Master Thesis:
The impact of financial constraints risk on stock returns:
Evidence from London Stock Exchange
MIF student: Miao Yujing (10403957)
Thesis Supervisor: Dr. Chris Florackis
August 2013
University of Amsterdam
Amsterdam Business School
Master in International Finance
Abstract
This study examines the impact of financial constraints risk on stock returns in the UK market. The main objective is to explore whether WW index (Whited and Wu, 2006) and KZ index (Kaplan and Zingales, 1997) are applicable for measuring financial constraints risk for UK firms and whether constrained firms yield higher stock returns. Based on 4,799 firm-year observations from Thomson DataStream over the period 1998-2011, I construct 10 portfolios sorted by WW index to represent different levels of financial constraints risk. The empirical results reveal that constrained stocks earn a significant abnormal risk-adjusted return of 6.63% per year on average using Fama-French Three-Factor Model (1993). Moreover, WW index developed by Whited and Wu (2006) is found to be a better proxy than KZ index to reflect the characteristics of constrained firms.
Table of Contents
1. Introduction ... 1
2. Literature review ... 4
3. Methodology and Data ... 7
3.1 Constructing measures of financial constraints risk ... 7
3.2 Data and Portfolio Construction ... 11
4. Empirical Results and Discussion ... 14
4.1 Descriptive statistics and difference of means test ... 14
4.2 Risk-adjusted performance: Market, Size and Value risk factors ... 16
5. Conclusions ... 19
References ... 21
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1. Introduction
Financial constraints risk has been put into dispute by a large body of literature for a long time. The term “financial constraints” refers to the financial frictions which impede the firm from funding investments due to credit constraints, incapacity to borrow or issue equity, dependence on bank loans and illiquidity of assets (Owen, Christopher and Jesus 2001, p.529). Researchers have provided certain evidence of the impact of financial constraints risk on corporate investment behaviors and stock returns in their econometrics studies. For example, Fazzari, Hubbard and Petersen (1988) show that more financially constrained firms exhibit greater investment-cash flow sensitivity than less constrained firms. In other words, a high sensitivity of investment-cash flow ratio represents an evidence of more financial constraints risk. Lamont et al. (2001) discover a common variation in the returns of constrained stocks, so does the study of Gomes, Yaron, and Zhang (2004). Other researchers, like Campello and Chen (2010) find that financial constraints risk is significantly correlated with macroeconomic movements, indicating that constrained stocks are quite sensitive to credit conditions, economic downturns or business cycle. However, the issues about how to define financially constrained firms and how to measure financial constraints risk are still in public controversy. Empirical studies develop different methods and proxies to capture the characteristics of financially constrained firms (Kaplan and Zingales, 1997 and White and Wu, 2006), but their results are in contrast with each other. Therefore, the first question that my thesis works on is about “how well could WW (Whited and Wu, 2006) and KZ (Lamont et al., 2001) indexes perform in measuring financial constraints risk?” or “which index could better reflect the characteristics of constrained firms as a proxy of financial constraints risk?”
The second issue on which most research papers post heated debate is about whether financial constraints risk is priced in assets market. The existing literature which mainly focuses on the impact of financial constraints risk on investment in US does not lead into consensus. For example, White and Wu (2006) argue that firm-level external finance constraints indeed represent a source of un-diversifiable risk that is priced in financial markets. But once financial constraints are taken into consideration, the usual result that smaller firms earn higher returns disappears, which implies that financial constraints risk premium is not an artifact of the well-known size effect by Chan and Chen (1991). Moreover, the WW index developed by Whited and Wu (2006) also stands in contrast to the KZ index used by Kaplan and Zingales (1997), Lamont et al. (2004) and Gomes, Yaron and Zhang (2004)
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in measuring financial constraints. The most famous and interesting topic is nothing more than “financial constraint puzzle” derived from Lamont, Polk and Saa-Requejo (2001). They find empirical evidence that constrained stocks’ returns move together over time, which proves the existence of financial constrains risk as a systematic factor. But surprisingly, constrained stocks yield lower returns than unconstrained stocks, suggesting that financial constraint is a “non-priced” systematic risk factor in market. We could see that there are many conflicts in studying the impact of external finance constraints on investment in US, but limited evidence from the pricing of financial constraints risk on London Stock Exchange. So the second objective of my thesis is to examine the relationship between financial constraints risk and the stock returns of the firms listed on London Stock Exchange. More specifically, the second research question to be addressed is: “Do financial constrained firms yield higher stock returns?” or “Is financial constraints risk priced in the UK market?”
By far, the heated debate on the relationship between financial constraints and corporate investment or stock returns has been mostly based on the data from firms listed in the US stock market. Yet, limited researchers employ financial data from firms quoted in the UK market. Kalchreuth and Murphy (2005) explore the data base for the CBI Industrial Trends Survey (ITS)1 to investigate the correlations between financial constraints and capacity restrictions in the United Kingdom. They pointed out that financially constrained firms are “more often capacity restricted and take longer to close capacity gaps than unconstrained firms.” In the paper of Alessandra Guariglia (2003), a large number of unquoted UK firms over the period 1993-2003 are employed to examine the effects of internal and external financial constraints on firms’ investment. The empirical results of the study unfold that the sensitivity of investment to cash flow ratio responds differently according to the financial constraints level. Particularly, investment by small and young firms with strong internal funding ability is more likely to be constrained because of lack of external finance, which reflects the issue of policy concern. My thesis takes on the objective to extend the existing studies on the financial constraints in the UK market. As the European financial market is less developed than the United States, financial constraints tend to be a bigger issue in Europe. Moreover, after experiencing over 15 years of sustained growth since
1 CBI Industrial Trend Survey (ITS) is an important survey for business cycle analysis in the United Kingdom,
which is conducted on a monthly and quarterly basis and covers 38 sectors of UK manufacturing industry at chief executive level.
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1993,the economy of the United Kingdom has been slowing down after 2008 financial crisis. The following Euro zone crisis increased the volatility of UK equity market and made it suffer from dramatic drop. Obviously, external finance becomes more difficult in a depressed economic environment, which suggests that firms will face stronger external financial constraints. Therefore, the UK market is quite an attractive object to study the relationship between financial constraints and stock returns. Whether this financial constraints risk is priced on the London Stock Exchange is the main topic we will address in this study.
Given the WW and KZ indexes from Whited and Wu (2006) and Kaplan and Zingales (1997), I use a sample of 4,799 firm-year observations from a range of 300 to 500 firms listed on FTSE All-share each year over the period from 1998 to 2011. WW and KZ proxies are then calculated to rank sample firms from the least constrained level to the most constrained. The post-ranking firms are allocated into 10 portfolios on a yearly basis by deciles. After analyzing the accounting and market data of these 10 portfolios, I consider WW index as a better proxy to reflect the characteristics of financially constrained firms. Next, I construct the equally-weighted returns of these WW post-ranking portfolios on a monthly basis. Each portfolio has twelve consecutive monthly returns annually, for example, starting from July 1999 to June 2000 while the WW index of this portfolio is constructed at the end of 1998. By analogy, I obtain a time series of 168 (14*12) monthly returns in total for each portfolio from July 1999 to June 2013. Finally, I estimate the abnormal returns (alpha) and market risk (beta) using two commonly used asset pricing models – CAPM and Fama-French 3 factor Model– to assess the portfolio performance and check whether more constrained stocks earn a higher return.
By analyzing the firm characteristics of WW sorted and KZ sorted portfolios, we find that firms deemed constrained by WW index have high leverage ratio, low cash flow ratio, low liquidity and low dividend payout ratio. On the contrary, constrained portfolios classified by KZ index are quite liquid and have low leverage ratio, high cash flow and current asset ratio. From the perspective of reflecting financial health of constrained firms, we would favorably choose WW index to measure the financial constraints risk. In other words, we consider KZ index not applicable for measuring financial constraints for vast majority of UK firms in our study. Surprisingly, we also observe that more constrained firms tend to be large size which coincides with Lamont et al. (2001), but stands in contrast with Whited and Wu (2006). The empirical results provide evidence to the hypothesis that constrained firms yield
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higher stock returns. The portfolios with upper 50% level of financial constraints risk earn a statistically significant abnormal return (CAPM alpha) of 7.68% per year on average while the regressions of the lower 50% unconstrained portfolios are either not significant or have weak explaining power. Fama-French Three-Factor Model regression proves that the abnormal returns of constrained stocks do not result from the small firm effect.
The rest of the thesis is organized as follows: Section 2 provides an overview of the debate on financial constraints risk from previous literature. Section 3 explains the process of collecting data, measuring financial constrains risk and constructing portfolio. Section 4 presents the empirical results and discussions. Section 5 gives conclusions and findings of this thesis.
2. Literature Review
My thesis mainly builds on the studies of White and Wu (2006) and Kaplan and Zingales (1997), which examine whether financial constraints represent a source of priced risk in the US. In the paper of Whited and Wu (2006), they developed an index to measure the financial constraints risk, which incorporates more accounting and market variables and removes Tobin’s q from the index, using firm-level data from the quarterly 2002 Standard and Poor’s industrial files from 1975 to 2001. The reason to remove Tobin’s q from the variables is that they believe Tobin’s q contains quite a lot of measurement error as a proxy for investment opportunities. The new index – WW index is based on the generalized method of moments (GMM) estimation of a structural model (investment Euler equation) and proved to capture the firm characteristics associated with external financial constraints. However, Whited and Wu (2006, p.557) achieved an absolutely contrast conclusion from that of Kaplan and Zingales (1997). Constrained firms by WW index were found to be small, under-invest, have low analyst coverage and do not have bond ratings while those deemed constrained by KZ index are large, over-invest, have high analyst coverage, and have higher incidence of bond ratings. The cross-sectional regressions of stock returns on WW index and firm characteristics proved that more constrained stocks yield higher returns and firm-level external financial constraints represent a source of priced and undiversified risk in financial markets.
To understand the differences between WW and KZ indexes, it is important to review the study of Kaplan and Zingales (1997). Their paper analyzed in depth 49 low-dividend
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firms, for a period of 15 years from 1969 to 1984, identified by Fazzari, Hubbard, and Petersen (1988) as financial constrained with high investment to cash flow sensitivity and investigated the correlation between corporate investment and cash flow. According to the qualitative information in the annual report, as well as the quantitative information in the company financial statements, Kaplan and Zingales (1997) classified the 49 firms into five categories. That is, 54.5% of firm-years are NFC (not financially constrained), 30.9% LNFC (likely not to be financially constrained), 7.3% PFC (possibly financially constrained), 4.8% LFC (likely to be financially constrained) and 2.6% FC (financially constrained). They also verified the accuracy of the classification scheme by estimating ordered logit models of the probability that a firm falls into one of the five groups. After running the regression of investment on cash flow and Tobin’s Q by different financially constrained status over the entire sample period and two sub-periods, Kaplan and Zingales (1997) uncovered that less financially constrained firms exhibit greater investment-cash flow sensitivity than more constrained firms. The result obviously stood in contrast with Fazzari, Hubbard and Petersen (1988) by indicating that a higher sensitivity of investment-cash flow is not necessarily an evidence of more financial constraints risk.
Following Kaplan and Zingales (1997), Lamont, Polk and Saa-Requejo (2001) constructed a “synthetic KZ index” – a linear combination of five accounting ratios – using the exact coefficients estimated in Kaplan and Zingales, but they analyzed data from a larger sample of all growing manufacturing firms during 1968 – 1997. Lamont et al (2001) classified all these firms into nine groups based on size and KZ index and compared the returns and characteristics of each group. After running regressions of the nine size/KZ-sorted portfolios’ returns on market, size and constraints factors, Lamont et al (2001) discovered a common variation in the returns of constrained stocks, but strikingly found no risk premium related to this systematic risk. In other words, the study proved the existence of financial constraints factor, but this factor is not priced in the financial markets. Obviously, this surprising result that constrained firms yield lower stock returns than unconstrained firms (financial constraint puzzle) was in contradiction with many previous studies, such as Chan and Chen (1991). Lamont et al (2001) also investigated into the relationship between macroeconomic variables and financial constraints, but did not find evidence that the performance of constrained firms reflects monetary policy, credit conditions or business cycles.
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Different from Lamont et al (2001), Campello and Chen (2010) uncovered that the financial constraint factors are significantly connected to macroeconomic movements, in both statistical and economical way. The stock returns of constrained firms are more sensitive to macroeconomic shocks (for example, credit conditions, economic downturns or expansions) than unconstrained firms. During economic recessions, the returns of constrained stocks go down more than those of unconstrained stocks. To the contrary, when economy recovers and expands with easy credit conditions, constrained firms always earn higher stock returns than unconstrained firms. The distinct point of Campello and Chen’s study (2010) is that they employ multiple schemes to classify and rank 12,170 nonfinancial firms into groups. This method overcomes the disadvantage that researchers have always debated on which firm characteristic should be used to identify the firms as financial constrained or unconstrained. In addition, in order to solve Lamont et al “financial constraint puzzle”, Campello and Chen (2010) proposed a new real-financial approach to explore the economic effects of financial constraints factor. The results of their study suggest that the financial constraint risk is priced in the financial markets and correlates with macroeconomic movements.
In the paper of Haehoon Hahn and Hangyong Lee (2009), they focus on exploring the effects of debt capacity on stock returns of manufacturing firms sorted across financially constrained and unconstrained factors. Based on a model of corporate investment under collateral constraints, they find that the impact of debt capacity on stock returns of financially constrained firms is both statistically and economically significant while the risk proxies such as size, beta, book-to-market, leverage, and momentum are controlled. That is, constrained firms with high debt capacity tend to be exposed to higher risks when the availability of internal and external funds for investment is changed. In this sense, high debt capacity firms are expected to earn higher returns than low debt capacity firms on average if other risk factors are controlled. However, when it comes to financially unconstrained firms, they do not find a systematic correlation between debt capacity and stock returns. Taken together, Haehoon Hahn and Hangyong Lee (2009) provide support to the theories of imperfect capital markets and suggest by empirical evidence that the impact of credit constraints on corporate investment behavior of manufacturing firms are reflected in the cross-sectional stock returns.
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(2008 and 2011). However, we need to be aware that “financial distress” and “financial constraints” are related but different concepts in our study. In Campbell et al (2011)’s paper, a firm is classified as distressed if it is very likely to file for bankruptcy under Chapter 7 or Chapter 11, de-list for relevant performance reasons, or receive a D rating from a rating agency. But a constrained firm could be a young and fast-growing entity whose investment behaviors are constrained because of difficult access to external funding. The main difference between “financial distress” and “financial constraints” exists in the fact whether the firm is on the verge of bankruptcy or just constrained on investment due to the lack of financing. The two papers of Campbell et al (2008 and 2011) focus on the measurement and pricing of distress risk. Taking the models of Shumway (2001) and Chava and Jarrow (2004), Campbell et al (2011) construct portfolios of different failure probability using three accounting and five market-based measures and compare the returns on these failure-sorted stock portfolios from 1981 to 2008. They also consider a portfolio which longs the safest 10% and shorts the most distressed 10% of the sample stocks in order that they could study the performance of distressed stocks across characteristics (such as size, value and analyst coverage) and over time. The final result of Campbell et al (2011) study disclosed that distressed stocks underperform S&P 500 significantly and possess high volatility and market betas. The underperformance of distressed stocks relative to safe stocks is observed across all size and value scope, but more concentrated in stocks with lower institutional holdings and analyst coverage. Although I distinguish financial constraints risk from financial distress risk in my study, the methodology of constructing portfolio employed by Campbell et al (2008 and 2011) provides me a good insight into forming the constrained and unconstrained portfolios. From previous literature, researchers mostly agrees on the existence of financial constraints factor in financial markets, but does not draw the same conclusion on whether this factor is systematically priced or earns risk premium. The divergence of these studies in terms of their findings motivates us to find out which proxy of WW and KZ indexes is more applicable in measuring financial constraints risk and whether financial constraints risk is priced in the London Stock Exchange.
3. Methodology and Data
3.1 Constructing measures of financial constraints risk
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financial constraints risk for FTSE All-Share listed companies using both KZ and WW indexes. The two indexes use different accounting and market-based variables as a measurement of financial constraints risk. I first construct WW and KZ proxies for all the listed firms by collecting annual accounting and market data at the end of each fiscal year, then sort the firms from least constrained to most constrained, and compare the summary statistics to determine which index is more appropriate to measure the financial constraints risk.
The WW index as a proxy of firms’ external finance constraints developed by Whited and Wu (2006) was constructed via a generalized method of moments (GMM) estimation of an investment Euler equation. The sample data originally came from quarterly 2002 Standard and Poor’s (S&P) COMPUSTAT industrial files. Based on 6 selection criteria, an unbalanced panel between 131 and 1390 firms per quarter from January 1975 to April 2001 was finally used in the regression process. Since the coefficients of the model were initially generated using data from US listed firms, we need to consider whether this model also applies to UK listed firms. Therefore, in this paper I assume that the international markets are integrated and the WW index is also applicable for measuring financial constraints risk of UK listed firms as most of the firms listed on S&P 500 and FTSE are multinational corporations and their stocks are internationally traded. The components of the index are shown as follows:
−0.091𝐂𝐅𝐢𝐭− 0.062𝐃𝐈𝐕𝐏𝐎𝐒𝐢𝐭+ 0.021𝐓𝐋𝐓𝐃𝐢𝐭− 0.044𝐋𝐍𝐓𝐀𝐢𝐭+ 0.102𝐈𝐒𝐆𝐢𝐭 − 0.035𝐒𝐆𝐢𝐭 (1)
where 𝐂𝐅𝐢𝐭 is the ratio of cash flow to total assets; 𝐃𝐈𝐕𝐏𝐎𝐒𝐢𝐭 is an indicator that takes the
value of one if the firm pays cash dividends; 𝐓𝐋𝐓𝐃𝐢𝐭 is the ratio of the long-term debt to
total assets; 𝐋𝐍𝐓𝐀𝐢𝐭 is the natural log of total assets; 𝐈𝐒𝐆𝐢𝐭 is the firm’s three-digit industry
sales growth; 𝐒𝐆𝐢𝐭 is firm’s sales growth.
In this index, both industry and firm sales growth are included to reflect the fact that only firms with good investment opportunities tend to invest enough to be constrained. In Whited and Wu’s paper (2006), they define these firms to have low individual sales growth but existing in high-growth industries. Firm-level debt to asset ratio is also included because constrained firms are likely to have a high leverage ratio. The first three variables reflect the financial health of a firm. We can see that the coefficients of variables in the index enter with the expected sign. For instance, the firms with good cash flow and dividends payout are less constrained while those with high leverage ratios tend to be more financially
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constrained. In fact, the original regression model also includes another 3 variables, that is, 𝐂𝐀𝐒𝐇𝐢𝐭 is the ratio of liquid assets to total assets, 𝐍𝐀𝐢𝐭 is the number of analysts following
the firm (analyst coverage) and 𝐈𝐃𝐀𝐑𝐢𝐭 is the three-digit industry debt to assets ratio. However, because these three variables are not individually significant and are jointly significant, Whited and Wu (2006) excluded them from the final WW index.
The KZ index developed by Kaplan and Zingales (1997) incorporated Tobin’s q as one of the variables. The KZ index used here is actually the “synthetic KZ index” improved by Lamont et al (2001) from a broader sample of firms.
−1.001909𝐂𝐅𝐢𝐭+ 3.139193𝐓𝐋𝐓𝐃𝐢𝐭− 39.36780𝐓𝐃𝐈𝐕𝐢𝐭− 1.314759𝐂𝐀𝐒𝐇𝐢𝐭 + 0.2826389𝐐𝐢𝐭 (2)
where 𝐓𝐃𝐈𝐕𝐢𝐭is the ratio of total dividends to assets and 𝐐𝐢𝐭 represents Tobin’s q which is the ratio of the market value of the firm over the replacement value of the firm’s assets. A high Q (larger than 1) implies that the company is overvalued because the stock is more expensive than the replacements costs of its assets. The positive sign of Tobin’s q means that an overvalued firm is more likely to be constrained. The coefficients of the other variables also have expected signs.
Actually, Whited and Wu (2006)’s study demonstrated a listed advantages of using structural WW index over KZ index in measuring financial constraints risk and sorting sample firms. I construct both KZ and WW indexes for all the sample firms on a yearly basis and sort them into 10 groups by deciles. To make sure that all the indexes calculated are positive and reasonable, I first omit firms whose ICB Industry Code is 8000 (Financial Firms) because Whited and Wu (2006) stated in their paper that their investment model is not appropriate for regulated or financial firms. Another reason exists in the fact that manufacturing or other industry firms are quite different from financial firms in accounting and market data. For example, most of the financial firms operate in high leverage ratio and thus should be expected to be more constrained in their investment behavior with a high WW and KZ indexes. However, in fact, large institutional investors, such as pension funds, endowments and banks are most active and determinant roles in the capital markets. Secondly, after calculating WW and KZ indexes for each sample firm, I observed that all the WW indexes and 80% of the KZ index present a negative number. In order to illustrate the relationship between the level of financial constraints risk and a variety of firm characteristics clearly and efficiently, I take the absolute value of the two indexes and sort the firms first by WW
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and second by KZ index. So the WW and KZ indexes in the following discussion are all in absolute values.
Table 1 reports the mean values of a variety of firm characteristics variables sorted into deciles first by WW index (panel A) and second by KZ index (panel B) from 1998 to 2011. Results in Panel A present 10 groups of firms’ characteristics sorted by WW index from the least constrained to the most constrained. It is obvious to observe in the second and third column of the table that as the WW index increases, the KZ index appears a downward trend. The ratio of total debt to total assets (TLTD) goes up significantly with growing financial constraints risk, and the ratio of liquid assets to total assets (CASH) decreases. This is mainly because constrained firms always have a high leverage ratio and more illiquid assets which impede them from getting access to external funding–incapacity to borrow or issue equity. The ratio of cash flow to total assets (CF) and total dividends to total assets (TDIV) also experience a slight downward trend which means firms with bad cash flow and low dividends are more financially constrained. In general, these four variables reflect the financial health of a firm. The results are consistent with our expectation of defining a financially constrained firm, that is, firms in good financial conditions are more flexible and less constrained in their investment behaviors with easy access to external and internal funding. Finally, an important feature deviated from Whited and Wu (2006) is that more constrained firms belong to low sales growth industries but have high individual sales growth. These firms possess good reinvestment opportunities, but due to their situation in the slowly developing industries, it is also possible for them to be exposed to financial constraints risk. Another notable feature which coincides with Kaplan and Zingales (1997) but in contrast with White and Wu (2006) is that constrained firms are deemed large in our results. Notice the “Total Assets” column in Panel A, as the financial constraints level increases, we find the size of the firms becomes larger. In sum, the firms classified as “financial constrained” by WW index are expected to associate with difficult excess to external funding.
However, in Panel B of Table 1, the same rules are not applicable for the firms sorted by KZ index. Firstly, the corresponding WW index of portfolios ranked by KZ index display a parabolic trend, as shown in Figure 1. The y-axis represents the corresponding WW index values while the x-axis represents the portfolios ranked by KZ index. If we assume that the firms with larger WW values should be more constrained (based on the discussion above),
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then most constrained portfolios ought to be portfolio 6 and 7 while the least constrained portfolios are 1, 2, 9 and 10. The relationship between WW and KZ index is first positively and then negatively correlated.
Figure 1
The corresponding WW values of the 10 portfolios ranked by KZ index
Secondly, as we could see in the third, fourth, eighth and ninth columns in Panel B, the variables CF, CASH and TDIV increase obviously while TLTD decreases sharply. If we assume that a higher KZ index would represent more constrained firm, this trend is in contrast to that in Panel A and not reasonable to explain the characteristics of constrained firms. An alternative is to assume that firms with lower KZ values should be more constrained. But the other variables, like Tobin’s q and total assets do not show a certain trend as the numbers fluctuate a lot. In this sense, WW index performs a better job in sorting firms than KZ index, given the differences in the results from using WW and KZ indexes discussed above. The following session will illustrate the data collection and portfolio construction process based on WW index.
3.2 Data and Portfolio Construction
According to the measurement of financial constraints risk using WW and KZ indexes, I gather both time series and cross-sectional data at a firm/year level from Thomson DataStream. Instead of going into US market where Whited and Wu (2006) based their study
0.605 0.610 0.615 0.620 0.625 0.630 0.635 0.640 0.645 0.650 0 1 2 3 4 5 6 7 8 9 10
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on S&P 500 firms, I focus on firms listed on London Stock Exchange. The sample firms are chosen from FTSE All-share which consists of FTSE 100, FTSE 250 and FTSE Small Cap. The reason is that FTSE All-share Index represents at least 98% of the full capital value of all UK companies that qualify as eligible for inclusion. Especially for FTSE 100, the index consists of 100 companies listed on the London Stock Exchange with the highest market capitalization. It is also considered to represent the business regulated by UK company law. The following FTSE 250 includes the next largest 250 companies after FTSE 100 and Small Cap consists of the 351st to the 629th the largest ones.
The “datatypes” which I employ to construct the proxies of financial constraints risk are explained in Table 2. The accounting and market measures used to reflect a range of firm characteristics include cash flow per share, total assets, total current assets, cash dividends paid total, long term debt, net sales or revenues, dividends per share, market value and etc. All the data except stock returns was collected on a yearly basis from 1998 to 2011 because the full sample is only available and complete in Thomson DatasStream from 1996. In terms of stock returns, the datatype RI, which shows a theoretical growth in value of a share over a specified period assuming that dividends are reinvested for the purchase of additional units of equity, is used to construct a series of monthly holding period returns. For example, the return of the month July 2012 equals (RI2012/8/1- RI2012/7/1) / RI2012/7/1. Besides, each firm is assigned to an industry code (datatype ICBIC) by FTSE/DJ Industry Classification Benchmark (ICB)2 hierarchy which provides 10 industries to help investors monitor broad industry trends. The industry code and corresponding industry name is also presented in Table 2. The industry sales growth is calculated as the average sales growth of the firms in the same industry. As I mentioned in Section 3.1, the Whited and Wu (2006)’s model is not applicable for financial firms, so the firms with the ICB Industry Code 8000 are excluded from the sample. The firms with missing data or accounting items or ratios are also omitted. But to make sure that the analysis is free from potential survivorship bias, I include both active and delisted stocks in the sample data. Finally, the dataset contains an unbalanced panel of 300 to 500 firms per year, with 4,799 firm-year observations in total for the entire sample period. In the next step, I allocate all the sample firms into 10 portfolios based on the rank of
2 The Industry Classification Benchmark (ICB) is a definitive system categorizing over 70,000 companies and
75,000 securities worldwide, enabling the comparison of companies across four levels of classification and national boundaries. The ICB system is supported by the ICB Database, an unrivalled data source for global sector analysis, which is maintained by FTSE International Limited.
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their WW index (absolute value) on an annual basis. Actually, portfolio construction plays a very important role in analyzing the impact of financial constraints risk on stock returns. From previous studies, we could see that most researchers reach a consensus on financial constraints risk as a systematic risk factor, but own different views on whether this risk is priced or not. Given the results from Kaplan and Zingales (1997), Lamont et al (2001), Whited and Wu (2006), Campello and Chen (2010) and etc., I assume in my thesis that the constrained firms share a common variation in their stock returns over time so that the financial constraints risk is considered as a systematic factor and cannot be diversified by investors in market. Under this assumption, I focus my study on the question whether the financial constraints risk is priced or not using data from London Stock Exchange listed firms. As we discussed in Section 3.1, WW index appears more rational and accurate in reflecting the characteristics of financially constrained firms than KZ index. So I select WW index as the proxy of financial constraints risk and rank the sample firms from lowest WW to highest WW each year. Then the post-ranking firms are classified by deciles into 10 portfolios from the least constrained to the most constrained. (The larger the absolute value of WW index is, the more constrained the firms are considered.) For instance, the first portfolio contains the stocks with the lowest ten percent of the financial constraints level (0010), and the second portfolio contains the next ten percent of the stocks with 10th to 20th financial constraints level (1020). The next 8 portfolios are constructed in the same way so that the entire spectrum of financial constraints risk is covered. The lowest to highest levels are emphasized as follows: 0010, 1020, 2030, 3040, 4050, 5060, 7080, 8090 and 9000. Besides, a portfolio that longs the highest 10% level of financial constraints and shorts the lowest 10% level will also be constructed. This long-short portfolio is constructed to test whether an arbitrage strategy of buying constrained stocks and selling non-constrained stocks could earn an abnormal return. Next, I check the historical rates of monthly return of the stocks and calculate the equally-weighted return of each sorted portfolio. We need to notice here that the financial constraints proxies are constructed on a yearly basis in December of each year, but our monthly returns are calculated starting from July of the following year and continue with 12 subsequent months. This accounts for disclosure and transparency rules of the Financial Services Authority (FSA), which allow UK firms to make
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public their annual financial reports within a certain period after the end of each fiscal year.3 For example, the 1-month return for the highest deciles portfolio, which is constructed on the basis of financial constraints proxy referring to fiscal year end in December 2011, is calculated in July 2012. After having constructed the return of July 2012, the following monthly returns are calculated starting from August 2012 till the end of June 2013. In this way, each portfolio has a time series of 168 monthly stock returns in total from the year July 1999 to June 2013. As I mentioned above, all the portfolios are formed on an annual basis, so it is necessary to rebalance the portfolios each year before calculating the monthly equally-weighted returns. At last, in order to assess the portfolio performance, I conduct difference of means test in Excel and regress on CAPM alpha and Fama-French 3-factor alpha in EVIEWS. The Capital Asset Pricing Model (CAPM) and the 3-factor Fama-French (1993) Model are both popular and primary asset pricing models to calculate the risk-adjusted returns, controlling for market, size and value factors. The empirical results of portfolios’ performance assessed by t-test and risk-adjusted returns are analytically discussed in Section 4.
4. Empirical results and Discussion
4.1 Descriptive statistics and difference of means test
We first analyze the empirical results by discussing descriptive statistics and difference of means test. Table 3 reports the mean, median, standard deviation, sample variance, kurtosis and skewness of WW index sorted portfolios’ monthly returns. As we illustrate in Section 3, these 10 portfolios cover the range of financial constraints risk from the lowest to the highest level. In order to have a clear view of changes in mean values of portfolio returns, I present the mean values in curve in Figure 2. As we could see from following figure, the mean values of the returns do not form a continuously rising trend because portfolio 4, 5, 7 and 9 show up at the bottom of the curve. But the whole curve present an uptrend as the portfolio returns are consistently reaching higher highs (portfolio 2, 6 and 8) and retracing to higher lows. The black lines are constructed to imitate the “Bollinger bands” used in “technical analysis” of stock prices. Despite the portfolio returns fluctuate a lot in the
3 For accounting periods beginning before 2007, firms listed on London Stock Exchange were allowed by the
Financial Services Authority (FSA) to make their financial reports public up to 6 months after the end of their fiscal year. Http://fsahandbook.info/FSA/html/handbook/DTR/4/1.
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upward channel of “Bollinger bands”, we could observe a certain pattern of this wavy line: the three peaks (returns of portfolio 2, 6 and 8) keep going up and the four bottoms (portfolio 1, 4&5, 7, 9&10) also experience a growth of returns except two outliers of portfolio 9 and 10 which are slightly lower than portfolio 7.
Figure 2
Mean values of WW index post ranking portfolios’ monthly returns
Generally speaking, the mean values of the portfolio returns take on a multiple upward trend respectively that we could have a preliminary judgment that more constrained stocks might earn a higher return than less constrained stocks. If we notice the fifth row in Table 3, that is, the standard deviation which reflects the volatility of portfolio returns, we could find that it displays a downtrend over the rising financial constraints risk. This phenomenon goes beyond my expectation because most constrained firms have bad financial health so that their stocks should have been exposed to higher risks than less constrained stocks. One possible explanation could be that less constrained firms are more flexible in their investment behaviors and thus their stock returns move together with the market to a large extent. On the other hand, more constrained firms might be limited to less riskier investment because of difficult access to external funding, making their stocks less exposed to market risk. But whether this explanation is reasonable or not, we need to double check the market beta regressed by asset pricing models in Section 4.2.
0.0000 0.0020 0.0040 0.0060 0.0080 0.0100 0.0120 0.0140 0.0160 0 1 2 3 4 5 6 7 8 9 10
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Table 4 presents the results from difference of means test between each portfolio’s monthly returns over the whole period from July 1999 to June 2013. Assuming unequal variances, the null hypothesis of the test is that the differences between the means of each pair of post-ranking portfolios’ monthly returns equal zero. If the t-statistic is small, we do not reject equality. If the tstatistic is large, for example, larger than 1.960 or smaller than -1.960, the null hypothesis (equality) is rejected under 95% confidence level. Looking at the figures in Table 4, we could find that the t-statistics are quite small and not statistically significant. One exception occurs between portfolio 1 and portfolio 8. The t-statistic, -1.350 < -1.282, is significant under 80% confidence level. From the perspective of descriptive statistics and t-test results discussed above, we get limited evidence to prove that constrained firms yield higher stock returns than unconstrained firms, but certain firms exposed to larger financial constraints risk do exhibit a higher yield than others. To confirm whether constrained stocks earn abnormal returns, it is necessary to examine risk-adjusted performance by utilizing asset pricing models.
4.2 Risk-adjusted performance: Market, Size and Value risk factors
In this section, we discuss the risk-adjusted portfolio performance over the period from July 1999 to December 2012, controlling for the market, size and value factors. The commonly used asset pricing models are CAPM and the Fama-French Three-Factor Model (1993), which allows us to test whether the post-ranking portfolios earn abnormal returns after adjusting for market risk, firm size and book-to-market ratio. The CAPM alpha and Fama-French 3-factor alpha can be estimated as follows:
Jensen’s alpha from the CAPM: 𝐫𝐢𝐭− 𝐫𝐟𝐭 = 𝛂𝐢+ 𝛃𝐢,𝐌𝐊𝐓𝐌𝐊𝐓𝐭+ 𝛆𝐢𝐭 (𝟑)
where 𝐫𝐢𝐭 is the return of portfolio i in year t, 𝐫𝐟𝐭 is the risk-free rate for year t and 𝐌𝐊𝐓𝐭 is
the excess market portfolio return,𝐫𝐦𝐭− 𝐫𝐟𝐭, in year t.
Three-factor alpha from Fama and French (1993) model:
𝐫𝐢𝐭− 𝐫𝐟𝐭 = 𝛂𝐢 + 𝛃𝐢,𝐌𝐊𝐓𝐌𝐊𝐓𝐭+ 𝛃𝐢,𝐒𝐌𝐁𝐒𝐌𝐁𝐭+ 𝛃𝐢,𝐇𝐌𝐋𝐇𝐌𝐋𝐭+ 𝛆𝐢𝐭 (𝟒)
where 𝐒𝐌𝐁𝐭 and 𝐇𝐌𝐋𝐭 stand for the size and value risk factors respectively. SMB = Small
Minus Big, for example, the return of a portfolio of small stocks in excess of the return on a portfolio of large stocks; HML = High Minus Low, for example, the return of a portfolio of stocks with a high book-to-market ratio in excess of the return on a portfolio of stocks with a low book-to-market ratio. The size and the book-to-market ratio work as proxies for
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exposures to sources of systematic risk not captured by the CAPM beta and thus result in the return premiums associated with these factors.
Table 5 exhibits the estimated annualized alphas and market betas of the 10 portfolios ranked by WW index. Results in Panel A and Panel B are derived from CAPM and Fama-French 3-Factor Model respectively. The corresponding t-statistics are reported in the brackets below the alpha and beta. Firstly, in Panel A, constrained firms with upper 50% level of financial constraints risk (from portfolio 6 to portfolio 10) earn a significant market-adjusted return (CAPM alpha) of over 5.33% per annual. The average abnormal return of these five portfolios is 7.68%. Especially for portfolio 8, the abnormal return reaches 11.01% per year which is over 5% higher than portfolio 4 and 5. If we look at portfolios with lower 50% level of financial constraints risk, the alphas are not statistically significant with the exception of portfolio 2 and portfolio 3. Even though the t-statistics of portfolio 2 and 3 are significant, the R-square is only around 0.50 which tells us that variation in the market excess returns only explains about 50% of the variation in the portfolio returns’ series. This number is quite small compared to those of the more constrained portfolios. As the R-square becomes larger, the model is more accurate and reliable to explain the past performance and predict future outcomes. In this sense, the estimated alphas and corresponding t-statistics are more credible for portfolio 6 to portfolio 10 with R-square larger than 60%. In terms of the market risk which is shown in the fourth row, the beta fluctuates around the market wide average beta of 1 and does not vary largely between portfolios. So the explanation proposed in Section 4.1 that more constrained firms possess smaller exposure to market risk due to the restriction of their investment behaviors cannot be proved here.
As shown in Panel B of Table 5, the Fama-French Three-Factor alpha is only significant for portfolio 3, 6, 8 and 10. Portfolio 6, 8 and 10 exhibit an abnormal return of 5.71%, 8.47% and 5.70% p.a. respectively while that of portfolio 3 is 4.91%. The average abnormal return of portfolio 6, 8 and 10 is equivalent to 6.63% which is slightly lower than 7.68% from CAPM alpha. Several significant alphas from CAPM, like portfolio 2, 7 and 9, disappear mainly because the firm size factor is taken into consideration in Fama-French Three-Factor Model. If we pay attention to the fourth row of Panel B, we could see that the SMB beta presents a downtrend as financial constraints risk level goes up. Remember the “Total assets” and “Market value” columns of summary statistics in Table 1, the growing assets and market value indicate that the constrained firms are found to be large, so their SMB betas in
Fama-18
French Model are quite small. For instance, portfolio 10 only has a SMB beta of 0.2. In other words, the abnormal return of constrained stocks is not a consequence of the famous small firm effect because most of these firms have large size. To the contrary, the SMB betas for portfolio 5 to portfolio 1 vary from a range of 0.70 to 0.90 which account for the abnormal return derived from CAPM to a large extent. Besides, the R-squares in Panel B exceed 70% by and large which implies a favorable goodness of fit of Fama-French 3-Factor Model. From this point of view, we could infer that more constrained firms do yield a higher return than less constrained firms. However, we still do not find evidence from the regressed market beta to explain why constrained portfolios have smaller standard deviation.
As mentioned in the Section 3.2, a long-short portfolio is constructed to test whether an arbitrage strategy of buying constrained stocks and selling short unconstrained stocks could earn an abnormal return. Table 6 reports the estimated alphas of long-short spreads between portfolio 6, 7, 8, 9, 10 and portfolio 1, where portfolio 6 to portfolio 10 represents the higher 50% level of financial constraints risk under WW index classification. From column 2, 4 and 6 of Table 6, we could see that the CAPM and 3-Factor Fama French alphas of these three spread portfolios are quite statistically significant, which is consistent with the results from Table 5 and Figure 2 that portfolio 6, 8 and 10 earn much higher stock returns than the least constrained portfolio 1. Especially for portfolio 8 which owns the most significant and highest alpha among other constrained portfolios, the abnormal return of long-short spread reaches 10.8% per year under Fama-French 3-Factor Model. The other two spreads, (6)-(1) and (10)-(1), derive a significant annualized Fama-French alpha of 8.07% and 8.05% similarly. In terms of the spread between portfolio 7 and portfolio 1, the abnormal return turns out to be over 6% per year but only significant under 80% confidence level. Except for portfolio 9, the empirical results from Table 6 stand in line with our expectations that a long position in constrained stocks and short position in unconstrained stocks would earn abnormal returns. In this sense, our findings of the long-short spread portfolios strongly support the existence of a financial constraints premium of UK stocks.
To sum up, in Section 4, we give a detailed discussion of descriptive statistics, difference of means test and risk-adjusted returns from two commonly used asset pricing models. We prove the hypothesis that financial constraints risk contribute to higher stock returns in market step by step. The strongest evidence exist in the regression of CAPM alpha and Fama-French Three-Factor alpha. The statistical significance of Fama-French alpha of
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constrained portfolios suggests that financial constraints risk is priced in the UK market and this is not a result of small firm effect. Besides, we find that the strategy of buying unconstrained stocks and selling short constrained stocks would destroy investors’ returns significantly. Unfortunately, we do not find sufficient empirical proof to solve the question why constrained portfolios have smaller volatility. It could only be inferred that constrained firms are more conservative about investment decisions to protect themselves from risky projects. But for unconstrained firms, they have more opportunities to invest in a range of high-risk high-yield projects with easy access to external funding. This flexibility exposes them to higher risks.
5. Conclusions
In this study, we examine the relationship between financial constraints risk and stock returns in the UK market. More specifically, we give answers to two mainly argued questions in previous literature: “How well could WW index and KZ index perform in measuring financial constraints risk?” and “Do financially constrained firms yield higher stock returns?” Previous researchers mostly agree on the existence of financial constraints risk, but dispute quite a lot on the issues mentioned above. Our study contributes to the previous research by employing data from London Stock Exchange listed firms from 1998 to 2011. The thesis starts with exploring whether WW and KZ indexes could be applied as proxies of financial constraints risk in the UK market. Based on a sample of 4,799 firm-year observations listed on FTSE All-Share from 1998 to 2011, we construct deciles portfolios sorted by WW and KZ indexes respectively. After analyzing the accounting and market data of post-ranking portfolios, we find that WW index takes the advantage of reflecting financial health conditions of constrained firms over KZ index. Firms deemed constrained by WW index have large size, high leverage, more illiquid assets, low cash flow ratio and low dividends payout ratio. But constrained firms based on KZ index exhibit a good financial health condition instead. In this sense, we extend the application of WW index from US to UK market and approve its superiority over KZ index.
In the next step, we construct a time series of monthly stock returns for WW index post-ranking portfolios. The hypothesis that constrained stocks earn higher returns is tested by regressing CAPM and Fama-French Three-Factor alpha. The empirical results show that constrained firms yield statistically significant abnormal returns with CAPM alpha 6.63% p.a.
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and Fama-French Three-Factor alpha 7.68% p.a. on average. Considering the size factor in the regression of Fama-French Three-Factor Model, the small firm effect reduces as the level of financial constraints increasing. This finding indicates that the financial constraints risk premium does not result from the famous size effect. By far, we provide certain evidence to the hypothesis that financial constraints represent a source of systematic risk that is priced in the UK market. However, the thesis does not give sufficient and reliable explanation to the following questions: why the constrained portfolios have slightly smaller standard deviation than unconstrained portfolios; why the difference of means test is not significant while we observe abnormal returns of constrained stocks? Although this study proves the impact of financial constraints risk on stock returns by undertaking the evidence from UK market, whether this risk factor correlates with other factors, such as momentum, macroeconomic and other fundamental factors (except size), remains unknown.
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Reference
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Appendix:
Table 1
Summary statistics of WW and KZ indexes sorted firms
The following table presents the mean values of a variety of firm characteristics variables sorted into deciles by WW index (panel A) and KZ index (panel B) from 1998 to 2011. Calculations are based on a full sample of nonfinancial firms (4,799 firm-year observations) from Thomson DataStream on a yearly basis. The WW and KZ indexes are in absolute values. The firms are more constrained if the indexes are larger in value. CF is the ratio of cash flow to total assets; TLTD is the ratio of long term debt to total assets; LNTA is the natural log of total assets; ISG is the industry sales growth; SG is the firm sales growth; TDIV is the ratio of total dividend to assets; CASH is the ratio of liquid assets to total assets; and Q represents Tobin’s Q of which the numerator is firm market value and the denominator is the book value of total assets.
Panel A: Firms sorted by WW index
WW KZ CF TLTD LNTA ISG SG TDIV CASH Q TOTAL
ASSETS LONG TERM DEBT MARKET VALUE* Least constrained 0,510 1,158 0,073 0,042 11,331 0,280 0,126 0,023 0,630 1,833 116266 5522 149,70 0,559 1,881 0,136 0,072 11,584 0,207 0,113 0,044 0,549 1,668 141037 12425 190,72 0,580 1,659 0,137 0,092 11,971 0,187 0,114 0,040 0,509 1,549 205430 21084 256,19 0,597 1,561 0,132 0,109 12,323 0,176 0,108 0,038 0,490 1,349 289745 34165 310,54 0,614 1,386 0,126 0,122 12,673 0,157 0,126 0,035 0,488 1,267 403757 50432 393,93 0,631 1,244 0,112 0,143 13,107 0,159 0,116 0,031 0,500 1,076 610338 92458 559,01 0,652 1,177 0,109 0,157 13,538 0,148 0,129 0,030 0,509 1,052 913278 147235 852,46 0,678 1,162 0,115 0,182 14,135 0,151 0,114 0,033 0,484 1,072 1655197 305027 1734,88 0,713 1,046 0,108 0,197 14,896 0,139 0,159 0,032 0,432 0,990 3634040 680775 3286,76 Most constrained 0,784 1,055 0,111 0,178 16,447 0,161 0,253 0,035 0,311 0,987 27102256 3906562 20654,97
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Panel B: Firms sorted by KZ index
KZ WW CF TLTD LNTA ISG SG TDIV CASH Q TOTAL
ASSETS LONG TERM DEBT Least constrained 0,244 0,626 0,080 0,207 13,347 0,200 0,309 0,017 0,377 1,257 3160480 631329 0,460 0,629 0,084 0,168 13,397 0,202 0,210 0,018 0,391 1,139 3674612 702346 0,626 0,633 0,092 0,170 13,451 0,192 0,117 0,021 0,414 1,038 3560624 652918 0,838 0,641 0,095 0,156 13,472 0,182 0,123 0,024 0,450 1,013 4268169 709500 0,990 0,633 0,101 0,140 13,292 0,184 0,126 0,025 0,484 1,065 2460010 437544 1,180 0,640 0,110 0,128 13,308 0,155 0,106 0,028 0,504 1,063 2125425 337291 1,400 0,645 0,114 0,106 13,409 0,158 0,078 0,031 0,544 1,065 7966242 764428 1,690 0,635 0,123 0,090 13,136 0,166 0,086 0,036 0,580 1,146 3325585 374831 2,151 0,628 0,146 0,074 12,887 0,157 0,093 0,047 0,586 1,410 2502643 361103 Most constrained 3,616 0,611 0,206 0,059 12,372 0,164 0,119 0,090 0,566 2,497 2304364 333309 Table 2
The datatypes of accounting measures from Thomson DataStream
This table explains the datatypes or the codes of accounting measures from Thomson DataStream, which are used to construct the proxies of financial constraints risk – WW and KZ indexes in Section 3.1. The variables used in WW and KZ indexes are calculated as follows:
CF=WC05001/(WC02999/WC05301); DIVPOS=1 if WC04551>0, otherwise zero; TLTD=WC03251/WC02999; LNTA=Ln(WC02999); SG=(WC01001n
- WC01001n-1)/WC01001n-1. ISG equals the mean value of the firms’ sales growth under the same industry. TDIV=WC05101*WC05301/WC02999;
CASH=WC02201/WC02999; Tobin’s Q=MV*1000/WC02999. Monthly return=(RIi–RIi-1)/RIi-1. All the variables except Total Stock Index (RI) are collected on a firm/year level at the end of each year from 1998 to 2011. Total Stock Index (RI) is obtained on a monthly basis for a period of twelve months starting from July of the following year. The portfolio constructing process is illustrated in detail in Section 3.2. The table also provides the code and corresponding name of the 10 industries classified by FTSE/DJ Industry Classification Benchmark (ICB).
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Datatype Variables Definition
WC05501 Cash flow per share Cash earnings per share of the company; the numerator is Funds from Operations
WC02999 Total assets The sum of total current assets, long term receivables, investment in unconsolidated subsidiaries, other
investments, net property plant and equipment and other assets
WC05301 Common shares
outstanding
The number of shares outstanding at the company's year end; the difference between issued shares and treasury shares.
WC04551 Cash dividends paidtotal The total common and preferred dividends paid to shareholders of the company which excludes:
dividends paid to minority shareholders.
WC03251 Long term debt All interest bearing financial obligations, excluding amounts due within one year; shown net of premium
or discount.
WC01001 Net sales or Revenues Gross sales and other operating revenue less discounts, returns and allowances.
WC05101 Dividends per share The total dividends per share declared during the calendar year for U.S. corporations and fiscal year for
Non-U.S. corporations
WC02201 Currentassetstotal
Cash and other assets that are reasonably expected to be realized in cash, sold or consumed within one year or one operating cycle; The sum of cash and equivalents, receivables, inventories, prepaid
expenses and other current assets in general.
ICBIC & ICBIN
Industry classification benchmark - Industry Code
& Industry Name
The code and the name of the ICB industry under which the equity is classified: 0001 Oil & Gas, 1000 Basic Materials, 2000 Industrials, 3000 Consumer Goods, 4000 Health Care, 5000 Consumer Services, 6000 Telecommunications, 7000 Utilities, 8000 Financials, 9000 Technology.
MV Market value (in millions) The share price multiplied by the number of ordinary shares in issue. The amount in issue is updated
whenever new tranches of stock are issued or after a capital change.
RI Total Return Index
A theoretical growth in value of a share holding over a specified period, assuming that dividends are re-invested to purchase additional units of an equity or unit trust at the closing price applicable on the ex-dividend date
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Table 3
Descriptive statistics of WW index post-ranking portfolios’ returns
This table reports the descriptive statistics (the mean, median, standard deviation, sample variance, kurtosis and skewness) of monthly stock returns of 10 portfolios ranked by WW index from the least constrained level to the most constrained. Each portfolio has a time series of 168 monthly stock returns in total over the period from July 1999 to June 2013. Portfolio 1 (0010) contains the stocks with the lowest ten percentage of the financial constraints level while portfolio 10 (9000) represents the most constrained 10% stocks. The rest of the portfolios (from 1020 to 8090) cover the spectrum of financial constraints risk from very low to very high level. The confidence level is 95%.
Monthly stock returns Portfolio 1 Portfolio 2 Portfolio 3 Portfolio 4 Portfolio 5 Portfolio 6 Portfolio 7 Portfolio 8 Portfolio 9 Portfolio 10
Level of financial constraints risk 0010 1020 2030 3040 4050 5060 6070 7080 8090 9000
Mean 0,004303 0,011215 0,010893 0,008362 0,008300 0,011856 0,009565 0,013784 0,008769 0,009012 Standard Error 0,005494 0,004846 0,004397 0,004265 0,004073 0,004348 0,004482 0,004373 0,004232 0,003518 Median 0,006035 0,010964 0,013730 0,014190 0,011534 0,015926 0,012933 0,017686 0,014077 0,015397 Standard Deviation 0,071210 0,062813 0,056993 0,055284 0,052793 0,056358 0,058096 0,056686 0,054850 0,045599 Sample Variance 0,005071 0,003946 0,003248 0,003056 0,002787 0,003176 0,003375 0,003213 0,003009 0,002079 Kurtosis 1,506193 4,132943 2,343140 3,063591 1,561632 1,977765 2,250386 2,009895 2,199679 1,416834 Skewness -0,030638 0,053547 -0,277016 -0,676124 -0,260496 -0,567427 -0,214794 -0,298631 -0,482473 -0,557050 Count 168 168 168 168 168 168 168 168 168 168 Confidence Level (95,0%) 0,010847 0,009568 0,008681 0,008421 0,008041 0,008584 0,008849 0,008634 0,008355 0,006946
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Table 4
T-statistics between each portfolio’s monthly returns from difference of means test
This table reports t-statistics between each portfolio’s monthly returns over the whole period from July 1999 to June 2013. The results come from Excel’s Difference of Means Test assuming unequal variances. The null hypothesis of the test is that the difference of mean values of each pair of post-ranking portfolios’ monthly returns equal zero. The alternative hypothesis is non-zero difference of means. Thus, this difference of means test is a two-tailed t-test. Critical t-values under different confidence levels are as follows: 90% confidence level – 1.645, 95% confidence level – 1.960, 99% confidence level – 2.576. Generally, under 95% confidence level, the null hypothesis is rejected if t-statistic < -1.960 or t-statistic > 1.960. However, the t-values in this table are not statistically significant so that there is not sufficient evidence to reject the null hypothesis.
T-statistics* Portfolio 1 Portfolio 2 Portfolio 3 Portfolio 4 Portfolio 5 Portfolio 6 Portfolio 7 Portfolio 8 Portfolio 9 Portfolio 10
Portfolio 1 - -0,943570 -0,936550 -0,583645 -0,584425 -1,078045 -0,720267 -1,350250 -0,643977 -0,721886 Portfolio 2 -0,943570 - 0,049219 0,441939 0,460553 -0,098408 0,249953 -0,393571 0,380281 0,367882 Portfolio 3 -0,936550 0,049219 - 0,413162 0,432696 -0,155693 0,211486 -0,466196 0,348136 0,334023 Portfolio 4 -0,583645 0,441939 0,413162 - 0,010590 -0,573613 -0,194446 -0,887586 -0,067646 -0,117569 Portfolio 5 -0,584425 0,460553 0,432696 0,010590 - -0,596900 -0,208959 -0,917728 -0,079832 -0,132382 Portfolio 6 -1,078045 -0,098408 -0,155693 -0,573613 -0,596900 - 0,366822 -0,312697 0,508838 0,508443 Portfolio 7 -0,720267 0,249953 0,211486 -0,194446 -0,208959 0,366822 - -0,673727 0,129237 0,097063 Portfolio 8 -1,350250 -0,393571 -0,466196 -0,887586 -0,917728 -0,312697 -0,673727 - 0,824201 0,850236 Portfolio 9 -0,643977 0,380281 0,348136 -0,067646 -0,079832 0,508838 0,129237 0,824201 - -0,044264 Portfolio 10 -0,721886 0,367882 0,334023 -0,117569 -0,132382 0,508443 0,097063 0,850236 -0,044264 - *Degrees of freedom > 300
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Table 5
Risk-adjusted performance of WW index post-ranking portfolios’ returns
This table presents the estimated annualized alphas and market betas of the 10 portfolios ranked by WW index using CAPM and Fama-French 3 Factor Model, as analytically discussed in Section 4.2. Column 2 to 6 present the results for unconstrained portfolios with lower 50% level of financial constraints risk (portfolio 1 to 5). Column 7 to 11 present the results for constrained portfolios with higher 50% level of financial constraints risk (portfolio 6 to 10). The annualized alpha equals monthly alpha multiplied by 12. The corresponding t-statistics are reported in parentheses under the alphas and betas. *, **, and *** indicate statistical significant under 90%, 95% and 99% confidence levels, respectively. R-squared reflects the goodness of fit of the regression models. A higher R-squared value indicates that the model is more accurate and reliable to explain the past performance and predict future outcomes.
Panel A: Jensen’s alphas from CAPM
Portfolio 1 Portfolio 2 Portfolio 3 Portfolio 4 Portfolio 5 Portfolio 6 Portfolio 7 Portfolio 8 Portfolio 9 Portfolio 10
CAPM alpha (% p.a.) -0,28 7,98 8,27 4,57 4,77 8,82 6,84 11,01 5,33 6,42
(-0,05) (1,86)* (2,25)** (1,32) (1,44) (2,59)** (2,02)** (3,33)*** (1,67)* (2,52)**
Market beta*** 1,11 1,05 0,99 0,99 0,95 1,03 1,09 1,07 1,03 0,87
(10,98) (12,62) (13,89) (14,69) (14,66) (15,61) (16,52) (16,69) (16,67) (17,69)
R-squared 0,43 0,50 0,54 0,57 0,57 0,60 0,63 0,64 0,63 0,66
