Master Thesis
Exploiting Corporate Governance
Characteristics in Portfolio Optimization
PAWEŁ ORZECHOWSKI *
Rijksuniversiteit Groningen – Faculty of Economics and Business
February 12, 2012
ABSTRACT
This paper analyzes the impact of incorporating the information about the quality of firm-level corporate governance, proxied by Gov-Score of Brown and Caylor (2004), in optimal asset allocation problem on optimal portfolio weights and portfolio performance using the approach of Brandt, Santa-Clara and Valkanov (2009). The results are vague: an improvement in terms of returns undermined with high standard deviation of returns and high turnover. Only the portfolio calculated using size, momentum and the quality of corporate governance consistently outperforms the equally-weighted portfolio and the optimal portfolio calculated using size and momentum in terms of returns, Sharpe ratio and turnover. (JEL: G11, G12, G34)
Keywords: portfolio optimization; stock characteristics; corporate governance.
The increasing list of literature on the effects of the quality of corporate governance on firm performance or stock returns indicates the importance of the topic. The investors taking an investment decision want to be assured that their interests will be protected and the company is steered in the right direction. The confirmation can be found analyzing corporate governance mechanisms, which set the balance between shareholders and
management. Despite the importance of corporate governance in asset allocation, the literature lacks a study implementing it in portfolio weights optimization. This paper addresses the deficit: using Brandt, Santa-Clara and Valkanov (2009) approach it discusses the impact of incorporating the information about the quality of firm-level corporate governance in asset allocation problem on optimal portfolio weights and portfolio performance.
Asset allocation literature is overwhelmingly dominated by models based on the traditional mean-variance approach of Markowitz (1952). Despite the effort that has been put in improving the Markowitz model, its out-of-sample performance remains relatively poor. The most prominent enhancements are summarized in DeMiguel, Garlappi and Uppal (2009), including Bayesian approaches to estimation error, moment restriction strategies, short-sell constrained portfolios and portfolios that combine other portfolios and allocate across them. In the study the performance in terms of the Sharpe ratio, the certainty-equivalent returns and the turnover of the abovementioned models is tested. The results from the comparison to the naïve equally-weighted portfolio suggest that the estimation errors of means and variances undermine any gains from optimal allocation, despite a number of refinements. Nevertheless, the authors suggest that more effort needs to be devoted to exploiting cross-sectional characteristics of assets. As an example of such approach they present the model by Brandt, Santa-Clara and Valkanov (2009), in which portfolio weights in each stock are set as a function of firm’s cross-sectional price-based characteristics: size, book-to-market value ratio and momentum. Due to the superior performance of the model, DeMiguel, Garlappi and Uppal (2009) suggest that exploiting stock characteristics in asset allocation may be a promising path. This paper addresses that suggestion.
recent scandals including Adelphia, Enron and WorldCom put an emphasis on the quality of corporate governance and resulted in policy makers concentrating on imposing higher standards. The Sarbanes-Oxley act of 2002 is one of the effects of the works.
Good corporate governance assures that the management acts in the interest of shareholders and leads to higher valuation, profits, sales growth, lower capital expenditures and fewer corporate acquisitions (Gompers, Ishii and Metrick (2003)). Good corporate governance attracts new investors, who provide new funds to the company. Those funds allow the company to undertake new profitable opportunities, grow and create value. Therefore, good governance reduces agency costs. On the other hand, well governed company may appear less risky to the investor, making him expect lower returns. Recent studies show that firm-level corporate governance mechanisms have an important impact on firm performance. The studies of Gompers, Ishii and Metrick (2003), Larcker, Richardson and Tuna (2007) and Cremers and Ferrell (2009) are the cornerstones in explaining the relation between corporate governance and performance. Moreover, Carvalhal and Nobili (2011) include a corporate governance index in Fama and French (1993) framework to study Brazilian stock returns. They find that corporate governance has a strong explanatory power.
In spite of the importance of firm-level corporate governance and the attempts to include it in asset pricing literature, the literature on portfolio management lacks a study which would incorporate it. Thus, I propose a model in which:
portfolio weights are parameterized as a function of stock characteristics and
corporate governance characteristic is incorporated.
According to the suppositions from the previous literature a portfolio build with such model will not only overperform the market but also give weights that are more stable over time reducing turnover and therefore transaction costs.
governance factor in asset allocation problem has a strong impact on optimal portfolio weights and portfolio performance. Moreover, I question and test the explanatory power of the characteristics, whereas usually the significance of the characteristics is taken for granted. Based on the results I build portfolios calculated based only on significant variables.
The research presents that when all four characteristics (size, marker-to-book value ratio, momentum and the quality of corporate governance) are included in the calculation of optimal weights of a long-short portfolio the average annualized returns are around three times greater than from the price-based portfolio of Brandt, Santa-Clara and Valkanov (2009) and twenty one times greater than from the equally-weighted portfolio. The increase in the returns is however undermined by more than proportional increase of volatility leading to the lowest Sharpe ratio among the three portfolios. I find it to be a result of extreme weights in the examined portfolio. Moreover, the portfolio assumes extremely short positions in quality corporate governance stocks and has extreme turnover. Imposing no-short-sale constraint leads to deterioration of returns: the returns from the portfolio of interest are higher than from the equally-weighted portfolio but lower than from the Brandt, Santa-Clara and Valkanov (2009) portfolio. Nevertheless, an improvement can be seen in volatility, making the portfolio’s Sharpe ratio rank second, weights and turnover, which is substantially lower than for the Brandt, Santa-Clara and Valkanov (2009) portfolio.
-Last but not least, the parameter estimates and the weighted portfolio characteristics are more stable in specifications including corporate governance characteristic, suggesting that an optimal portfolio has a specific set of values of the characteristics and the quality of the corporate governance plays an important role in it.
The remainder of this thesis is organized as follows. Section I presents the overview of the literature relevant for this study. The methodology that is used to calculate and test the performance of the portfolios is described in Section II, whereas Section III contains the description of the data and the characteristics used in the study. Section IV presents the results of the analysis and section V concludes the paper.
I. LITERATURE OVERVIEW
Santa-Clara’s and Valkanov’s model as an alternative to moments exploiting approaches and find that it outperforms the equally-weighted portfolio in terms of Sharpe ratio. They conclude that exploiting information about cross-sectional characteristics of assets lead to an improvement in asset allocation and suggest that this may be a promising path.
provisions out of 24 appearing in the G-index. The results of the study show a strong positive relationship between good governance and firm valuation, and between good governance and abnormal stock returns.
An approach towards including corporate governance factors in asset management is presented in Carvalhal and Nobili (2011). They incorporate corporate governance factor, build in a similar way to the aforementioned G-Index, in Fama and French three-factor model and investigate Brazilian stock returns. They document evidence for strong explanatory power of the governance factor. According to their results it is in fact more powerful than firm size and book-to-market ratio in explaining stock returns.
The next section of this paper presents parametric portfolio policy approach of Brandt, Santa-Clara and Valkanov (2009), which is used to calculate optimal portfolio weights. Moreover, the section describes the methodology used to evaluate the performance of the portfolio calculated using corporate governance characteristics.
II. METHODOLOGY
The core of the methodology is based on the approach presented in Brandt, Santa-Clara and Valkanov (2009). In the approach the main problem is the maximization of the investor’s expected utility from the portfolio’s return by choosing optimal portfolio weights . The problem can be presented as follows:
[ (
)]
[ (∑
)]
,
where t denotes date, the number of available stocks at date t with a return of from date t to t+1 each and described by a vector of stock characteristics .
The approach parameterizes optimal portfolio weights as a linear function of stock characteristic. The function used in this paper can be generally presented as follows:
(
) ̅
̂
,
where ̅ is the weight of stock i at date t in a benchmark portfolio, is a vector of coefficients that are estimated by maximizing the expected utility (1) and ̂ are
cross-(1)
sectionally standardized characteristics of stock i at date t. The benchmark portfolio used in this paper is the equally-weighted portfolio. The choice is dictated by the findings of DeMiguel, Garlappi and Uppal (2009) showing that none of the 14 optimal asset allocation models studied in the research consistently outperform the equally-weighted portfolio.
The coefficients of the optimal weights function are estimated by maximizing the investor’s average utility from the portfolio’s return over the historical period in the case of the policy from equation (2). The final problem can be presented as:
∑
(∑
( ̅
̂
)
)
.
The investor’s preferences over wealth are assumed to be described by a power utility function specified as follows:
( )
( )
,
with the constant relative risk aversion coefficient of five. The choice of the utility function is arbitrary, as the approach can be applied to any objective function having a unique solution, including maximum Sharpe ratio, minimum variance or behavioral utility functions.
The parameterization enables the weights to be dependent on the stock characteristics rather than on the historical returns and variance. That fact makes the approach appealing from the theoretical point of view: two stocks of exactly the same characteristics should be expected to have the same returns, regardless of their historical performance. The reasoning is in line with the Capital Asset Pricing Model or the three-factor model of Fama and French (1996). Moreover, the model encapsulates the long -short portfolio approach of Fama and French (1993), extended further in Fama and French (1996), Carhart (1997), or Carvalhal and Nobili (2011). The regression equation studied in the latter can be expressed as follows:
(3)
(4)
where are the returns of each portfolio formed based on size, book-to-market value ratio and the quality of corporate governance, are the returns of the market portfolio and is the risk-free rate, in month t. SMBt, HMLt, WMLt and PMGt are the returns of
portfolios based on size (small minus big), book-to-market value ratio (high minus low), momentum (winners minus losers) and corporate governance (poor minus good) respectively, in month t. In the parametric portfolio policy of Brandt, Santa-Clara and Valkanov (2009) (1) with the linear parameterization (2) the model of Carvalhal and Nobili (2011) (5) can be reflected if the benchmark portfolio weights are the market value weights and the characteristics in vector are defined as 1 if the stock is in the top 30%, -1 if the stock is in the bottom 30% and 0 if the stock is in the remaining 40% of all the stocks at time t ranked based on market value, book-to-market value ratio, momentum and the quality of corporate governance. The return of the portfolio at date t can be then expressed as:
∑
∑
∑
∑
,
where is the return on market portfolio, , , , are the returns of the portfolios based on size (small minus big), book-to-market value ratio (high minus low), momentum (winners minus losers) and corporate governance (poor minus good) respectively and , , , are the coefficients.
in the original specification of Brandt, Santa-Clara and Valkanov (2009) and are used in this paper to form a benchmark portfolio for the evaluation of the effect of incorporating corporate governance, proxied by Gov-Score, in the portfolio weights optimization. The inclusion of a corporate governance factor is a novelty in portfolio optimization problems and directly follows the results of Gompers, Ishii and Metrick (2003), Brown and Caylor (2004), Larcker, Richardson and Tuna (2007), Cremers and Ferrell (2009) and Carvalhal and Nobili (2011) on the effect of firm-level corporate governance measures on returns, valuation and performance. The last study concludes that corporate governance factor is more powerful in explaining stock returns than size and book to market ratio. Therefore, the paper presents the results for two specifications: including all four factors and including only those factors that are proven to be significant in a regression analysis over the entire sample: size, momentum and corporate governance. The regression description and the results are presented in Appendix A.
Moreover, the study presents the results for both short portfolios and long-only portfolios. The weight of stock i at date t in the long-long-only portfolio is calculated by truncating the optimal weights from Equation (1) at zero and dividing them by the sum of all truncated weights:
∑
.
The optimal portfolio weights and the portfolio returns in month t are calculated by solving problem (3) on a subsample consisting of data for months from 1 to t-1. The procedure is then repeated twelve times to obtain weights and returns in months T-11 to T, where T is the last month in the sample. Subsequently, the resulting portfolios are tested by comparing their out-of-sample performance to the performance of equally-weighted portfolio in terms of returns and Sharpe ratio following the approach of DeMiguel, Garlappi and Uppal (2009). Moreover, standard deviation of the returns, minimal and maximal weights, average portfolio parameters and weighted characteristics, the sums and percentages of negative weights (only for long-short portfolios) and the turnovers of the portfolios are presented. All the calculations described above are executed in MathWorks MATLAB. The code written by the author is provided in Appendix B.
The following section describes the construction of the characteristics used in portfolio optimization, presents the data used in the study and shows several descriptive statistics.
III. DATA
The following stock characteristics are used in the research: returns, market value, market-to-book value ratio, momentum and the Gov-Score for each stock are used. The returns (r) at time t+1 are the returns calculated as a logarithm of stock price at time t+1 divided by the price at time t. Market value (MV) at time t+1 is a logarithm of the company’s share price multiplied by the number of ordinary shares in issue expressed in millions at time t. Market-to-book value ratio (MTB) used at time t+1 is a logarithm of the company’s market value of the company’s common equity divided by its book value at time t. Momentum (MOM) at time t+1 is defined as lagged one-year log returns on the stock between months t-2 and t-13. Gov-Score (GOV) is an index describing the quality of firm-level corporate governance and can assume values ranging from 0 to 51. Each point is added for a good governance practice in a given category. The Gov-Score for February each year is used as a stock characteristic from August that year to July next year. Leaving the lags makes it certain that the information is available to all the investors and therefore, is reflected in the returns.
Monthly data for stock prices, market values and market -to-book ratios for companies listed on NYSE and NASDAQ are obtained from Thomson Reuters Datastream. Gov-Scores are taken from a database used in Brown and Caylor (2004) and Brown and Caylor (2006), which contains the results for 2,538 firms as of February 1, 2003, 2,749 firms as of February 1, 2004, and 3,258 firms as of February 1, 2005. Gov-Scores are based on the information on corporate governance provided by Institutional Shareholder Services and can be used freely.
TABLEI SUMMARY ST ATISTIC S Mean Std. Deviation Minimum 25th Percentile Median 75th Percentile Maximum r 0.004 0.056 -0.649 -0.019 0.005 0.029 0.716 MV 1.307 0.361 -1.000 1.114 1.350 1.538 3.322 MTB 0.530 0.188 0.057 0.403 0.494 0.617 1.911 MOM 0.068 0.165 -1.027 -0.013 0.059 0.141 1.447 GOV 26.8 5.6 14 22 26 31 43
The table presents summary statistics (mean, standard deviation, minimum, 25th percentile, median, 75th percentile and maximum) for non-normalized data used in the study (908 stocks listed on NYSE or NASDAQ in the period between August 2003 and July 2006) : returns (r) defined as log of price in month t+1 divided by price in month t, log of market value (MV) in month t, market-to-book value (MTB) in month t, momentum (MOM) defined as lagged one-year log returns on the stock between months t-2 and t-13and finally governance-score (GOVGov-Score from February each year is used as a stock characteristic from August that year to July next year.
Table I and Figure 1 present several summary statistics for non-standardized data. We can see that the data represents a bull market with positive average returns of 0.004 over the entire sample period and with positive returns in the majority of the months in the sample. From Figure 1 we can see that the standard deviation of returns w as consistently decreasing over the sample period. Moreover, market value, market-to-book value ratio and the Gov-Score were increasing over the entire sample period. The behavior of the Gov-Score can be attributed to the Sarbanes-Oxley act: companies were pressured to implement new corporate governance provisions, which explains the increase of the average Gov-Score. However, from the plot of its standard deviation (Figure 1) we see that not all of the companies were able to accommodate to the new legal act, which explains the increase of standard deviation of the Gov-Score in August 2004. Furthermore, the average value of momentum was positive in the majority of the periods, with an interesting hump in the middle of 2004 and decreasing standard deviation over the entire sample period.
FIGURE1
PLOTS OF CR OSS-SECTI ON AVE R AGE V ALU E S OF V ARI AB LES
The figure shows plots of cross-sectional averages (left column) of characteristics and their standard deviations (right column) for non-normalized data used in the study (908 stocks listed on NYSE or NASDAQ in the period between August 2003 and July 2006) : returns (r) defined as log of price in month t+1 divided by price in month t, log of market value (MV) in month t, market-to-book value (MTB) in month t, momentum (MOM) defined as lagged one-year log returns on the stock between months t -2 and t-13and finally governance-score (GOV,Gov-Score) from February each year is used as a stock characteristic from August that year to July next year.
This property is highly required, as it allows taking asset allocation decisions based on the parameters estimated based on historical data and applying those parameters to current firm characteristics.
The next section presents the results of the analysis for two assumptions: the investor believes that all characteristics (size, market-to-book ratio, momentum and the quality of corporate governance) are significant and the investor rationally questio ns the significance of the characteristics and chooses only the significant for the purpose of portfolio optimization.
IV. RESULTS
A. All Factors
This subsection describes the results for the portfolio of interest, in which the weights put in each stock depend on its size, market-to-book value ratio, momentum and the quality of corporate governance. The portfolio is compared to the model, in which weights are functions of the factors used in Brandt, Santa-Clara and Valkanov (2009): size, market-to-book value and momentum. Moreover, two types of portfolio s are discussed: allowing short-sales and restricting them.
weights’ deviations from 1/N weights increase in size, market-to-book value ratio and momentum and decreases in the quality of corporate governance. The differences in coefficients between the two models are reflected in the average weighted characteristics (standardized) of the optimal portfolios presented in rows five to eight. The governance -based portfolio overweighs size and momentum stocks and underweighs market-to-book value and good governance stocks, relative to the price-based portfolio.
TABLEII
LON G-SHORT PORTF OLI OS
Parametric Portfolios EW PB GB ̅MV - 8.6623 82.9648 ̅MTB - 14.0789 1.6185 ̅MOM - -8.0745 16.1236 ̅GOV - - -176.5161 MV 0.0000 8.3837 19.7720 MTB 0.0000 13.0415 7.7374 MOM 0.0000 -2.8455 25.9059 GOV 0.0000 3.2392 -144.0869 ̅ 0.0553 0.4012 1.1951 ( ) 0.0154 0.0464 0.3580 SR 3.5806 8.6434 3.3380 min 0.0011 -0.0849 -0.5160 max 0.0011 0.1195 0.6198 ( ) - -5.9910 -68.8703 ( ) - 0.5060 0.4994 | | - 3.7533 32.6762
The table presents the estimates of the equally-weighted portfolio (EW), an optimal portfolio generated by price-based characteristics (PB): market value, market-to-book value ratio and momentum, and an optimal portfolio generated by the price-based characteristics plus the governance-based characteristic (GB): Gov-Score. The results are optimized for a power utility with a relative risk aversion of five using data for 908 stocks listed on NYSE or NASDAQ in the period between August 2003 and July 2006. The data from August 2003 to July 2005 is used to estimate the coefficients of the optimal portfolio for August 2005. In every subsequent month the coefficients are recalculated extending the sample. The values in the table are reported for the period between August 2005 and July 2006. The first four rows present the average coefficient estimates for market value, market-to-book value ratio, momentum and Gov-Score of optimal portfolios. The subsequent four rows present the average weighted values of the characteristics. Rows nine to eleven report on the average annualized portfolio returns, the standard deviations of returns and Sharpe ratios. The following five rows show average portfolio weights’ statistics: minimal, maximal weights, the sum of negative weights, the fraction of negative weights in the portfolio and the turnover of th e portfolio.
to 5.53% for the equally-weighted portfolio. The returns for the governance portfolio are even more impressive: 119.51%. Nevertheless, the returns are obtained by an aggressive policy: the standard deviation (tenth row) for the portfolio equals to 35.80%, as opposed to 4.64% for the parametric portfolio and 1.54% for the equally-weighted portfolio. The huge difference in standard deviations is reflected in the values of the Sharpe ratio presented in the eleventh row (labeled SR) of table II. We can see that the Sharpe ratio for the parametric portfolio is more than double of the equally-weighted portfolio: 8.64 opposed to 3.58. The result for the governance portfolio is lower than both of these numbers: 3.34. Therefore, the increase in the returns related to the inclusion of the Gov-Score in the optimization of portfolio weights does not compensate the increase in the volatility of returns.
The explanation of the risk of the governance portfolio can be found in rows twelve through sixteen of table II, which are describing the weights of the portfolios. The minimal weights are equal to 0.11%, -8.49% and -51.60% for the equally-weighted portfolio, the parametric portfolio and the governance portfolio respectively. The maximal weights are equal to 0.11%, 11.95% and 61.98% respectively. The sum of negative weights in the governance portfolio is more than eleven times greater than in the parametric portfolio: -6887%, compared to -599%, even though the percentage of stocks assigned negative weights is lower than in the parametric portfolio: 49.94%, compared to 50.60%. These statistics prove that the allocation is very aggressive in the case of the governance portfolio leading to extreme weights. That proves the governance portfolio to be an extreme equity hedge fund offering surprisingly high returns but for the cost of more than proportional risk. Moreover, the average turnover of the governance-based portfolio (3268%) is almost nine times greater than the turnover of the price-based portfolio (375%), which leads to higher transaction costs.
the plots of weighted characteristics. That means that the expected returns for the quality governance stocks increased relative to big stock and stocks with high market-to-book value ratio.
FIGURE2
PLOTS OF T HE V ALUES OF T HET AS AND WEI GHTED C HAR ACTER ISTICS F OR T HE PRI CE-B ASED PORTF OLI O
The figure plots the values of parameter estimates (top graph) and weighted characteristics (bottom graph) of an optimal portfolio generated by price-based characteristics (PB): market value, market-to-book value ratio and momentum for the period between August 2005 and July 2006. The results are optimized for a power utility with a relative risk aversion of five using data for 908 stocks listed on NYSE or NASDAQ in the period between August 2003 and July 2006. The data from August 2003 to July 2005 is used to estimate the coefficients of the optimal portfolio for August 2005. In every subsequent month the coefficients are recalculated extending the sample. In the top graph the dash-dotted line represents the values of the coefficients for
market-FIGURE3
PLOTS OF T HE V ALUES OF T HET AS AND WEI GHTE D C HAR ACTER ISTICS F O R T HE GOVE RN ANCE
-B ASED P ORT F OLI O
The figure plots the values of parameter estimates (top graph) and weighted characteristics (bottom graph) of an optimal portfolio (GP) generated by: market value, market-to-book value ratio, momentum and Gov-Score for the period between August 2005 and July 2006. The results are optimized for a power utility with a relative risk aversion of five using data for 908 stocks listed on NYSE or NASDAQ in the period between August 2003 and July 2006. The data from August 2003 to July 2005 is used to estimate the coefficients of the optimal portfolio for August 2005. In every subsequent month the coefficients are recalculated extending the sample. In the top graph the solid line represents the values of the coefficients for market value, the dashed line represents Aug-2005 Sep-2005 Oct-2005 Nov-2005 Dec-2005 Jan-2006 Feb-2006 Mar-2006 Apr-2006 May-2006 Jun-2006 Jul-2006-15
-10 -5 0 5 10 15 20 Date P a ra m e te rs
Aug-2005 Sep-2005 Oct-2005 Nov-2005 Dec-2005 Jan-2006 Feb-2006 Mar-2006 Apr-2006 May-2006 Jun-2006 Jul-2006-10 -5 0 5 10 15 20 Date W e ig h te d C h a ra ct e ri st ics
Aug-2005 Sep-2005 Oct-2005 Nov-2005 Dec-2005 Jan-2006 Feb-2006 Mar-2006 Apr-2006 May-2006 Jun-2006 Jul-2006 -300 -200 -100 0 100 200 Date P a ra m e te rs
TABLEIII LON G-ON LY PORT F OLIOS Parametric Portfolios EW PB GB ̅MV - 8.6623 82.9648 ̅MTB - 14.0789 1.6185 ̅MOM - -8.0745 16.1236 ̅GOV - - -176.5161 MV 0.0000 0.4800 0.2325 MTB 0.0000 1.2483 0.0976 MOM 0.0000 -0.2220 0.2176 GOV 0.0000 0.1456 -1.0285 ̅ 0.0553 0.0820 0.0727 ( ) 0.0154 0.0139 0.0166 SR 3.5806 5.9091 4.3680 min 0.0011 0.0000 0.0000 max 0.0011 0.0166 0.0095 | | 0.0000 0.2652 0.1432
The table presents the estimates of the equally-weighted portfolio (EW), an optimal long-only portfolio generated by price-based characteristics (PB): market value, market-to-book value ratio and momentum, and an optimal long-only portfolio generated by the price-based characteristics plus the governance-based characteristic (GB): Gov-Score. The results are optimized for a power utility with a relative risk aversion of five using data for 908 stocks listed on NYSE or NASDAQ in the period between August 2003 and July 2006. The data from August 2003 to July 2005 is used to estimate the coefficients of the optimal portfolio for August 2005. In every subsequent month the coefficients are recalculated extending the sample. The values in the table are reported for the period between August 2005 and July 2006. The first four rows present the average coefficient estimates for market value, market-to-book value ratio, momentum and Gov-Score of optimal portfolios. The subsequent four rows present the average weighted values of the characteristics. Rows nine to eleven report on the average annualized portfolio returns, the standard deviations of returns and Sharpe ratios. The following three rows show average portfolio weights’ statistics: minimal, maximal weights and the turnover of the portfolio.
FIGURE4
PLOTS OF WEI GHTED C HA R ACTE RISTICS F OR LON G-ON LY P ORTFOLI OS
The figure plots the values of weighted characteristics) of an optimal long-only price-based (PB) portfolio generated by: market value, market-to-book value ratio and momentum (top graph) and of an optimal long-only governance-based (GP) portfolio generated by: market value, market-to-book value ratio, momentum and Gov-Score (bottom graph) for the period between August 2005 and July 2006. The results are optimized for a power utility with a relative risk aversion of five using data for 908 stocks listed on NYSE or NASDAQ in the period between August 2003 and July 2006. The data from August 2003 to July 2005 is used to estimate the coefficients of the optimal portfolio for August 2005. In every subsequent month the coefficients are recalculated extending the sample. In the top graph the dash-dotted line represents the weighted market-to-book ratio, the solid line represents the weighted market value the dotted line represents the weighted Gov-Score and the dashed line represents the weighted momentum. In the bottom graph the solid line represents the weighted market value, the dashed line represents the weighted momentum, the dash-dotted line represents the weighted market-to-book ratio and the dotted line represents the weighted Gov-Score.
B. Significant Factors Only
This subsection describes the results for portfolios generated by characteristics proven to be significant in the regression analysis described in Appendix A: size, momentum and governance. It compares the portfolio based on all three significant characteristics with the portfolio based only on significant price-related characteristics: size and momentum. Again, two types of portfolios are discussed: allowing short -sales and restricting them.
Aug-2005 Sep-2005 Oct-2005 Nov-2005 Dec-2005 Jan-2006 Feb-2006 Mar-2006 Apr-2006 May-2006 Jun-2006-1 Jul-2006 -0.5 0 0.5 1 1.5 Date W e ig h te d C h a ra ct e ri st ics
TABLEIV
LON G-SHORT PORTF OLI OS:MAR KET-T O-BOOK RATI O EXC LU DED
Parametric Portfolios EW PB GB ̅MV - 6.5336 80.3335 ̅MOM - -6.1848 15.4745 ̅GOV - - -169.7625 MV 0.0000 4.8808 19.4086 MTB 0.0000 -0.3637 6.7187 MOM 0.0000 -4.5585 24.8072 GOV 0.0000 2.0626 -138.4278 ̅ 0.0553 0.0800 1.1891 ( ) 0.0154 0.0393 0.3370 SR 3.5806 2.0330 3.5291 min 0.0011 -0.0559 -0.5099 max 0.0011 0.0518 0.6029 ( ) 0.0000 -2.7977 -65.7656 ( ) 0.0000 0.3966 0.5036 | | 0.0000 2.2733 27.7054
The table presents the estimates of the equally-weighted portfolio (EW), an optimal portfolio generated by price-based characteristics (PB): market value and momentum, and an optimal portfolio generated by the price-based characteristics plus the governance-based characteristic (GB): Gov-Score. The results are optimized for a power utility with a relative risk aversion of five using data for 908 stocks listed on NYSE or NASDAQ in the period between August 2003 and July 2006. The data from August 2003 to July 2005 is used to estimate the coefficients of the optimal portfolio for August 2005. In every subsequent month the coefficients are recalculated extending the sample. The values in the table are reported for the period between August 2005 and July 2006. The first four rows present the average coefficient estimates for market value, market-to-book value ratio, momentum and Gov-Score of optimal portfolios. The subsequent four rows present the average weighted values of the characteristics. Rows nine to eleven report on the average annualized portfolio returns, the standard deviations of returns and Sharpe ratios. The following five rows show average portfolio weights’ statistics: minimal, maximal weights, the sum of negative weights, the fraction of negative weights in the portfolio and the turnover of the portfolio.
with the ratio of 2.03. Nevertheless, it is still smaller than the Sharpe ratio of the equally-weighted portfolio. Similarly as in the case presented in table II, the reason can be seen in the extreme weights the portfolio assigns to some of the stocks. The minimal weight in the governance-based portfolio is -50.99% and the maximal weight equals to 60.29, and more than the half of the stocks are assigned negative weights. Moreover, the turnover of the portfolio is around 12 times greater than the turnover of the price-based portfolio. Taking those results into account, long-short governance-based portfolio can be again seen as a very active and risky equity hedge fund.
The coefficient estimates of the price-based portfolio suggest that positive size effects exist (6.5336), whereas the estimate for the MOM coefficient is -6.1848, thus momentum negatively affects the expected returns. Similar to the specification with all characteristics included described in the previous subsection, the inclusion of the Gov-Score in the optimization of governance-based portfolio causes the sign of the coefficient estimate for momentum switch to positive: 15.4745. Similarly, the general mag nitude of the estimates is bigger than in the price-based portfolio, with extremely low estimate for GOV: -169.7625. The behavior of the parameters and weighted characteristics over time (Figures 5 and 6) does not change either compared to the previous specification: increasing over time portfolio characteristics of the price based model and relatively stable, with one breakpoint in March 2006 for the governance-based portfolio.
FIGURE5
PLOTS OF T HE V ALUES OF T HET AS AND WEI GHTED C HAR ACTER ISTICS F OR T HE PRI CE-B ASED PORTF OLI O
(SIGNIFIC ANT V ARI AB LES ON LY)
The figure plots the values of parameter estimates (top graph) and weighted characteristics (bottom graph) of an optimal portfolio generated by price-based characteristics (PB): market value and momentum for the period between August 2005 and July 2006. The results are optimized for a power utility with a relative risk aversion of five using data for 908 stocks listed on NYSE or NASDAQ in the period between August 2003 and July 2006. The data from August 2003 to July 2005 is used to estimate the coefficients of the optimal portfolio for August 2005. In every subsequent month the coefficients are recalculated extending the sample. In the top graph the solid line represents the values of the coefficients for market value, the dash-dotted line represents the values of the coefficients for momentum. In the bottom graph the solid line represents the weighted market value, the dotted line represents the weighted Gov-Score, the dash-dotted line represents the weighted market-to-book ratio and the dashed
FIGURE6
PLOTS OF T HE V ALUES OF T HET AS AND WEI GHTED C HAR ACT ER ISTICS F OR T HE GOV E RN ANCE
-B ASED P ORT F OLI O
(SIGNIFIC ANT V ARI AB LES ON LY)
The figure plots the values of parameter estimates (top graph) and weighted characteristics (bottom graph) of an optimal portfolio (GP) generated by: market value, momentum and Gov-Score for the period between August 2005 and July 2006. The results are optimized for a power utility with a relative risk aversion of five using data for 908 stocks listed on NYSE or NASDAQ in the period between August 2003 and July 2006. The data from August 2003 to July 2005 is used to estimate the coefficients of the optimal portfolio for August 2005. In every subsequent month the coefficients are recalculated extending the sample. In the top graph the solid line represents the valu es of the coefficients for market value, the dash-dotted line represents the values of the coefficients for momentum and the dashed line represents the values of the coefficients for Gov-Score. In the bottom graph the dashed line represents the weighted momentum, the solid line represents the weighted market value, the dash-dotted line represents the Aug-2005 Sep-2005 Oct-2005 Nov-2005 Dec-2005 Jan-2006 Feb-2006 Mar-2006 Apr-2006 May-2006 Jun-2006 Jul-2006-10
-5 0 5 10 Date P a ra m e te rs
Aug-2005 Sep-2005 Oct-2005 Nov-2005 Dec-2005 Jan-2006 Feb-2006 Mar-2006 Apr-2006 May-2006 Jun-2006 Jul-2006-10 -5 0 5 10 Date W e ig h te d C h a ra ct e ri st ics
Aug-2005 Sep-2005 Oct-2005 Nov-2005 Dec-2005 Jan-2006 Feb-2006 Mar-2006 Apr-2006 May-2006 Jun-2006 Jul-2006 -250 -200 -150 -100 -50 0 50 100 150 Date P a ra m e te rs
turnover: 13.11% compared to 32.59%. Therefore, the differences in after-cost returns are even greater than for before-cost returns.
TABLEV
LON G-ON LY PORT F OLIOS:MAR KET-T O-BOOK RATI O EX C LUD ED
Parametric Portfolios EW PB GB ̅MV - 6.5336 80.3335 ̅MOM - -6.1848 15.4745 ̅GOV - - -169.7625 MV 0.0000 0.5247 0.2234 MTB 0.0000 0.0036 0.0619 MOM 0.0000 -0.5678 0.2071 GOV 0.0000 0.1467 -1.0385 ̅ 0.0553 0.0601 0.0721 ( ) 0.0154 0.0144 0.0165 SR 3.5806 4.1740 4.3597 min 0.0011 0.0000 0.0000 max 0.0011 0.0136 0.0096 | | 0.0000 0.3259 0.1311
The table presents the estimates of the equally-weighted portfolio (EW), an optimal long-only portfolio generated by price-based characteristics (PB): market value and momentum, and an optimal long-only portfolio generated by the price-based characteristics plus the governance-based characteristic (GB): Gov-Score. The results are optimized for a power utility with a relative risk aversion of five using data for 908 stocks listed on NYSE or NASDAQ in the period between August 2003 and July 2006. The data from August 2003 to July 2005 is used to estimate the coefficients of the optimal portfolio for August 2005. In every subsequent month the coefficients are recalculated extending the sample. The values in the table are reported for the period between August 2005 and July 2006. The first four rows present the average coefficient estimates for market value, market-to-book value ratio, momentum and Gov-Score of optimal portfolios. The subsequent four rows present the average weighted values of the characteristics. Rows nine to eleven report on the average annualized portfolio returns, the standard deviations of returns and Sharpe ratios. The following three rows show average portfolio weights’ statistics: minimal, maximal weights and the turnover of the portfolio.
an interesting result, as it means that a long-only optimal portfolio has its optimal characteristics that remain relatively constant regardless of the moment in time.
FIGURE7
PLOTS OF T HE V ALUES OF WEI GHTED C HAR ACTE RISTICS F OR L ON G-ON LY P ORTF OLI OS
(SIGNIFIC ANT V ARI AB LES ON LY)
The figure plots the values of weighted characteristics) of an optimal long-only price-based (PB) portfolio generated by: market value and momentum (top graph) and of an optimal long-only governance-based (GP) portfolio generated by: market value, momentum and Gov-Score (bottom graph) for the period between August 2005 and July 2006. The results are optimized for a power utility with a relative risk aversion of five using data for 908 stocks listed on NYSE or NASDAQ in the period between August 2003 and July 2006. The data from August 2003 to July 2005 is used to estimate the coefficients of the optimal portfolio for August 2005. In every subsequent month the coefficients are recalculated extending the sample. In the top graph the dash-dotted line represents the weighted market-to-book ratio, the solid line represents the weighted market value the dotted line represents the weighted Gov-Score and the dashed line represents the weighted momentum. In the bottom graph the solid line represents the weighted market value, the dashed line represents the weighted momentum, the dash-dotted line represents the weighted market-to-book ratio and the dash-dotted line represents the weighted Gov-Score.
It seems that the governance portfolio is superior to the other examined portfolios in case the investor does not believe in the explanatory power of the market-to-book value and prefers a long-only portfolio. It outperforms the equally-weighted portfolio and the basic portfolio in terms of returns and the Sharpe ratio, and has a significantly lower turnover. Therefore, it can be seen as a cost and return-volatility-effective investment fund.
Aug-2005 Sep-2005 Oct-2005 Nov-2005 Dec-2005 Jan-2006 Feb-2006 Mar-2006 Apr-2006 May-2006 Jun-2006-1.5 Jul-2006 -1 -0.5 0 0.5 1 1.5 Date W e ig h te d C h a ra ct e ri st ics
The next section concludes the paper, presents the limitations of the study and several explanations for the results.
V. CONCLUSIONS
This paper studies the impact of inclusion firm-level corporate governance, proxied by Gov-Score of Brown and Caylor (2004), in portfolio weights optimization using the framework of Brandt, Santa-Clara and Valkanov (2009), in which the optimal portfolio weights are parameterized as a function of stock characteristics. I find that the long-short portfolio calculated using size, market-to-book ratio, momentum and the quality of corporate governance assumes long positions in big stocks and extremely short positions in stocks with poor corporate governance. This leads to the average annualized returns that are around three times greater than from the price-based portfolio of Brandt, Santa-Clara and Valkanov (2009) and twenty one times greater than from the equally-weighted portfolio. However, the increase in the volatility of returns is more than proportional, which leads to inferior performance in terms of Sharpe ratio. The portfolio has extreme weights and high turnover. Imposing no-short-sale constraint reduces the returns, which for the governance-based portfolio are higher than for the equally-weighted portfolio but lower than for the price-based portfolio of Brandt, Santa-Clara and Valkanov (2009). The standard deviation of the returns decreases as well, causing the governance-based portfolio rank second in terms of Sharpe ratio. Long-only portfolio has moderate weights and low turnover: lower than the price-based portfolio.
equally-and Valkanov (2009). Additionally, the weights are modest, without extreme allocation to any stocks.
The parameter estimates and the weighted portfolio characteristics are more stable when the corporate governance characteristic is included in the optimization of the portfolio weights, especially under the long-only specification that uses only significant characteristics in the optimization of the weights. It means that the optimal portfolio has its optimal characteristics that remain stable regardless of the moment in time and that the quality of corporate governance plays an important role.
The optimal portfolio policy that includes the quality of corporate governance, proxied by the Gov-Score, in optimizing the weights allocates substantially more in poor governance stocks. It provides good performance in terms of returns in both long -short and long-only specification, both including market-to-book ratio and not. Moreover, it outperforms the other portfolios in terms of Sharpe ratio and turnover when the optimal weights are calculated using only significant characteristics and the no -short-sale constraint is imposed. However, it means that the policy enco urages low quality of corporate governance.
Another explanation is that an optimal level of the quality of corporate governance exists and passing that point has a negative effect on stock returns. From that perspective, it may be argued that the stocks forming the sample used in this study consists mainly of stocks whose level of corporate governance is higher than optimal, which would explain that the deviation from the benchmark weights increases in poor governance.
Moreover, the situation may also be explained from the agency theory perspective. The fact that the optimal weights deviation from the benchmark weights decreases in the quality of corporate governance, may be related to the fact that the implementation of new provisions, increasing the quality of corporate governance, increases shareholder protection. Therefore, the investment in high-quality corporate governance stocks can be seen less risky, requiring lower expected returns.
estimates, as they are calculated over the whole historical period. Longer sample would also give an opportunity to test the performance of the model in various market circumstances: bull and bear markets, a long sample including both at a time, or samples with a structural break. Thirdly, it follows the period of the introduction of the Sarbanes-Oxley act of 2002. Despite the fact that the sample from that period is more diversified, the behavior of the market in that period might have been influenced by the shift in the legal environment biasing the analysis.
Taking into account the aforementioned, a study examining the effect of incorporating corporate governance characteristics in portfolio weights optimization using a sample spanning longer time period and the whole universe of stocks available to the investor is needed. It would give an overview on the performance of the portfolio under diverse market circumstances and for a bigger number of entities. Moreover, it could give an answer to whether the influence of corporate governance on portfolio weights was different in the period following the introduction of the Sarbanes-Oxley act.
APPENDIX A: Regression Results
To test the significance of the characteristics in explaining stock returns regression analysis is run. The equation is estimated using two-way fixed effects model and is of the following form:
,
where are the monthly returns of stock i at date t, is its log of market value, is the log of one plus its market to book ratio, is its momentum, is the firm’s Gov-score and is the error term.
Table A.I presents the regression results for a specification including GOV in the equation (A.1). Size (MV), momentum (MOM) and the quality of corporate governance (GOV) are all significant at a 5% significance level. Market -to-book value ratio (MTB) with its p-value of 0.1667 is not significant at that level. However, at a greater significance level, for example 20%, the investor would assume it is significant in explaining stock returns.
TABLEA. I
REGRESSI ON RESU LTS
Variable Coefficient Std. Error t-statistic p-value
MV 0.0132 0.0014 9.6202 0.0000 MTB 0.0012 0.0009 1.3828 0.1667 MOM -0.0069 0.0004 -18.2969 0.0000 GOV -0.0012 0.0006 -2.0432 0.0410 C 0.0040 0.0003 13.8441 0.0000 R2 0.1632 Adj. R2 0.1382
The table presents the results of estimating equation A.1 using two-way fixed effects model over the whole period from August 2003 and July 2006, and including market value (MV), market-to-book value (MTB), momentum (MOM) and Gov-Score (GOV) plus the constant term (C) in the set of explanatory variables. The columns of the upper part of the table presents the following the variables, the values of the coefficients, standard errors, t-statistics and p-values. The lower part presents R-squared and adjusted R-squared of the regression.
Table A.II shows the results of the redundant fixed effects test. All the p-values are low, indicating that the specification is appropriate.
TABLEA. II
FIXED EFFECT S SPE CIFIC ATI ON TE STS
Effects Test Statistic
Deg. of
Freedom p-value
Cross-section Chi2 4882.01 35 0.0000
Period Chi2 1015.97 907 0.0066
Cross-Section/Period Chi2 5758.90 942 0.0000
The table presents the results of the redundant fixed effects test for the regression summarized in Table A.I. The columns of the table show the following: the name of the test, test statistic, degrees of freedom and the p-value of the test.
Table A.III presents the regression results for a specification excluding GOV from the equation (A.1). Size (MV) and momentum (MOM) are significant at a 5% significance level. Market-to-book value ratio (MTB) with its p-value of 0.1738 is not significant at that level. But if the investor assumes a higher significance level, for example 20%, the variable can be assumed to be significant.
TABLEA. III
REGRESSI ON RESU LTS
Variable Coefficient Std. Error t-statistic p-value
MV 0.0132 0.0014 9.6417 0.0000 MTB 0.0012 0.0009 1.3601 0.1738 MOM -0.0069 0.0004 -18.4040 0.0000 C 0.0040 0.0003 13.8434 0.0000 R2 0.1631 Adj. R2 0.1381
The table presents the results of estimating equation A.1 using two-way fixed effects model over the whole period from August 2003 and July 2006, and including market value (MV), market-to-book value (MTB), momentum (MOM) and Gov-Score (GOV) plus the constant term (C) in the set of explanatory variables. The columns of the upper part of the table presents the following the variables, the values of the coefficients, standard errors, t-statistics and p-values. The lower part presents R-squared and adjusted R-squared of the regression.
TABLEA. IV
FIXED EFFECT S SPE CIFIC ATI ON TE STS
Effects Test Statistic
Deg. of
Freedom p-value
Cross-section Chi2 4881.41 35 0.0000
Period Chi2 1031.00 907 0.0025
Cross-Section/Period Chi2 5771.32 942 0.0000
APPENDIX B: MatLab Code
This appendix provides the MatLab code written by the author and used in the calculation of the equally-weighted portfolio, the long-short governance-based portfolio and the long-only governance-based portfolio using all for characteristics. It can be freely used for academic purposes after noticing the author.
%The code below calculates a vector of monthly returns for the last 12 %months in the sample (ew), annualized average returns over that period %(ret_ew) and sharpe ratio (sr_ew) of 1/N portfolio policy.
ew=zeros(12,1); l = size (ret, 2); for t = l-11:l N = size(ret(:,t), 1); port = 0; for i = 1:N port=port + (1/N)*ret(i,t); end; ew(t-(l-12))=port; end; clear port t i N l; ret_ew = mean(ew)*12; sr_ew = ret_ew/std(ew);
%The code below uses function power_ut to calculate a vector of monthly returns for the last 12
%months in the sample (p), annualized average returns over that period %(ret_p) and Sharpe ratio (sr_p) of the model with mv, mtb, mom and gov. Also parameter
%coefficients (parameters) and weights matrix (w).
parameters=zeros(12,4); p=zeros(12,1);
w=zeros(908,13); l = size (ret, 2);
opt=optimset('Display', 'off', 'MaxFunEvals', 10000, 'TolFun', 1e-5,
'TolX', 1e-5); for t = l-12:l N = size (ret, 1); mv = mv_hat; mtb = mtb_hat; mom = mom_hat; gov = gov_hat; r = ret;
[x] = fminsearch (@(x) power_ut(x, N, t, mv, mtb, mom, gov, r), [0 0 0 0], opt);
w(i,t-(l-13)) = 1/N + (1/N)*x(1)*mv_hat(i,t) + (1/N)*x(2)*mtb_hat(i,t) + (1/N)*x(3)*mom_hat(i,t) + (1/N)*x(4)*gov_hat(i,t); end; end; for t = 1:12 p(t)=transpose(w(:,t))*ret(:,t+24); end; clear port t i x; ret_p = mean(p)*12; sr_p = ret_p/std(p);
function f = power_ut(x, N, T, mv, mtb, mom, gov, r)
%The function calculates the sum of utilities over the historical sample %perios; including corporate governance factor. It is used in the code above gamma=5; funT = 0; for t=1:T funN = 0; for n=1:N funN = funN + ((1/N) + (1/N)*x(1)*mv(n,t) + (1/N)*x(2)*mtb(n,t) + (1/N)*x(3)*mom(n,t) + (1/N)*x(4)*gov(n,t))*r(n,t); end
funT = funT + ((1+funN).^(1-gamma))/(1-gamma); end;
f = -funT;
%The code below puts a long-only constraint on the weights and calculates annualized average return of the portfolio (ret_p_pos) and the Sharpe ratio for the portfolio (sr_p_pos).
for t=1:12 sum_w = sum(w_pos(:,t)); for i=1:N w_pos(i,t)=w_pos(i,t)/sum_w; end end p_pos1 = zeros(12,1); for t = 1:12 p_pos(t)=transpose(w_pos(:,t))*ret(:,t+24); end; p_pos=transpose(p_pos); ret_p_pos = mean(p_pos)*12; sr_p_pos = ret_p_pos/std(p_pos); clear i t;
%The code below calculates the sum of negative weights for the long-short portfolio. sum_neg=zeros(12,1); N = size (ret, 1); for t=1:12 for i=1:N if w(i,t) < 0 sum_neg(t)=sum_neg(t) + w(i,t); end; end; end;
% The code below calculates the percentage of negative weights for the long-short portfolio. neg=zeros(12,1); N = size (ret, 1); for t=1:12 for i=1:N if w(i,t) < 0 neg(t)=neg(t) + 1; end; end; end; neg=neg/N;
% The code below calculates the turnover for the long-short portfolio. turnover=zeros(11,1);
N = size (ret, 1); for t=2:12
for i=1:N
% The code below calculates the turnover for the long-only portfolio. turnover_pos=zeros(11,1);
N = size (ret, 1); for t=2:12
for i=1:N
turnover_pos(t-1)=turnover_pos(t-1) + abs(w_pos(i,t) - w_pos(i,t-1));
end; end;
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