlin, 2000). However, Chan(1988) reports that the overreaction effect disappears if the regressions are estimated with CAPM betas from the period in which reversals occur; FF (1996) finds that their three-factor model captures this reversal of prior returns; and Lewellen(1999) provides time-series evidence that after controlling for risk, he finds that book-to-market equity provides no incremental information about expected returns.
Accordingly, the second objective of the paper is to investigate whether size and book-to-market factors are proxies for firm-specific and/or macroeconomic risk in the ISE. We believe that the ISE is a suitable market to test the size and book-to-market effects and their rational risk explanation. First, it is still not fully integrated with the world markets, is in a stage of institutional development, and the stock market doesn’t yet play a major role in financing so that it is less likely for the market participants to have learned and arbitraged out a possible size/book-to-market anomaly. Recent research has found that most of the anomalies have weakened or disappeared in the developed markets after the papers that initially discovered them were published and practitioners started to implement such strategies to “beat the market” (see for example, Dimson and Marsh, 1999 and Schwert, 2002). Second, there are very few institutional investors that are expected to enhance market efficiency. Finally, there has been a lot of country-specific political and economic instability leading to frequent market upturns and downturns most of which are not caused by common information flows among world markets. Thus, we expect to observe positive HML and SMB risk premiums and positive loadings on these additional risk factors, especially during economic downturns. Furthermore, we expect BE/ME to be an understated proxy for an ISE firm’s true financial distress risk due to the use of historical cost accounting in a chronically inflationary environment that renders book values meaningless, especially for firms that have older asset bases.[iv] Hence, we expect size to be a more robust proxy for risk in the ISE.
We use both portfolio based and individual security based asset-pricing tests to address the concerns of Berk(2000) and Ferson et al.(1999) related to the econometric pitfalls of running tests on only attribute-sorted portfolios. The latter authors also posit that it is incumbent on the researcher to relate the attributes to explicit risk factors. Accordingly, we directly examine the relation between the risk proxies used here and micro and macro fundamentals. We can be more confident that the over-performance of the small and value portfolios is because of higher risk born by investors, rather than mispricing if: i) we observe both higher returns and higher risk in these small and value portfolios; ii) these firms are entrenched in their portfolios over the years; iii) they perform worse in economic downturns; and iv) if the risk premiums are related to macro-economic fundamentals and the loadings on the premiums are more significant in bad states.
In our portfolio-based analysis, we examine the average monthly returns to portfolios sorted on size and BE/ME. We find that small (high book-to-market) firms indeed have higher average returns except in the year 1997 (1996). A market-risk adjusted ranking of portfolio performance based on Sharpe ratios also confirms the existence of a size and book-to-market effect in the ISE. To test the risk-proxy explanation of the size and the book-to-market effects, we evaluate some leverage and profitability ratios of stocks that fall into these ranked portfolios. Consistent with most prior research, we find that larger and low book-to-market firms are indeed more profitable and big firms have lower leverage than small firms. However, we also find that firms with lower BE/ME use more debt than high book-to-market firms, a finding inconsistent with the risk explanation. We conclude that, overall, size seems to be a better overall predictor of firm-specific financial distress risk in the ISE. We also evaluate the turnover rate in our extreme size/book-to-market portfolios and examine how these portfolios fare in economic downturns and booms. [v]
We apply both the one-factor CAPM and the three-factor FF(1993) asset-pricing models to average monthly excess returns, on both portfolio and individual firm level. We find the highest explanatory power for the market premium, followed by the size premium. While the factor loadings are robust for the market and size premiums, they seem to vary under different economic conditions for the book-to-market factor. In regressions of excess returns to the 16 size-BE/ME sorted portfolios against the risk factors, we find that high BE/ME portfolios have the highest and the most significant coefficients on HML regardless of their sizes while low BE/ME portfolios consistently have insignificant or negative coefficients. A similar regularity holds in small size portfolios. Overall, our evidence is consistent with our expectations and the findings for other markets except that the size effect seems to be more robust than the BE/ME effect in the ISE.
The rest of the paper is organized as follows. Section two reviews prior research in some EMs and in the ISE. Section three discusses the data, sample selection, the design of the size/book-to-market sorted portfolios on which most of our analyses are conducted, and the one factor and the 3-factor asset pricing models used in our analysis. In section four, we describe the characteristics of our sample over the sample period and then provide evidence of a robust beta and a size effect and a weaker book-to-market equity effect in the ISE. We then investigate if these two attributes are related to firm-specific and macro-economic fundamentals. A summary and some concluding remarks are presented in the final section.
2. Prior research on ISE and other emerging markets
Researchers and investors are also interested in marginal and understudied markets in which more than half of global trading takes place. As noted in Bruner et al.(2002), investment flows to EMs will continue to grow since their economies grow at higher rates than developed countries and they account for a higher percentage of the world population, land mass and natural resources. In addition to providing higher returns as a result of their riskier environments, the EMs provide investors two other distinct benefits. They provide ample opportunities for diversification because of their low or negative correlations with each other and with the developed markets. For example, the correlations between the U.S. markets and the stock markets in Peru, Turkey and Venezuela have been negative during the 1991-1995 period (Khanna, 1996). Another attraction, as Goetzmann et al.(2001) suggests, is the enhancement of the investors’ opportunity set in periods of free capital flows during which return correlations increase.[vi] Aided by recent improvements in the quality of available data, EMs also provide researchers independent samples to study asset pricing and predictability issues.
The EM evidence, so far, is mixed. While Claressens et al.(1995) find limited evidence of a small firm effect in 19 emerging markets, FF(1998) report a premium for both small and value stocks in 16 emerging markets. Corhay and Rad(1993) find that although the size effect is significant in Dutch firms, its significance is reduced when the return interval is increased. However, for the same stock market, Doeswijk(1997) finds an insignificant size effect. Herrera and Lockwood(1994) document a small firm effect and a market beta effect for Mexican firms. Chui and Wei(1998) find a weak relationship between average stock returns and beta in five Pasific-Basin emerging markets. BE/ME is the only explanatory variable in Hong Kong, Korea, and Malaysia while size effect is significant in all markets except Taiwan. In Korea, annual stock returns have been positively related to book-to-market equity, and negatively to firm size (Mukherji et al., 1997). Wong(1989) reports a size effect in the Singapore Stock Exchange. Rouwenhorst(1999) reports that when averaged across all 20 emerging markets, stocks exhibit momentum; small stocks outperform large stocks; and value stocks outperform growth stocks. More recently, using aggregate data for 35 emerging markets over a 15 year period, absolute and relative size and value measures, parametric and non-parametric tests based on portfolio returns and cross-sectional regressions, Barry et al.(2001) find evidence of a strong book-to-market effect and mixed evidence for a size effect. Recent evidence shows that the profitability of value investing holds at the country level as well. Kouwenberg and Salomons (2004) document that countries with high average BE/ME ratios significantly outperform those with low ratios.
The studies that link these anomalous return patterns with the global and local risk factors have been scarce in EMs. Even though Rouwenhorst (1999) was not been able to explain the value premium with global risk factors, very few studies (see Bilson et al., 2001 and Kouwenberg and Salomons, 2004) have, so far, attempted to relate EM returns to local macroeconomic factors, which might be better proxies for local non-diversifiable risk. This paper attempts to fill a part of this void in literature as well.
So far, little is known about the price determination process in the ISE. Using the IFC Emerging Markets Database (EMDB), Rouwenhorst(1999) report that high E/P and high BE/ME stocks outperform those with lower ratios but has found no size, market beta or momentum effects during the 1989-1997 period. However, the findings based on this database may be biased due to its shortcomings noted by the author himself: missing data, data errors, and return outliers that range from zero entries for insignificant returns to 100,000% per month. Furthermore, the IFC database is biased toward larger stocks, which reduces power as one searches for a size effect. The empirical studies that directly use the ISE database also report conflicting results. Karan(1995) reports that low P/E portfolios overperform high P/E ones during the 1988-1993 period. Karan(1996) also finds evidence of a price/sales (P/S), P/E, and ME/BE effect during the same time period and that the P/E effect absorbs the P/S and ME/BE effects. Demir et al.(1996) document that the average returns to low P/E portfolios are greater than those of high P/E portfolios during the period 1990-1996, but the difference disappears when risk-adjusted returns are used. They also report a significant size effect and a negative earnings effect. In contrast, using value-weighted portfolio returns, which biases the results against small firms, Gonenc and Karan(2001) find that growth stocks and big stocks outperform small, value stocks, and that they both perform worse than the local market index. Evidently, the same debate over market anomalies prevails in the research on ISE.
Unlike previous studies on ISE, this study employs two common asset pricing tests on both ranked size/book-to-market portfolio returns and monthly excess returns on individual securities and for the first time tries to link the size and book-to-market factors with both firm-specific and macroeconomic fundamentals.
3. Sample selection, design, and method of analysis:
3.1. Data Sources
Consistent with prior research, the sample includes only non-financial firms that traded in the ISE during the 1993-2001 period. The sample size increases from 106 firms in 1993 to 206 firms in 2001. Since the sample period involved numerous economic and political upturns and downturs, it is suitable for examining the relative explanatory power of the return factors and determine whether they are risk proxies. Monthly stock returns, adjusted for dividends and splits, the National 100-market index (ISE-100) returns and the firm-specific financial data are obtained from the electronic ISE database for listed companies. The macroeconomic indicators and government bond-rates, used as a proxy for the risk-free rate, are obtained from the Central Bank electronic database.
3.2. Portfolio Formation
To be included in a portfolio, a firm must be trading in the ISE both in Decembert-1 and in Junet and it must have a fiscal year end of December 31. The number of firms that meet these data requirements ranges from 106 in 1993 to 173 in 1998. Size (ME) is measured as the stock’s price times the number of shares outstanding as of June 30t. Size portfolios are formed on June 30t to prevent the look-ahead bias.[vii] Hence, a period of six months, from December 31t-1 to June 30t, is arbitrarily determined as sufficient for the market to react to any new information in the annual reports. We use the December 31t-1 values of equity to calculate the BE/ME ratios for year t. To summarize, monthly stock returns are calculated from July 1t to June 30t+1, for portfolios based on December 31t-1 BE/ME values and June 30t sizes.
We replicate the FF(1993) design in the construction of the six size/book-to-market portfolios from which we form the SMB and HML portfolios that mimic the additional risk factors related to size and book-to-market equity. Negative book-equity firms are excluded from the portfolios consistent with prior research.[viii] The stocks in the sample are first sorted each year from smallest to largest in terms of market capitalization. They are then allocated to two groups, small (S) and big (B), using the median market equity for the ISE stocks as the breakpoint. All firms are then independently sorted, again each year, into three book-to-market equity partitions designated as low (L), medium (M), and high (H). The BE/ME partitioning is based on the breakpoints for the bottom 30%, middle 40%, and the top 30% of the BE/ME values for the ISE stocks. From the intersections of the two size and three BE/ME partitions, we form the six size/book-to-market equity portfolios: S/L, S/M, S/H, B/L, B/M, and B/H. For each of the six portfolios, equally weighted average monthly returns are calculated from July 1 of year t to June 30 of year t+1. We use equal weights not to give more weight to big and low book-to-market firms and thus maximize power, as there is a very big size difference between the small and the large firms in the ISE. As we rebalance the portfolios each year, we also examine the turnover of stocks in the most extreme portfolios.
Finally, to determine whether SMB and HML indeed capture common factors in returns related to size and book-to-market equity, we also construct 16 size/book-to-market sorted portfolios and regress their excess returns against the three risk factors. Here, we use a sequential rather than an independent sort to avoid the inevitable smaller sample sizes when one tries to form 16 independently sorted portfolios using the two factors. We first sort the sample firms into four size groups form smallest to largest (S1 to S4). Each size group is then ranked into four partitions according to their book-to-market ratios from lowest to highest (BM1 to BM4) to finally form the 16 portfolios ranked first on size then on book-to-market (S1/BM1, S1/BM2,…, S4/BM3, S4/BM4). We again rebalance the portfolios each year. We evaluate the firm-specific risk profiles and the average excess returns in these 16 portfolios and determine their risk-adjusted performance by using Sharpe ratios. We finally examine how the most extreme portfolios, portfolios 4 and 13, fare in economic upturns and downturns.
3.3. The CAPM and the three- factor FF(1993) model:
The one-factor CAPM model is estimated by the following simple linear time-series regressions of the monthly average excess returns to a portfolio of stocks, Ri-Rf , against monthly excess market returns, Rm-Rf ,
both measured from July 1t to June 30t+1 each year:
Ri - Rf = αi + βi (Rm - Rf) + (i (1)
where, the excess monthly returns are assumed to be independently and identically distributed (IID) through time and jointly multivariate normal. The same distributional assumptions hold for (i which is an estimate of the non-systematic risk in the context of the CAPM and we also assume that the E ((i ) = 0 and variance ((i ) = σ2(.[ix] We use the ISE-100 Index as the proxy for Rm, the market return, and the monthly government bond rates as the proxy for Rf, the monthly risk-free rate. These rates have been very high as a result of the government’s domestic funding requirements caused by the big budget deficits and paucity of foreign credit and they have . been the major culprit of the high inflation rates of 50%-100% over the sample period. For example, the average monthly treasury-bond rate between 6/1/1991 and 10 /1/1997 has been 6.2% with a standard deviation of 1.6%..Using actual prices from the secondary government bond market, we use the effective rate for the bond whose term best approximates the relevant return month. The slope of the regression line, βi , is then the sensitivity of the average monthly excess returns to the variation in the market premium.
We also estimate the following three-factor asset- pricing model of FF (1993) under the same set of assumptions in a multivariate setting:
Ri - Rf = αi + βi (Rm - Rf) + si (SMB) + hi (HML) + (i (2)
The additional factors, SMB and HML are formed from the 6 size/book-to-market portfolios described above. SMB is measured each month as the difference between the simple average return on the three small size stock portfolios, S/L, S/M, and S/H, and the simple average return on the three big size stock portfolios, B/L, B/M, and B/H. Similarly, HML is measured as the difference between the simple average return on the two high book-to-market equity portfolios, S/H and B/H, and that of the two low book-to-market equity portfolios, S/L and B/L. Hence, the return differences due to size and BE/ME are free of the effect of each other by construction. The coefficients are the loadings of the monthly excess returns on the three risk-premia. We expect more significant loadings, closer to zero intercepts, and a higher adjusted R2 metric in the better-specified model.
We use two levels of aggregation for the excess returns to be tested as in Griffin’s (2002) analysis of country specific and global FF factors. In the first specification, we use the time-series of monthly average excess returns to individual stocks as the dependent variable to address Berk’s (2000) concern that the use of portfolios sorted on the basis of an empirical regularity may lead to Type I errors in asset-pricing tests. He suggests testing without sorting into groups. Accordingly, we regress the average monthly excess returns of all stocks in the sample from July 1993 to Dec 2001 against the market premium in the one-factor CAPM model and against the market, SMB and HML premiums in the FF 3-factor model. In the second specification, the dependent variable is the monthly average excess returns to each of the 16 size and BE/ME sorted portfolios and we expect positive and significant loadings in the smaller and higher BE/ME portfolios.
4. Results
4.1. Sample characteristics
We first examine the summary statistics for the market and accounting based fundamentals of the ISE firms during the sample period. Our aim is both to describe the average financial profiles of the ISE firms and to get a feel of whether the recurrent boom and bust cycles are reflected in their financial profiles. The Turksih economy has gone through three boom and three bust cycles in our short sample period: the financial crisis and a sizable devaluation at the begining of 1994; the initial contagion effects of the Asian and Russian crises in 1997/1998; and finally, the sudden flee of foreign capital, ensuing financial and political crisis, and the economic stagnation in early 2001. The relative upturn in the economy during the short periods in between are considered to be the boom periods. The reader is referred to Akyuz and Boratav (2001), Boratav and Yeldan (2001) and Alper and Onis (2002) for a more in debth analysis of the financial, political, and economic sources of these crises. For each year t, we calculate the mean, median and standard deviation of leverage [total liabilities/total assets (TL/TA)], return on assets [operating income/total assets (OI/TA)], earnings per share (EPS), P/E, ME and BE/ME as of December 31t-1. The distributions are right-skewed, especially for the latter four ratios for which the medians are considered a more useful statistic.
The sample firms’ average leverage is around 0.5 throughout the sample period and the highest ratios are observed in 1993. 1994, 1998, and 2000, the years of high financial and economic uncertainty in Turkey. The two profitability ratios are measured in millions of US$. The mean and median OI/TA decreases from 1995 onwards and assumes its lowest values again in the 1993 and after 1998. Similarly, the mean and the median EPS decreases monotonically starting in 1995, parallel to the depreciation of the Turkish Lira and the increase in the number of shares outstanding. Leverage and profitability ratios have the highest standard deviations during the financial crisis years of 1993 and 1994. The median P/E ratio, which reflects market’s perception of future prospects of the ISE firms, increases from an average annual median value of 9.2 to 10.51 in 1998 and further to 19.2 in 2000, reflecting the decline in profitability and the extent of overvaluation in relation to fundamentals.
In general, ISE firms are smaller than the firms in developed markets in terms of market capitalization. For example, in 1995, sample ISE firms had a total market cap of $20.78 billion which corresponds to 1.1 % of the total EM and 0.12 % of the total world market capitalization. The average (median) sample capitalization of $200 (42) million is consistent with that of $139 million observed by Rouwenhorst (1999) for the period 1989-1997. The sample firms’ mean (median) BE/ME ranges from 0.30 to 1.22 over the sample period, but the medians (0.25 to 0.93) are much lower. The average annual BE/ME ratios of ISE firms in the 1993-1997 period are reported as 0.14, 0.16, 0.37, 0.25, 0.11 in the December, 1999 issue of the IFC Factbook, Monthly Review and these are the lowest values among the 18 EMs covered. This may suggest that the ISE firms are overvalued. However, the low values may also be attributed to the use of the IFC data base which includes only 58 large ISE firms. In our more representative sample, we observe a higher average BE/ME ratio of 0.61, still on the low side. Another reason for the low BE/ME ratios may be the understated book values caused by the use of historical-cost accounting in Turkey’s inflationary environment. This measurement error may have also made it harder for researchers to detect a BE/ME effect in the ISE.
4.2. Size and book-to-market equity effects in ISE returns
This section examines the relation between the returns and size and book-to-market equity in the ISE. We evaluate the returns in our ranked portfolios over the sample period and apply the one-factor and three-factor asset pricing models to both individual and portfolio excess returns.
4.2.1. Porfolio returns and performance:
Table 1 reports the equally-weighted, average monthly local currency returns to the six size and book-to-market equity ranked portfolios, measured from July 1t to June 30t+1 , for each sample year. We evaluate the monthly average returns to our 16 portfolios as well. Since the results are qualitatively the same, they are not reported in the table to save space. Nevertheless, the average % return differences between the small (high BE/ME) and the big (low BE/ME) portfolios are given in parantheses in the discussion below. The average monthly excess returns to these 16 portfolios over the sample period is presented in Table 6, Panel A.
There is a consistent negative relation between size and the average returns in all sample years, except for only the year ’96-’97 in which the three big firm portfolios overperform the three small ones by only 0.1%. The average monthly portfolio returns range from as high as 18.1% (15.3% for the 16 portfolios) for the small portfolio with the highest return to a low of -0.008 % (-0.51% for the 16 portfolios) for the big portfolio with the lowest return over the sample period compared to the monthly average return range of 1.64% to 0.88% for the 12 size portfolios in the FF (1992) sample. The overperformance of our three small portfolios over the three big ones ranges from as low as 1.5% in year 2000-2001 to as high as 18.9% in ’94-’95 and the annual average of the eight-year return differential between these two groups of portfolios is 7.2%.
(Table 2 about here)
Holding size constant, the relationship of BE/ME with returns is not as strong and only in half of the sample years (’95-96, ’96-97, ’97-98, and ’00-01) do the two highest BE/ME portfolios overperform the two lowest BE/ME ones. Nevertheless, the average overperformance of the lowest BE/ME portfolios is only 1.8% over these four years whereas the average overperformance of the highest BE/ME is 5.75% over the rest of the sample period. Furthermore, the annual average monthly return to the highest and lowest BE/ME portfolios with the highest and the lowest returns are, respectively, 17.5% and -0.008 % while the similar monthly average return range for the 12 BE/ME portfolios is only 1.92% to 0.3% in the FF (1992) sample. Finally, the average annual return differential between the highest two and the lowest two BE/ME portfolios is 1.9% over the eight years and the range is from a low of -3% in ’97-98 to a high of 11.2% in ’93-94. An interesting observation is that both the size and the book-to-market effects seem to wane off after ’97-98 at which time the return differentials between big and small and high and low starts to decrease, under the caveat that statistical tests are not carried out to substantiate this contention which is out of the scope of this paper.
On average, small firms and high book-to-market firms have higher standard deviations of monthly returns in the ISE, confirming that they have higher total risk. Accordingly, we also calculate the Sharpe Index, Sharpe’s summary measure of portfolio performance, which adjusts the performance of our 16 portfolios for risk (Fischer and Jordan, 1987):
St = (rt - rf*) / (t (3)
where: St = Sharpe ratio for portfolio t
rt = average return on portfolio t
rf* = riskless rate of interest
(t = standard deviation of the returns to portfolio t (total risk of the portfolio)
Table 2 provides evidence that the smaller portfolios and the portfolios with higher book-to-market ratios overperform the bigger and lower book-to-market portfolios except in column BM3, the portfolio next to the one with the highest BE/ME stocks. When the 16 portfolios are collapsed into four by taking averages of the two small and two big portfolios and the two low and the two high book-to-market portfolios, the average risk-adjusted performance difference between the small and big portfolios is 9.8% for low book-to-market firms and 16.5% for the high book-to-market firms. The corresponding difference between the high and the low book-to-market portfolios is 6.1% for small firms, but -0.006 for big firms. The univariate analyses in Tables 1 and 2 suport a robust size effect and a weaker and not as robust book-to-market effect in the ISE.
(Table 2 about here)
4.2.2. Time-series regressions of the one-factor and the three-factor pricing models:
We then regress the average monthly excess returns, Ri-Rf from July, 1 1993 to December 31, 2001, against the explanatory risk factors Rm-Rf of the one-factor CAPM and the additional risk premiums related to small size and distress, SMB and HML, of the three-factor FF (1993) model. All the three premiums are expected to be positive. As the dependent variable Ri-Rf, we use either the average excess monthly returns on all sample stocks or the excess returns to the 16 portfolios. The average monthly excess returns to be explained by the alternative asset pricing models range from –37% to 42% and their mean and the standard deviation are 2.5% and 16%, respectively, indicating the extreme volatility of the ISE. We regress the monthly excess returns both over the whole sample period and for each year.
In spite of the negative monthly average returns to these portfolios in about half of the 102 month sample period, the mean values of the monthly market, size and distress premiums are still positive (0.84%, 2.31%, and 1.23% per month, respectively), with the lowest premium observed for the market factor. In Table 2 of FF (1993), the average monthly SMB premium is 0.27% while the average HML premium is 0.40% in the U.S., both lower than the ISE premiums. FF (1998) report that the annual value-weighted (equally-weighted) average HML is 16.91% (14.13%) in the 16 EMs they studied. When the sample average monthly excess returns are annualized, the ISE value premium is 14.76%, which is close to the average of the 16 emerging markets. They also report an annual value-weighted average size premium of 14.89% (t=1.69) and an equally-weighted average premium of 8.70% (t=1.98) in these EMs. The ISE has a much higher annualized size premium of 27.7%.
The standard deviations of the monthly risk premiums are very high: 12.4% for the market premium, 8.3% for SMB and 9.2 % for HML. In FF (1996, 1997), the average annual HML premium has the smallest standard deviation while the standard deviation of SMB is the smallest in this study. Hence, only average monthly SMB premium is significantly different from zero, with a t-value of 2.15, while the average HML return has a t-value of 2.60 and is the only significant factor in FF (1996). Hence, while the premium for HML is the closest to present an arbitrage opportunity in the US, the size premium seems to fulfill that role in the ISE.
Table 3 includes the results for the one-factor CAPM model, a two-factor model with either SMB or HML, and the three-factor FF (1993) model regressions on the 52 average monthly excess returns. The intercept values, the coefficients of the explanatory variables, their t-values, and the R2 for the various specifications are presented in the table. When the market factor, SMB, or HML are used as the only regressors, their coefficients are positive and significant but these simple regressions all have significant intercepts, likely due to model misspecifications and omitted risk factors. In these simple regressions, the coefficient for the market factor of the CAPM has the highest t-value resulting in the highest R2 (85%).
(Table 3 about here)
When only market beta and SMB are included in the model, both have significant coefficients and R2 increases to 95%. When only beta and HML are included in the model, both factors are significant but R2 drops to 86%. However, in the three-factor model, that includes the market factor, SMB and HML, HML loses its significance. Only the market and size factors are now significant and R2 again attains its highest value of 0.95. In the ISE, the market factor seems to capture the risk proxied by HML. Accordingly, we next calculate the Pearson correlation coefficient between the market factor and HML and, as suspected, find a strong correlation between them (0.58). In comparison, the correlation coefficient is -0.38 in FF (1993) for the US market. However, the size factor is less correlated with the market factor in the ISE (0.05) than in the US market (0.32) and hence has a higher incremental explanatory power with the market factor already in the model. Furthermore, in our study the correlation between SMB and HML is also higher than desired (0.26) while it is -0.08 in the FF study. These high correlations are important in two respects. First, it means that we were not able to clearly distinguish the size and book-to-market factors from one another as successfully through the portfolio formations. Second, the lower explanatory power of size in the FF (1993) study and of book-to-market in this study may be partly due to the high correlation between the market factor and SMB in the FF study and between the market factor and HML in this study.
We finally regress the 52 excess monthly returns to the 16 size-BE/ME sorted portfolios against the three risk factors to determine whether SMB and HML indeed capture common factors in returns related to size and book-to-market equity. The monthly explanatory returns are the same as those employed in the regressions of excess returns on all sample firms reported in Table 5. Summary statistics for the dependent variable, the average excess returns on the 16 size-BE/ME sorted portfolios, are presented in Table 6, Panel A. As expected, the portfolios produce a wide range of monthly average excess returns, from 0.75% to 8.45%. The portfolio returns again confirm the negative (positive) relation between size (book-to-market equity) and average return, though the relation with book-to-market equity is not as monotonic as the relation with size. Still, the average excess return for the four highest book-to-market portfolios is 3.7% while it is 2.58% for the portfolios with the lowest ratio, a difference of 1.12% per month. The average monthly excess return difference between the small and big portfolios is a more impressive 2.36% per month. However, the standard deviations of the portfolio excess returns are very high and they decrease (increase) with size (book-to-market equity) as expected.
(Table 6 about here)
The results of time-series regressions on each one of the 16 portfolio excess returns are summarized in Table 6, Panel B. When the portfolio excess returns are regressed against the market factor in the single factor CAPM (not reported in the table), the R2 ranges from 0.29 to 0.74 and the intercepts are significant in all of the four smallest portfolios and in the four highest book-to-market equity portfolios. Of course, these extreme portfolios are the ones for which the additional factors SMB and HML are the most likely to exhibit marginal explanatory power. Indeed, when SMB and HML are included in the regressions, smallest portfolios (highest book-to-market portfolios) consistently have the highest and the most significant coefficients on SMB (HML). Furthermore, big (low book-to-market equity) firms have either insignificant or negative loadings on SMB (HML). The inclusion of the two additional risk factors also improves the explanatory power of the regressions with R2s of 0.52 to 0.88.
4.2.4. Annual regressions and a link to macroeconomic fundamentals
We also estimate the one-factor CAPM and the three-factor FF (1993) model regressions separately for each of the sample years to evaluate if SMB and HML have higher explanatory power in periods of higher uncertainty and distress, with the caveat that the results should be interpreted with caution due to small sample sizes in these annual regressions. As depicted in Table 7, the intercepts are again larger and more significant in the one-factor model than in the three-factor one. Even though the coefficient on excess market return is positive and significant at (=0.0% in all years, the large intercepts indicate larger pricing errors; therefore, we again conclude that the market factor is not sufficient in explaining the variation in annual returns. In the three-factor model, the sensitivity of excess monthly returns to the variation in the market premium is the most significant and has t-values of 8.25, 10.93, 12.39, and 9.03 for each sample year, respectively. The second significant factor across the sample years is again SMB. Its coefficient estimate is positive and significant (at least at (=0.01) except in 1995 when its p-value declines to 0.11.
(Table 7 about here)
The slope of HML is positive and weakly significant for the years 1993-1994 and 1996-1997 while it is negative for the sample years in-between. This provides an explanation for the insignificance of its coefficient in the above regressions covering the whole sample period. Prior research has found that long-term losers (distressed stocks or industries) tend to have positive loadings on HML and thus higher future returns while long-term winners (strong firms or industries) have negative loadings on HML and lower future returns (FF, 1995). Hence, a reason for the negative (though insignificant) loadings on HML could be that the Turkish economy was relatively healthier between the financial crisis at the beginning of 1994 and the onset of political uncertainty and economic deterioration of fundamentals starting in 1997. For instance, the macroeconomic indicators of Turkey, available upon request, show that the lowest GDP growth, the biggest hikes in the consumer and wholesale price indices, the largest deterioration in TL/US$ exchange rates, and the biggest increase in the debt stock as a % of GNP have occurred in the 1993-1994 and in 1997-1998 periods. Hence many firms may have become more susceptible to these adverse economic conditions and the ensuing financial distress risk proxied by HML during the two periods of distress at each end of our sample period. This yearly analysis again suggests that SMB and HML may be proxies for different dimensions of systematic risk in the ISE returns.[x]
4.3. Size and book-to-market equity as firm-specific and macroeconomic risk proxies
This section directly examines the relation between size/book-to-market equity and firm-specific and macroeconomic risk. We examine the turnover, profitability and leverage characteristics of our sorted portfolios and evaluate how they fare in different states of the macro-economy. We also estimate the relationship between our risk factors and various macroeconomic indicators.
4.3.1. The relationship of size and book-to-market equity with firm-specific financial distress
Table 8 reports the means and standard deviations of some firm-specific fundamentals in the four most extreme of our 16 portfolios.[xi] On average, high BE/ME firms have smaller sizes and larger firms have lower book-to-market equity. As expected, larger (low BE/ME) firms have higher profitability both in terms of return on assets and EPS (except for the smallest firms in 1993). Although higher BE/ME firms are expected to have lower P/E ratios, this is not clearly discernable in the table.
(Table 8 about here)
Figure 2 also depicts the relationship between profitability (OI/TA) and size/book-to-market equity in our six ranked portfolios for each year in the 1993-1997 period. Lowest profitability ratios are encountered in 1993. Small firms seem to have suffered more due to the foreign exchange crunch and the following major devaluation in the 1993-1994 period.
(Figure 2 about here)
As expected, smaller firms have higher leverage measured as the ratio of total assets to total liabilities (TA/TL). A surprising result is the higher debt ratio in the low book-to-market equity firms (see Figure 3). Their higher leverage may be necessitated by their fast growth and/or these firms can more easily afford and access debt capital. Although cost of borrowing is very high in Turkey, companies may still prefer high leverage due to its tax benefits, hyperinflation that lends being a net borrower adventageous, and the infancy of the stock market.[xii] Debt ratio also assumes its highest value during the 1993 crisis. We conclude that when financial distress is defined as high leverage, size is a better proxy for financial distress than book-to-market equity in the ISE.
(Figure 3 about here)
4.3.2. Portfolio turnover
A characteristic that would make the stocks in the portfolios riskier is the persistence of their size and book-to-market characteristics over a long period of time. If small and high BE/ME stocks with a high risk of financial distress are entrenched in their portfolios , this would make them more susceptible to booms and busts in the economy. Hence, as we rebalance the portfolios each year, we calculate the percentage of stocks that remain entrenched in the two most extreme of our six portfolios over the five years. Indeed, we find that 32 of the 54 firms (60%) that entered the smallest/highest (SH) portfolio anytime in the first four years stayed in SH for at least two years and 22 of the 34 firms (65%) that entered SH in the first two years stayed in SH for at least two more years and 24% stayed there for four or five years. Similarly, 35 of the 46 (76%) firms that entered the biggest/ lowest (BL) portfolio in the first four years stayed in BL for at least two years and 55% stayed in that portfolio for four or five years. 17 of the 31 (55%) that entered BL in the first two years stayed in BL for either four or five years and 87% stayed there for at least two years.[xiii]
4.3.3. The performance of extreme size/book-to-market portfolios in different states of the
economy
We now examine how our extreme portfolios fare in the good and bad states over the sample period. We report the mean and the standard deviation of excess monthly returns to our smallest and highest book-to-market portfolio P4 and the biggest, lowest book-to-market portfolio P13 in these different states. In panel A of Table 9, we define as bad states the political and economic crises in 1993-1994 and in 1997-1998, summarized in Appendix 2, and the years in between as the good states. As
expected, we find that P4 performs worse (better) than P13 in the bad (good) states and has higher standard deviation of returns in both states. We then rank the quarters in our sample period according to the rate of growth in GNP and evaluate the performance of our extreme portfolios in these high/low growth periods. Panel B, Table 9 shows that both of the extreme portfolios have lower returns in bad states of low growth compared to good states and the standard deviation of excess returns are higher for the risky portfolio prior to both the good and the bad states.
4.3.4. Regression analysis: The relation between the SMB/HML and the macroeconomy
In this section, we directly explore the relation between the HML and SMB strategies and future economic growth through multiple regression analysis. We use the following regression equation, similar to that employed in Liew and Vassalou (2000) to regress the future growth in the economy on past holding period’s returns:
Growth t, t+1 = a + b (Rm - Rf) t-1, t + c SMB t-1, t + d HML t-1, t (4)
where, t = the holding period (a month or a quarter)
growth = future growth in Gross National Product (GNP), Industrial Production Index (IPI),
Consumer Price Index (CPI) or local currency and foreign exchange interest rate risk
(IR-TL and IR-FX)
b,c,d = the coefficients of the market, HML, and SMB strategies
We expect the slope coefficients to be positive if high (low) returns to these strategies are associated with future good (bad) states of the economy, i.e., high returns in these strategies will be followed by periods of high growth and vice versa.
Since we use monthly returns to measure the independent variables in our study, we first use, as the dependent variable, the change in the following macroeconomic indicators, measured monthly by the Central Bank as opposed to GNP which is available only quarterly: Industrial Production Index (IPI), the Consumer Price Index (CPI), and interest rate on local currency (IR-TL) and foreign exchange (IR-FX). Using several macroeconomic fundamentals as the dependent variable in our regressions also allows us to investigate the relation of HML and SMB with different kinds of distress indicators in the economy. Table 10 presents the estimated regression coefficients for the independent variables used to predict our macroeconomic fundamentals, the excess market returns and the returns to SMB and HML strategies, the t-statistics for their mean values, and their p-values. Panel A presents the explanatory power of the monthly risk premiums in predicting next month’s economic growth indicators. We find that SMB strategy has the highest explanatory power, in that its coefficient estimate has the correct sign and is significant, in predicting inflation risk and both local and foreign currency interest rate risk at α = 8%, 6.5%, and 4.7%, respectively. That is, small stocks underperform before periods of high inflation and interest rate hikes. HML returns are significantly associated with foreign exchange IR risk and weakly significant in predicting IPI growth and local currency IR risk. Excess market returns are significantly related to only local currency interest rate risk.
In the second model specification, we add our continuously compounded monthly returns to convert them to quarterly returns which we then relate to future quarterly or yearly growth in GNP and IPI. Panel B shows that the coefficient estimate of HML has the correct sign and is significant at α = 0% in predicting next quarter’s IPI, but has the wrong sign in predicting GNP growth. In contrast, there is a positive relation between SMB and growth in GNP but SMB is not related to future IPI growth. To summarize, our return strategies are related to economic fundamentals, they seem to predict facets of macro-economic risk, and again SMB seems to be a more robust predictor of future economic growth.
5. Summary and concluding remarks
This study contributes to the extant market-anomalies literature by examining the link of size and book-to-market equity with macroeconomic and firm-specific fundamentals and average returns in the ISE during the 1993-1997 period. Our results confirm that, on average, high book-to-market and small capitalization stocks provide significant excess returns and this predictability is largely related to firm- specific and macro-economic distress. Our results support the findings of FF (1992. 1993, 1995, 1998) and Liew and Vassalou (2000) and justify models for additional risk factors in returns.
In our analysis of the determinants of returns in the ISE, we apply the single-factor CAPM and the three-factor FF (1993) model regressions to individual stock returns and find that only the market and the size factors are significant. This result portrays the greatest similarity to the strong size and market beta effects observed in the Mexican market. Nevertheless, the results are as significant for HML in portfolio-based regressions. The portfolios with small (high BE/ME) stocks have the highest and the most significant coefficient estimates of SMB (HML).
We finally investigatewhether the size and book-to-market effects are related to firm-specific and macroeconomic distress risk. To this end, we evaluate certain market and accounting based profitability and leverage ratios of our size/book-to-market sorted portfolios. We find that size and BE/ME are related to profitability. However, while size is a robust proxy for both firm-specific profitability and leverage, the relation between book-to-market ratio and leverage is not as clear cut. An analysis of economic upturns and downturns through the sample period and estimation of the three-factor FF model separately for each year reveals that the variation through time in the loadings of monthly excess returns on HML reflects these upturns and downturns. We also find that the turnover of firms in the extreme size/book-to-market portfolios is low over the years and these extreme portfolios underperform in bad states of the economy. Finally, in regressions of economic growth and distress indicators against the three risk factors, we find that HML and SMB are indeed related to future economic fundamentals and SMB is a more robust predictor of economic growth while HML is more significant in predicting inflation and interest rate risk.
In conclusion, using an out-of-sample data set, we find reasonable evidence for both the size and value effects and conclude that these premiums are proxies for additional distress related risk factors in returns not captured by the one factor CAPM. As such., our results should be of interest to both practitioners interested in EMs and researchers investigating return predictability issues and benchmark asset-pricing models. An interesting follow-up research should explore whether and how fast practitioners have started implementing these strategies in the ISE to profit from them and, in the process, cause these anomalies to disappear. This would highlight whether there is a learning effect in the ISE as was observed for the US market.
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| | | |Table 1 | | | | |
| |Monthly average returns on the six portfolios formed on size and BE/ME: 1993-2001 |
| | | | | | | | |
|Equally-weighted average monthly portfolio returns are measured from July 1t to June 30t+1 for portfolios based on December 31t-1 |
|book-to-market ratios and June 30t sizes. The 6 portfolios are constructed by taking the intersections of firms first sorted into two size |
|ranked groups (small and big) and then, independently, into three book-to-market groups (low, medium and high BE/ME).Portfolios are rebalanced |
|each year. N is the number of firms in the sample for each year. S-B (H-L) is the average annual return differential the three small (highest |
|two BE/ME) portfolios and the threee big (lowest two BE/ME) ones. |
| |
| |
| |
| |
|93-94 (N=106) |book-to-market equity (BE/ME) |
| | |Mean | | | |Std. dev. | |
|size |Low (L) |Medium (M) |High (H) |S-B |Low (L) |Medium (M) |High (H) |
| | | | | | | | |
|Small (S) |0.084 |0.109 |0.129 |0.066 |0.182 |0.288 |0.316 |
|Big (B) |0.064 |0.061 |0.131 | |0.143 |0.173 |0.287 |
| |H-L: |0.112 | | | | | |
|94-95 (N=117) |L |M |H | |L |M |H |
| | | | | | | | |
|S |0.147 |0.181 |0.175 |0.189 |0.185 |0.192 |0.227 |
|B |0.090 |0.113 |0.111 | |0.130 |0.141 |0.146 |
| | |0.049 | | | | | |
|95-96 (N=136) |L |M |H | |L |M |H |
| | | | | | | | |
|S |0.060 |0.066 |0.073 |0.049 |0.154 |0.149 |0.143 |
|B |0.073 |0.046 |0.031 | |0.159 |0.128 |0.142 |
| | |- 0.029 | | | | | |
|96-97 (N=155) |L |M |H | |L |M |H |
| | | | | | | | |
|S |0.081 |0.076 |0.080 |-0.001 |0.117 |0.134 |0.187 |
|B |0.081 |0.081 |0.076 | |0.144 |0.174 |0.201 |
| | |-0.006 | | | | | |
|97-98 (N=174) |L |M |H | |L |M |H |
| | | | | | | | |
|S |0.051 |0.052 |0.032 |0.056 |0.062 |0.068 |0.071 |
|B |0.051 |0.036 |0.042 | |0.068 |0.060 |0.085 |
| | |-0.03 | | | | | |
|98-99 (N=190) |L |M |H | |L |M |H |
| | | | | | | | |
|S |0.161 |0.138 |0.154 |0.044 |0.067 |0.048 |0.040 |
|B |0.110 |0.127 |0.172 | |0.049 |0.049 |0.058 |
| | |0.055 | | | | | |
|99-00 (N=204) |L |M |H | |L |M |H |
| | | | | | | | |
|S |0.014 |-0.002 |0.016 |0.021 |0.064 |0.028 |0.062 |
|B |-0.008 |0.000 |0.001 | |0.029 |0.053 |0.055 |
| | |0.011 | | | | | |
|00-01 (N=206) |L |M |H | |L |M |H |
| | |mean | | | |std dev | |
|S |0.087 |0.050 |0.077 |0.015 |0.098 |0.042 |0.067 |
|B |0.065 |0.068 |0.066 | |0.054 |0.045 |0.053 |
| | |-0.01 | | | | | |
Table 2
Sharp performance indices for the 16 size/book-to-market portfolios: St = ( rt - rf* ) / (t ,
where: St = Sharpe ratio for portfolio t, rt = average return on portfolio t, rf* = riskless rate of interest. and ( t = standard deviation of the returns to portfolio t. Panel A presents the overall risk-adjusted performance of the 16 size/book-to-market ranked portfolios by calculating their Sharpe ratios over the sample period 1993-2001. To form the 16 portfolios, we first sort the sample firms into four size (S) groups form smallest to largest (S1 to S4). Each size group is then sequentially ranked into four partitions according to their book-to-market ratios (BM) from lowest to highest (BM1 to BM4) to finally form the 16 portfolios ranked first on size then on book-to-market (S1/BM1, S1/BM2,…, S4/BM3, S4/BM4). The portfolios are rebalanced each year. In Panel B, the 16 portfolios are collapsed into four by taking averages of the two small and two big portfolios and the two low and the two high book-to-market portfolios.
____________________________________________________________________________________________________________________
Panel A: Sharp ratios for the 16 portfolios
| | |Book-to- |market ratio | |
| | | | | |
| |BM1 (Lowest) |BM2 |BM3 |BM4 (Highest) |
|Size | | | | |
|S1 (Smallest) |0.292 |0.286 |0.463 |0.386 |
|S2 |0.168 |0.163 |0.086 |0.217 |
|S3 |0.198 |0.126 |0.100 |0.051 |
|S4 (Biggest) |0.134 |0.058 |0.157 |0.182 |
Panel B: Sharp ratios for the 16 portfolios collapsed into four
Book-to-market ratio
| | | | | | | |
| | |Average BM1 |Average BM22 | | | |
| |Size | | | | | |
| |Average S1 |0.227 |0.288 | | | |
| |Average S2 |0.129 |0.123 | | | |
| | | | | | | |
Table 4
| | | | | |
Table 5
1-factor, 2-factor and 3-factor model regressions on monthly excess returns: 1993-1997 (n=52)
3-factor model: R(t) – Rf(t) = a + b [ Rm(t) – Rf(t) ] + s [ SMB(t) ] + h [ HML(t) ] + e(t)
Panel A: 1-factor model: SML, HML or (Rm – Rf ) as the only explanatory variables
s h b
coefficient est. (t-value) 0.79 (2.79) 1.08 (5.86) 0.97 (16.85)
constant est. (t-value) 0.007 (0.31) 0.008 (0.18) 0.017 (1.87)
R2 0.13 0.41 0.85
Panel B: 2-factor model: (Rm – Rf ) and SML & (Rm – Rf ) and HML as the explanatory variables
s b
coefficient est. (t-value) 0. 69 (10.47) 0.95 (29.46)
constant est. (t-value) 0.000 (0.17)
R2 0.95
h b
coefficient est. (t-value) 0. 25 (2.30) 0. 88 (12.88)
constant est. (t-value) 0.013 (1.57)
R2 0.86
Panel c: 3-factor model: SML, HML and (Rm – Rf ) as the explanatory variables
s h b
coefficient est. (t-value) 0.67 (9.72) 0.06 (0.89) 0.93 (23.11)
constant est. (t-value) 0.0006 (0.11)
R2 0.95
|Table 6 |
|Regressions of excess returns to 16 portfolios formed on size and BE/ME |
|on excess market returns (Rm-Rf) and excess returns to (SMB) and (HML) factors: |
|July 1993-October 1997 |
|R(t) - Rf(t) = a + b [ Rm(t) – Rf(t) ] + s [ SMB(t) ] + h [ HML(t) ] + e(t) |
|PANEL A: Dependent variable: Excess returns (Std.dev.s) to the 16 size, BE/ME portfolios |
|Book-to-market equity quartiles |
|low 2 3 high |
|Size quartiles |
|small 4.69 (19.10) 4.77 (20.18) 8.45 (22.10) 6.92 (21.89) |
|2 2.22 (16.23) 2.27 (16.31) 1.29 (17.71) 3.95 (21.63) |
|3 2.44 (14.32) 1.91 (17.14) 1.87 (16.41) 1.10 (18.46) |
|big 1.58 (13.03) 0.75 (13.75) 2.26 (13.50) 3.75 (19.33) |
|PANEL B: |
|Book-to-market equity quartiles |
| |low |2 |3 |hi| |low |2 |3 |
| | | | |gh| | | | |
| |
|Annual means (std. dev.) of firm-specific fundamentals in the four most extreme |
| |
| |
| |
| |
| |
| |
| |
| |
|1993 |
|1994 |
|1995 |
|1996 |
|1997 |
| |
| |
| |
| |
|mean TL/TA |
| |
| |
| |
|SLb |
|1.05 |
|(0.35) |
|0.77 |
|(0.38) |
|0.75 |
|(0.26) |
|0.75 |
|(0.27) |
|0.76 |
|(0.17) |
| |
|SH |
|0.39 |
|(0.21) |
|0.38 |
|(0.22) |
|0.59 |
|(0.24) |
|0.44 |
|(0.24) |
|0.42 |
|(0.26) |
| |
|BL |
|0.55 |
|(0.20) |
|0.51 |
|(0.14) |
|0.46 |
|(0.14) |
|0.55 |
|(0.21) |
|0.63 |
|(0.17) |
| |
|BH |
|0.39 |
|(0.16) |
|0.36 |
|(0.13) |
|0.41 |
|(0.20) |
|0.43 |
|(0.20) |
|0.39 |
|(0.20) |
| |
| |
| |
| |
|mean OI/TA |
| |
| |
| |
|SL |
|-0.05 |
|(0.16) |
|0.24 |
|(0.30) |
|0.24 |
|(0.28) |
|0.11 |
|(0.22) |
|0.22 |
|(0.15) |
| |
|SH |
|0.05 |
|(0.16) |
|0.06 |
|(0.21) |
|0.12 |
|((0.16) |
|0.09 |
|(0.07) |
|0.1 |
|(0.13) |
| |
|BL |
|0.28 |
|(0.15) |
|0.41 |
|(0.08) |
|0.32 |
|(0.17) |
|0.23 |
|(0.12) |
|0.19 |
|(0.20) |
| |
|BH |
|0.1 |
|(0.17) |
|0.18 |
|(0.10) |
|0.23 |
|(0.10) |
|0.26 |
|(0.09) |
|0.18 |
|(0.09) |
| |
| |
| |
| |
|mean EPS |
| |
| |
| |
|SL |
|-.289 |
|(0.38) |
|0.048 |
|(0.11) |
|0.008 |
|(0.07) |
|-0.016 |
|(0.5) |
|0.003 |
|(0.01) |
| |
|SH |
|-0.033 |
|(0.08) |
|0.009 |
|(0.07) |
|0.015 |
|(0.02) |
|0.003 |
|(0.01) |
|0.004 |
|(0.01) |
| |
|BL |
|0.211 |
|(0.12) |
|0.263 |
|(0.30) |
|0.038 |
|(0.03) |
|0.03 |
|(0.02) |
|0.028 |
|(0.05) |
| |
|BH |
|0.064 |
|(0.11) |
|0.047 |
|(0.09) |
|0.017 |
|(0.02) |
|0.035 |
|(0.04) |
|0.017 |
|(0.02) |
| |
| |
| |
| |
|mean P/E |
| |
| |
| |
|SL |
|-0.78 |
|(15.9) |
|88.13 |
|(193.90) |
|19.97 |
|(31.70) |
|6.42 |
|(11.42) |
|6.71 |
|(93.03) |
| |
|SH |
|15.36 |
|(28.6) |
|-92.18 |
|(303.70) |
|13.19 |
|(12.40) |
|-12.11 |
|(62.62) |
|4.83 |
|(17.87) |
| |
|BL |
|13.51 |
|( 3.8) |
|18.03 |
|(3.52) |
|10.45 |
|(12.19) |
|39.04 |
|(62.26) |
|23.59 |
|(20.60) |
| |
|BH |
|2.84 |
|(3.7) |
|15.72 |
|(15.63) |
|21.14 |
|(37.78) |
|5.58 |
|(2.14) |
|7.09 |
|(2.77) |
| |
| |
| |
| |
|mean ME |
| |
| |
| |
|SL |
|9.37 |
|(11.9) |
|21.528 |
|(13.76) |
|12.188 |
|(6.82) |
|10.184 |
|(8.66) |
|19.978 |
|(28.14) |
| |
|SH |
|3.25 |
|(3.62) |
|14.055 |
|(8.45) |
|10.068 |
|(7.98) |
|10.183 |
|(6.27) |
|10.233 |
|(5.54) |
| |
|BL |
|270.2 |
|(252) |
|954.364 |
|(1052.93) |
|456.569 |
|(371.04) |
|440.517 |
|(356.1) |
|710.141 |
|(740.67) |
| |
|BH |
|153.3 |
|(129) |
|458.569 |
|(494.88) |
|307.488 |
|(441.21) |
|314.371 |
|(457.27) |
|288.321 |
|(369.08) |
| |
| |
| |
| |
|mean BE/ME |
| |
| |
| |
|SL |
|0.065 |
|(1.53) |
|0.11 |
|(0.17) |
|0.14 |
|(0.16) |
|0.14 |
|(0.30) |
|0.16 |
|(0.14) |
| |
|SH |
|5.3 |
|(4.76) |
|0.57 |
|(0.37) |
|0.48 |
|(0.05) |
|1.16 |
|(0.47) |
|1.02 |
|(0.52) |
| |
|BL |
|0.19 |
|(0.07) |
|0.11 |
|(0.02) |
|0.17 |
|(0.04) |
|0.17 |
|(0.07) |
|0.13 |
|(0.06) |
| |
|BH |
|2.39 |
|(1.51) |
|0.41 |
|(0.12) |
|0.47 |
|(0.05) |
|0.65 |
|(0.11) |
|0.62 |
|(0.16) |
| |
|size/book-to-market equity portfolios a |
a Definitions of our risk proxy variables are as reported in Table 1 legends.
b These are the most extreme four of the 16 portfolios formed from the four size and BE/ME quartiles of ISE stocks first sorted on size and then
on BE/ME. Accordingly, SL and SH denote portfolios composed of smallest 25% firms with lowest and highest 25% book-to-market
equity ratios, while BL and BH denote the portfolios containing the biggest 25% firms with the lowest and highest 25% book-to-market
ratios.
| | | | | | |
| | |Table 9 | | | |
|Performance of the extreme portfolios in different states of the economy: |
|The values are the mean monthly excess returns (standard deviations) to the extreme smallest and highest book-to-market portfolio |
|(P4) and the biggest and lowest book-to-market portfolio(P13) over good and bad states of the economy from 1993 to 1997. |
| |Bad states | |Good states | | |
| | mean (std.dev.) | | mean (std.dev.) | | |
|Panel A: States |defined by the state of the economic and political environment | |
| | | | | | |
| P4: Ri - Rf |1.35 (21.12) | | 8.42 (21.45) | | |
| | | | | | |
|P13: Ri - Rf |2.17 (14.93) | |-5.46 (11.49) | | |
| | | | | | |
| | | | | | |
|Panel B: States |defined as good/bad by annual growth in GNP | | |
| | | | | | |
| P4: Ri - Rf |4.73 (26.87) | | 8.54 (17.78) | | |
| | | | | | |
|P13: Ri - Rf |1.36 (17.08) | | 2.25 (8.65) | | |
| | | | | | |
| |
|Future economic growth / stagnation is measured as the growth in Gross National Product (GNP), Industrial Production Index (IPI), the change in the Consumer Price Index (CPI), the change in the |
|interest rate on local currency (IR-TL), and the interest rate on US$ (IR-FX) in the next holding period. The independent variables are the excess return to the market portfolio ( Rm-Rf ), and the|
|two return based risk premiums related to small size (SMB) and high book-to-market equity (HML). The return to the SMB strategy is measured each month as the difference between the simple average |
|return on the three small size stock portfolios, S/L, S/M, and S/H, and the simple average return on the three big size stock portfolios, B/L, B/M, and B/H. Similarly, HML return is measured as |
|the difference between the simple average return on the two high book-to-market equity portfolios, S/H and B/H, and that of the two low book-to-market equity portfolios, S/L and B/L. |
| | | | | |
| | | | | | | | | |
|Panel A: |Monthly factor returns predict future economic growth | | | | |
|IPI t, t+1 | | |-0.056 |-0.565 | |0.081 |0.467 | |0.187 |
|IR-FX t, t+1 | |-4.184 |-0.275 | |-53.32 |-2.04 (4.7%) | |43.62 |-1.73 (9%) |
|Panel B: |Quarterly factor returns predict future growth | | | | |
IPI t, t+1 | | |-0.144 |-2.14 (5%) | |0.049 |0.39 | |0.213 |2.08 (0%) | |GNPt, t+1 | | |0.064 |1.14 | |0.243 |2.33 (3%) | |-0.264 |-3.09 (0%) | | | | | | | | | | | | | | | | | | | | | | | | | |
-----------------------
Endnotes
[i] Furthermore, the explanatory power of these two variables does not seem to be a result of the survivorship bias in Compustat samples (Kothari et al., 1995) or data snooping (Black, 1993) since it also holds on a holdout sample of financial firms (Barber and Lyon, 1997), in the pre-Compustat era (Davis, 1994), and outside the U.S. markets (see, e.g., Chan et al., 1991 and Barry et al., 2001).
[ii] These differences and the resultant disagreement on a “best practice” model for valuing securities in EMs was also noted by Bruner et al. (2002) in the Batten Institute/AIMR/Emerging Markets Review conference on EMs.
[iii] A short history of the establishment and development of the ISE is available from the author upon request.
[iv] In line with the Turkish GAAP, only plant, property and equipment type of assets are allowed to be revalued by a WPI- based rate published by the Ministry of Finance in every December. This rate usually falls short of the real inflation rate.
[v] A summary of local macroeconomic indicators, and fundamentals of the public and financial sectors for the sample years are available from the author upon request.
[vi] In their study covering the last 150 years and 101 stock exchanges, Turkey
#JKLRSinquy}~£©ª¯°ÕÖÙÚIMNOðÝðÎðÝðÝð½ð¯ ¯ ’¯ ¯ ’‚r‚fWI has the third highest average annual index return in $ terms (38.6%), the fourth highest standard deviation of index returns (68.6%) and the correlation of the Turkish index return with their equal-weighted portfolio of index returns is 0.397, with 25 exchanges having lower correlations.
[vii] In Turkey, the December 31 fiscal year-end firms are required by the Capital Markets Board to send their audited financial reports to the ISE within ten weeks of the fiscal year-end to be disseminated to public, but some are not made public until April or even May. The requirement is six weeks following the second quarter for semi-annual financial statements and four weeks after the related quarter end for quarterly reports.
[viii] Negative BE/ME firms are usually risky firms just like high BE/ME firms and hence would lead to difficulty (inconsistency) in ranking the stocks and interpreting the relation between BE/ME and returns. Furthermore, there is far too few firms with negative BE/ME (1-4/sample year) as to lead to a survivorship bias.
[ix] Apart from the stringent assumptions, there are some common problems encountered in testing the CAPM. First, researchers use an arbitrary market index even though the CAPM requires that the market portfolio should include all risky investments and is mean- variance efficient. A second problem is the difficulty of finding a good proxy for the risk-free rate, which is really risk-free only if it is held to maturity and does not include any inflation expectations. Nevertheless, the specification true to the theoretical CAPM where we deal with risk premiums, rather than total returns, is used here since one of the objectives of the paper is to compare the explanatory power of the CAPM with that of the 3-factor FF model. Furthermore, the interpretation of beta, (i, and statistical measures such as the R2, standard error of the regression and the t-statistics have interesting and unique interpretations under the CAPM.
[x] However, one should be cautious in making such a generalization because the period covered in the analysis is too short and the efficiency of the coefficient estimates in annual regressions with sample sizes of 12 monthly excess returns are suspect. Furthermore, the negative sign and the insignificance of the HML coefficients in two of the sample years may be due to the high correlation between the market and HML premiums.
[xi] The counterpart of Table 8 for each of the 16 portfolios is also available but not presented here due to its length and consistency of the results.
[xii] Since taxes are levied on historical cost financial statements and use of inflation accounting is not allowed, high leverage, which allows firms to pay lower taxes on fictitious inflationary profits, is preferred to equity financing
[xiii] In fact, entrenchment seems to be a common characteristic of all portfolios. For example, 67% (74%) of stocks that entered portfolio 1 (16) anytime in the first four years stayed there for at least two years.
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