Bachelor Thesis, 2015
32 Pages, Grade: 1,3
I. List of Tables
2. Quality Measures and the Gordon Growth Model
3. Performance of Quality based on 10 Quality-ranked Portfolios
4. The pricing of HML, SMB and UMD
5. The QMJ factor and different economic environments
6. QMJ and the Sentiment Index
7. QMJ and the Q-factor Model
Table I - Performance of Quality
Table II - Pricing HML, SMB and UMD
Table III - QMJ Factor and Sub-periods
"That is quite common sense” are among the most frequent words the author has come across in conversations about this topic. To buy securities of good quality and to sell securities of bad quality certainly seems to be a very intuitive approach. So intuitive that most people would agree that a high- quality company has characteristics that would justify a higher price for its stocks. In their recent paper, Asness, Frazzini, Pedersen (2014) (hereafter Asness et al.) have not only shown that quality characteristics are persistent, but also that they indeed do lead to higher prices of stocks, even when scaled by book values. It is therefore even more surprising that this obvious strategy, "a quality-minus-junk (QMJ) factor that goes long high-quality stocks and shorts low-quality stocks earns significant risk-adjusted returns” (Asness et al., 2014, p.1). More specifically, we will see that both abnormal returns, characterized as alpha, and excess returns, characterized as returns above the risk-free rate, are consistently high for any of the 3 major asset-pricing models. Their important findings, their holistic approach to quality, through the implementation of a single quality score per stock rather than single measures of quality, such as high profitability or low leverage, and the design and implementation of the QMJ factor will certainly lead to much more work and research into this direction. This particular thesis is going to go through the main findings and observations that Asness, Frazzini and Pedersen have made in their research on the QMJ factor and is also going to extend on some further examination of QMJ. We will use the upcoming chapter to briefly discuss the intuition behind using the Gordon Growth Model as the basis of the quality score and the four main quality measures which are derived from it and which were used in the design of the QMJ strategy. The decision to use that model was certainly not part of a random process in such a major research project. Chapters 3, 4 and 5 are dedicated to retest the findings using three years of additional data and its most recent updates as of May 2015, as the entire history of data is updated as soon as changes to it occur (AQR Capital Management, LLC, 2015). In Chapter 3 we will test performance for different levels of quality. Chapter 4 will focus on the role of the QMJ factor in the pricing of other risk-model factors and in Chapter 5 we analyze QMJ for different economic environments. From there on we will add new aspects to our analysis. In Chapter 6 we are going to see how the QMJ strategy has performed during different levels of the Sentiment Index and the last Chapter 7 is going to deal with the Q-factor model to see how well it does to explain the QMJ factor performance. There are three main questions that are pursued and dealt with in this thesis. 1. What has changed in terms of the main findings for the QMJ strategy with the new and updated data? 2. The price of quality and the premium paid for higher quality constantly changes, especially for different market cycles and environments (Asness et al., 2014). It would therefore be interesting to see what one of the most popular measures of market sentiment, the Sentiment Index by Baker and Wurgler (2006) can tell us about the QMJ factor and vice versa. Is there any potential relation between the two? 3. As we will see, the QMJ factor returns are very high and beyond the scope of market efficiency. This however, could be a statistical problem that lies within the conventional risk-models. Is the Q- factor model, which, according to their authors Hou et al. (2014), is said to be better at explaining anomalies in security returns, able to do so?
This thesis and the work that it analyses is mainly based on the idea of grouping securities into high and low quality. Consequently, one of the most essential questions and tasks is to define what a high quality security actually is. This in turn will always be subject to a certain degree of personal opinion and subjectivity and an easy target for academic criticism, for example with regard to data mining. A solid theoretical model and an objective approach is crucial for the success of this research project. And to use the Gordon Growth Model is a good way to achieve this. Asness et al. (2014) justifiably argue that a quality security possesses characteristics that investors should be willing to pay a higher price for. The Gordon Growth Model is all about that; input variables that lead to a certain price. This model is well known and an early part of academic programs in the field of finance and economics. It is mathematically solid and well accepted and therefore an effective tool to achieve this objectivity. But the output of the formula, the price, is an absolute value. To make prices comparable, easy to analyze and "more stationary over time and in the cross section”, Asness et al. (2014, p.3) scale prices by their book values. Dividing by a stock’s book value and multiplying by (profit/profit) leads to the following formula which forms the basis for the subsequent definition of quality (Asness et al., 2014, footnote 1).
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The resulting variation of the Gordon Growth Model, which is just a "special case of a general present-value relation” (Asness et al., 2014, footnote 2), mathematically confirms what intuition suggests should be a quality characteristic that leads to higher prices. The first part of the numerator represents a companies’ profitability, which is profit per unit of book value. A high quality company is able to generate more profits for a given book value than lower quality companies, all else being equal. The second part of the numerator is the payout ratio, which is the amount of net payouts distributed to shareholders as a fraction of total profits. Although relevant for all quality measures discussed here, Asness et al. (2014) particularly emphasize the ceteris paribus assumption for this payout measure. If a high payout ratio will lead to weak performance in the future, e.g. because of lower growth or efficiency, it will have a negative effect on the other quality characteristics. So all else equal, high payout companies are seen as more shareholder friendly, with a reduced risk of possible agency problems between shareholders and management (Jensen, 1986, (as citend in Asness et al., 2014)). Growth is self-explanatory with the idea here that a fast-growing company should be superior to a slower-growing company, again, all else being equal. As taught in many finance courses early on, required return is generally related to risk. Riskier projects demand or should yield higher required returns, while low- risk projects generally require lower returns. The quality measure that Asness et al. (2014) use here is safety. Both naturally and mathematically, as described in the formula, investors should be willing to pay a quality premium for stocks with lower required returns, as they are safer, or in other words less risky. So what are the advantages of this approach, as the possible reason and intuition behind using the Gordon Growth Model in this research project? As mentioned earlier, it is a mathematically rigid and a well-known and accepted concept which does not leave a lot of room for subjectivity. But even if there should be some room for subjectivity, it is counteracted by a second important advantage. Through the above mentioned formula manipulation, we have arrived at four different inputs and four proxies of quality, which should all lead to a higher price. Moreover, each quality measure itself is described by several quality variables, with more than 20 quality variables in total that are used to arrive at one total quality score (see Asness et al., 2014, p. 10). The high number of variables ensures that, even if there are errors in measurement, inadequate quality measures or extreme values in the data sample, the average of these variables, which leads to one quality score per company, will yield a solid and robust assessment of quality. Not necessarily with an easy absolute interpretation, but, more importantly, with an easy comparison of companies with each other, which is the cornerstone of designing the QMJ factor.
In this chapter we are going to have a look at the returns of quality and see what kind of results we get with the new and updated data. This chapter is mainly going to replicate and check the findings of Asness et al. (2014) as summarized in Table IV of their paper and any reference or comparison in this chapter directly refers to that table. In order to enhance comparability, the set-up of the table was replicated as well. The raw data for the QMJ factor, portfolios and factor returns was provided by AQR Capital Management, LLC, 2015 and has about two more years of additional observations, but lacks the time period Jun 1956 to July 1957 and now spans from July 1957 to February 2015, in comparison to the time span in the working paper of 2014. This will hold true for all the tables unless stated otherwise. Asness et al. (2014) have worked on both a longer US sample and a shorter Global sample from 1986 to 2012. The focus of this thesis will be the US sample only. Table I below captures the most important numbers of this analysis. Appendix A2 displays the original table for comparison.
Table I - Performance of Quality
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As in the original table, Beta is the realized loading on the market portfolio. This number, the ratios and the Adjusted R2 all pertain to the 4-factor regressions. Returns and alphas are in monthly percent and bold numbers indicate statistical significance at the 5% level. Ratios were annualized (see footnote 1 and 2). It is also necessary to note that Q-factor model regressions are based on 504 observations as opposed to 692 for the entire sample, as data for the Q-factor model is readily available for the time span January 1972 to December 2013. The first clear observation is that the numbers are different, which is not surprising given the fact that we have about three years of additional data. Some numbers, however, differ to such an extent that at a first glance seems to be hard to explain by the simple addition of two more years of data for a total time span of about 59 years, although the last couple of years certainly were very special for the financial markets under the influence of unprecedented monetary policy. A detailed analysis of this is beyond the scope of this thesis. The remaining difference is most likely attributable to the constant change and improvement of the data gathered, both on behalf of the databases and Asness et al. (2014) themselves. A quick analysis of excess returns that omit the latest two years confirms this, as returns are consistently lower for all eleven portfolios (See Appendix A1). But this is not too much of a problem as the underlying trend and message of this analysis still holds fundamentally true. High quality leads to higher performance and outperforms the lower quality portfolios by a significant margin. Excess Returns are very low for the lowest quality stocks and there is a sudden increase from portfolio 3 onwards accompanied by statistical significance. From there on it increases more or less steadily to its maximum for portfolio 10. Controlling for various risk factors of the four different riskmodels leads to an even stronger result. Abnormal returns are very negative for lower quality portfolios and increase almost linearly to, again, their maximum for portfolio 10. Asness et al. (2014) point to the fact that a steady reduction of factor and market exposure is potentially the main reason for this. More detailed information on these factor loadings is not available in the original work (Appendix A3 provides an overview on these numbers as generated for this analysis). As assumed, an increase in quality, as described by the quality score, leads to a reduction of market exposure, also shown in Table I by the decreasing beta, and, more astonishingly, to an almost complete elimination of SMB exposure. This suggests that small stocks on average tend to be stocks that receive a lower quality score as defined by Asness et al. (2014). And apparently, this reduction mostly enables this significant abnormal returns. But in general, the change in abnormal returns is not very profound for the portfolios in the "middle”. For portfolios P5 to P8 alphas are more or less around 0 and mostly not significant. It appears that for a significant outperformance it is crucial to identify the very extremes of quality. In fact, buying the highest ranked and shorting the lowest ranked (the H-L portfolio), leads to very high alphas and very solid performance ratios, at least using these risk models, which gives a lot of room for additional thought and analysis on risk models and market efficiency, especially because the regressions show very strong explanatory power, as shown by the Adjusted R2 numbers. Asness et al. (2014) mention that one explanation for that could be that the common models fail to capture certain risks factors. One important addition in this thesis is therefore the application of an additional risk model. We have used the relatively new Q-factor model as designed and described by Hou et al. (2014). As we can see, the results are less strong than described above, which is very surprising given the initial very solid performance among all risk models. The slightly lower and only significant alpha, both statistically and literally, is observable for portfolio 10. The abnormal returns for the lowest two portfolios are significantly less negative than for the other models. It is also very interesting to observe that, for portfolios 3 to 9, there seem to be no abnormal returns whatsoever and also no effect of rising quality on performance, as alphas remain very flat around 0 and do not move into any clear direction. Potentially, the Q-factor model possesses factors that are able to explain the abnormal returns that Asness et al. (2014) have found. We will come back to this issue in Chapter 7.
In this chapter as well, we are going to replicate an important analysis of the QMJ factor that Asness et al. (2014) summarized in Table IX of their paper (please see Appendix A4 for detailed comparison). We follow the same approach as in Chapter 3 and the format of the numbers is the same as in Table I of this thesis. Namely, the set-up and the name of the table are the same as in the original paper. Numbers are monthly, except for the ratios, which were annualized. Here as well, we try to explain each of the three factors that, apart from the market factor, comprise the 4-factor model with each other both with and without the QMJ factor. Table II below summarizes the most important numbers.
Table II - Pricing HML, SMB and UMD
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Unlike the original numbers, the new data does not show significant excess returns for the SMB strategy and even lower returns of about 10 basis points, with an equally low and insignificant alpha. One could have expected a slightly better result, given the extremely bullish market environment for stocks in the past 2 years, which naturally is a supportive environment for small stocks. But a quick analysis (see Appendix A5) of the SMB excess returns from Jan 2013 onwards even shows negative returns (although not statistically significant) which mostly explains the lower number and actually seems to confirm that the size effect on its own just "appears to be a fluke” (Asness et al., 2014, p. 25). But the most important observation and confirmation is that controlling for quality, adding the QMJ factor on the right- hand side of our regression, allows to generate relatively good results.
Adding a substantial amount of "quality stocks” to a small stock investment, or another interpretation, buying small stocks of good quality helps to turn the SMB strategy into a significantly profitable strategy with monthly abnormal returns of 50 bps and a high Information Ratio. The value factor HML, which already shows high alphas, although again, much lower than with the original data sample, experiences a similar improvement when adding the QMJ factor, with a very high Information Ratio of 1. Asness et al. (2014) refer to a similar potential explanation for this as well. As for the SMB factor, high book- to-market stocks, or cheaper stocks, tend to be of lower quality, as some or many certainly are cheap for reasons of financial or operational distress.
 Sharpe Ratios were calculated manually according to the [Abbildung in dieser Leseprobe nicht enthalten] of Excess Returns As we need annualized values, we multiply by 12 and V12 for the standard deviation, as the underlying data is monthly. We use the Stata output “mean” for Excess Returns and “Std. Dev.” of the command “summarize”.
 Information Ratios were calculated manually according to the formula: [Abbildung in dieser Leseprobe nicht enthalten].
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