Does Magic Formula Investing Work in Hong. Kong Stock Market?

Transcription

1 Does Magic Formula Investing Work in Hong Kong Stock Market? Si Fu and Chun Xia The University of Hong Kong ABSTRACT We test the Magic Formula strategy of Greenblatt (2006) in Hong Kong stock market. We rank companies by their return on capital and earnings yield, and then to buy the stocks with the best combined rank. We find that the top 10% of stocks with the best combined rank have an equal-weighted average portfolio return of 2.53% per month while the bottom 10% stocks has only 1.30% average portfolio return per month. We construct six portfolios as the intersections of two portfolios formed on the firm size and three portfolios formed on the combined ranking computed from the magic formula. We show that, for both large and small stock groups, the portfolios of stocks with high rankings from the magic formula outperform the portfolios with low rankings. For the large stocks, the portfolio with high rankings has 14.61% higher annualized return than that with low rankings. For the small stocks, the portfolio return of high ranking stocks is 6.04% higher than that of the low ranking stocks. The time-series regression shows that the risk factor constructed from the ranking calculated from the magic formula has explanatory power to the variation of stock returns in addition to the Fama-French three factors. 1

2 It is well known that the majority of ideas in finance were either invented or developed in academia, before they crossed over into practice. To name a few, the portfolio theory pioneered by Markowitz (1952), the option pricing theory by Black and Sholes (1973), and Merton (1973), the asset allocation model of Black and Litterman (1992), the low volatility investing of Haugen and Heins (1975) and Ang, Hodrick, Xing and Zhang (2006) have witnessed their broad and extensive applications in the investment industry. It is also true some famous investment strategies were first initiated or discovered by practitioners and then later examined, refined, and extended by finance researchers. Notable examples include the value and growth investing, the momentum strategies. A recent specific example is the all-weather strategy popularized by Ray Dalio, the founder of a leading hedge fund Bridgewater Associates. It is also known as the risk-parity investing because it aims at creating a portfolio where each included asset class contributes equally to the overall risk of the portfolio. 1 This strategy has inspired academic studies such as Qian (2005), Martellini (2008), and Choueifaty and Coignard (2008) as well as many other funds including AQR where their research (Hurst, Johnson, and Ooi, 2010, and Asness, Frazzini, and Pedersen, 2012) has further made the idea of this strategy accessible to both professional and individual investors. In this chapter we plan to do a similar exercise and choose to exploit the investment idea behind a strategy called the magic formula, by back-testing its effectiveness using data from the Hong Kong stock market. This stock-picking strategy is employed by Joel Greenblatt, a value styled manager of the hedge fund Gotham Capital (with asset under management of AUM $2.74 billion in 2013) and an adjunct professor at the Columbia University Graduate School of Business. Greenblatt s investment philosophy presented in his book The Little Book That Beats the Market published in 2006 can be summarized as buying stocks of good companies that have high returns on capital when they re traded at bargain prices so that their earnings yields are high. In other words, the magic formula invests in companies 1 Bridgewater launched the first investment product based on risk parity called the All Weather fund in 1996, and the term risk parity was originally coined by Edward Qian in

3 through a ranking system. The higher return on capital and higher earnings yield is a company, the higher the rank this company enjoys. The idea is akin to the famous quote from Warren Buffett: It s far better to buy a wonderful company at a fair price than a fair company at a wonderful price. Greenblatt defines the return on capital and earning yield in the following unique way. Return on Capital = EBIT/Tangible Capital Employed Earning Yield = EBIT/EnterpriseValue where EBIT is the operating earnings before interest and tax, tangible capital employed is the sum of net working capital (NWC) and net fixed asset (NFA), and enterprise value (EV) is the sum of market value of equity (including preferred equity) and net interest bearing debt. We will explain why Greenblatt uses these two definitions instead of more common measures in the next section. When investing in the stocks traded in the New York Stock Exchange, the magic formula strategy achieved a compound annual return of 30.8% from 1988 to 2004, while the compound annual return of S&P 500 was only 12.4% during the same period. 2 The numbers become 22.9% and 12.4% respectively when the strategy was applied to the largest 1000 companies stocks, all of which had a market value over $1 billion. Greenblatt claims these results can be replicated using a database Point in Time from Standard & Poor s Compustat that is free of look-ahead bias and survivorship bias. It is also found that when companies are divided into 10 equal portfolios based on their rankings and the portfolios were rebalanced each month, then the compound annual returns from 1988 to 2004 were ranked in a decreasing manner from the best-ranked portfolio to the worst-ranked one. Alpert (2006) reports that 2 Specifically, Greenblatt rank the largest 3,500 stocks on the U.S. stock exchanges from 1 to 3,500 based on their return on capital and earnings yield, respectively. The stock with the highest return on capital is assigned a rank of 1, and the stock with the lowest return on capital receives a rank of 3,500. Similarly, the stocks are ranked by the earnings yield as well, assigning number 1 to the one with the highest earning yield and number 3,500 to the one with the lowest. Then, the two rankings are added. The stocks with the small total ranks have a combination of high return on capital and high earnings yield. Getting excellent rankings in both categories would be better than being the top-ranked in one category but being the bottom-ranked in the other under this system. Portfolios are formed based on the total ranking and rebalanced once a year. 3

4 Greenblatt s hedge fund has averaged over 40% annual returns since the 1980s. Even though the magic formula investing is well known among investment community, a robust analysis of its effectiveness is lacking. 3 In addition, the value investing professionals often has a different view of risk from academic researchers. They argue that volatility is not a proper measure for risk because the upside moves of prices should not be deemed as an increase in risk. They view risk to be the probability of losing money so that they develop a systematic way to pick up undervalued stocks. We believe it would be interesting and necessary to examine Greenblatt s magic formula strategy through a traditional view of risk via asset pricing models such as CAPM and Fama-French 3-factor model. Prior to our research, there are a few studies that back-test the magic formula investing using different data sources in order to judge whether this investing strategy can truly outperform the market or other risk-adjusted returns. First, Alpert (2006) reports that various replications of Greenblatt s strategy using the U.S. data of the same period show similar results, although the replicated returns are lower than Greenblatt s claims, probably due to difference in accounting measures. For instance, ClariFI, a partner firm of Compustat, finds the magic formula investing can achieve an average return of 28 percent and 17.5 percent using the largest 3500 and 1000 U.S. stocks, respectively. Second, replication study by Montier and Lancetti (2006) test the strategy on US, European, UK and Japanese markets between 1993 and 2005 and find it beat the market (an equally weighted stock index) by 3.6%, 8.8%, 7.3% and 10.8% in the various regions respectively. These studies do not examine the outperformance of magic formula from a traditional asset pricing model. The only exception that we are aware of is a study by Persson and Selander (2009), who use stocks data in the Nordic Region between 1998 and 2008 and find that the portfolio formed on the magic formula during had a compounded annual return of 14.68% compared to 9.28% for the MSCI Nordic and 4.23% for the S&P 500, respectively. However, they also demonstrate 3 Greenblatt s book has become a bestseller since its initial publication. Several websites have been built for investors to employ the magic formula investing, including and 4

5 that the excess return was not significant from zero when testing against the CAPM or Fama French 3-factor model on the 5% level. To our best knowledge, whether the magic formula investing is effective in the Hong Kong stock market is yet to be examined. We analyze the Hong Kong listed firms from 2001 to 2014 with the same approach as Greenblatt (2006). We find that, if we invest in the top 10% of the sample stocks with a combination of high return on capital and high earnings yield, a 2.53% monthly return can be achieved for the whole sample period. As we separate the stocks in half according to their market capitalization, we find the top 30% of the large stocks with high magic formula measure would earn an annualized return of 20.26% while the bottom 30% with low magic formula measure would earn only 5.65% annually. Similarly for the small stocks, the portfolio of stocks with high magic formula measure has 6.04% more return annually than the portfolio with low magic formula measure. We compare performance of the portfolios formed on the size and value factors and that of the portfolios formed following the magic formula, and show that the new factor created following the magic formula has extra power to explain the stock returns in addition to the size and value factors. Comparing the estimates of regressions on the constructed Fama- French three factors with and without the magic formula factor, we find that the magic formula measure is statistically significant in the time-series regressions, and when added, the adjusted R-square increases about 1%, indicating that it contributes to explain the timeseries variation in the stock returns slightly. As the correlation of MF and the Fama-French factors are low, we find that the estimated coeffi cients of the Fama-French factors do not change much when we add the magic formula to the regression. The interception term, known as alpha, is not significant, and all the factors together explain about 67% of timeseries variation in returns of the whole sample. Besides, we show that the results using the revised magic formula measure (MF2) are quite similar as we use the original magic formula measure (MF1). This indicates that whether to include the intangible asset in the calculation of return on capital does not change the performance of the magic formula dramatically. We 5

6 also find that the explanatory power of the size and value factors for large stocks is weak. The MF2, however, more significantly influences the returns of large stocks. The Fama-MacBeth regression shows that only the MF1 factor has a significant and positive risk premium of 0.19 and the MF2 factor has a positive risk premium of 0.15 at the 1% significant level. The Fama-French three factors do not bear significant risk premium. We examine the estimated risk premium in months and find that the risk price of MF factor tends to be positive for most of the months, but the risk prices of the size and value factors are not always positive. The time-series variation of the estimates is a possible reason for that we do not observe statistically significant risk premium of the size and value factors. Comparing the MF factor and the Fama-French value factor, MF rankings tends to provide a more comprehensive measure to evaluate both the profitability of a firm and its market valuation together. Hence, the MF rankings seem to be a stricter criterion to distinguish stocks, and this may be another potential reason for that we observe more stable risk premium estimates on the MF factor. Our paper contributes to the literature in two-fold. First, our analysis joins the new trend that academic seriously examines investment strategies advocated by practitioners who often emphasize the return outperformance without the risk-adjustment considerations. The test of magic formula investing through a standard asset pricing exercise helps us to understand its effectives and risk-return tradeoff. Besides, we also observe that existing studies on Hong Kong stock market are still quite limited (e.g., Chang, Cheng, and Yu, 2007). Our study is useful to enhance our understanding of the performance of magic formula investing in Hong Kong. Second, our study also belongs to the new trend that tries to find new risk factor beyond the well-known factors such as Fama-French 3-factor, momentum factor (Jegadeesh and Titman, 1993, Carhart, 1997), liquidity factor (Pastor and Stambaugh, 2003). These new factors include idiosyncratic volatility (Ang, Hodrick, Xing, and Zhang, 2006), failure probability (Campbell, Hilscher, and Szilagyi, 2008), asset growth (Cooper, Gulen, and Schill, 2008), profitability (Fama and French, 2006), among others. Our study shows that 6

7 the magic formula has return predictability beyond that of Fama-French 3 factor and deserves more attention. The rest of this chapter is organized as follows. Section 2 presents Greenblatt s justifications of using the magic formula. Section 3 explains our data resources and summary statistics. Sections 4 and 5 present the portfolio performance and risk-return analysis, respectively. Section 6 concludes. 1. The Ideas Behind the Magic Formula The magic formula investing is a variant of the well-known value investing which aims at systematically finding above-average companies that can be bought at below-average prices. The behavioral argument for its effectiveness can be briefly summarized as follows: After a company releases some bad news or is expected to receive some unfavorable news in the near future, its stock price could be driven down unfairly in the short term by investors low sentiments or other behavioral biases. However, over time different forces such as smart investors hunting for bargain opportunities, companies repurchasing their own stocks, and bidding companies taking over the undervalued company would work together to drive up the stock prices toward its fair value eventually. Of course, the standard finance argues that the long-term higher return of such a stock comes from the compensation for its higher risk. However, Greenblatt believes that magic formula investing provides returns far superior above the market averages, and more significantly, it achieves those returns on much lower risk than the overall market. One of the objectives of our paper is to test his claim in the rigorous asset-pricing framework. Before our formal statistical analysis, we explain why Greenblatt define the return on capital and earning yields in a different way from the commonly used ones. 7

8 1.1. Return on Capital Greenblatt defines return on capital by measuring the ratio of the 12 month trailing EBIT (or operating earnings before interest and taxes) to tangible capital employed. This ratio is used instead of the more common return on equity (ROE, earnings/equity) or return on assets (ROA, earnings/assets) for a number of reasons. EBIT replaces reported earnings because companies operate with different levels of debt and differing tax rates. Using EBIT allows investors to compare the operating earnings of different companies without the distortions resulting from differences in tax rates and debt levels. It is therefore possible to compare each company s actual earnings from operations, i.e., EBIT to the cost of the assets used to produce those earnings, i.e., tangible capital employed. Moreover, Greenblatt assumes that depreciation and amortization expense are roughly equal to maintenance capital spending requirements. It is, therefore, assumed that EBIT is the EBITDA net of maintenance capital expenditures. Tangible capital employed (the sum of net working capital and net fixed assets) replaces total assets or equity (used in ROA and ROE calculation respectively) in order to find out the amount of capital that is actually required to carry out the company s business. Net working capital is a component because a company has to fund its receivables and inventory (excess cash not used to operate the business is excluded) but does not have to spend money for its payables that are effectively an interest-free loan (short-term interest-bearing debt is excluded from current liabilities). Besides net working capital, a company has to purchase fixed assets, such as real estate, plant, and equipment, to operate its business. The depreciated net cost of these fixed assets plus the net working capital constitute an estimate for tangible capital employed. Notably, intangible assets are excluded in the calculation because in general, return on tangible capital alone is a more accurate estimate of a business s return on capital going forward. In contrast, the ROE and ROA calculations are often distorted by ignoring the difference between reported equity and assets, and tangible equity and assets, on top of the distortions due to differing tax rates and debt levels. 8

9 1.2. Earnings Yield Greenblatt uses the concept of earnings yield in order to find out how much a business earns relative to the purchase price of the business. Earnings yield is the ratio of EBIT to enterprise value (EV), i.e., the sum of market value of equity (including preferred equity) and net interest-bearing debt. This ratio is used instead of the more common price/earnings ratio (P/E ratio) or earnings/price ratio (E/P ratio) for a number of reasons. Enterprise value (EV) of a company is used rather than just the company s total market capitalization, because EV takes into account both the price paid for an equity stake in a business and the debt financing employed by the company to generate operating earnings. By comparing EBIT to EV, we can calculate the pre-tax operating earnings relative to the price of equity plus any debt assumed, which allows us to place companies with different levels of debt and different tax rates on an equal footing when their earnings yields are compared. In other words, EBIT/EV is not affected by changes in debt levels and tax rates, whereas P/E and E/P ratios are. In this paper, we not only follow Grinblatt s method to construct the magic formula, but also consider an alternative measure of capital employed that includes both tangible and intangible assets for two reasons. First, existing studies have shown the importance of intangible asset in understanding stock returns (e.g. Chan, Lakonishock, and Sougiannis (2001), Li and Liu (2012)). Second, because other replications produce returns lower that what s reported by Greenblatt (2006), we are interested in other measure of asset employed in the magic formula. 2. Data Our sample includes the listed firms on the Main Board (MB) and Growth Enterprise Market (GEM) of the Hong Kong Exchange from January 1, 2000 to June 30, Table 3.1 reports the numbers and the total market capitalization of firms listed on the MB and GEM 9

10 at the end of each year during the sample period. On June 30, 2014, there are 1495 firms listed on the MB with total market capitalization of HK$ billion, and 194 firms listed on the GEM with total market capitalization of HK$164.2 billion. 4 We collect our sample of Hong Kong listed firms from Compustat Global database and exclude financial firms with SIC number between 6000 and 6999 and utility firms with SIC number between 4000 and By the end of June 2014, our sample contains 1194 firms which account for about 70% of the whole market. The total market capitalization of our sample firms is HK$ billion, about half of the whole market capitalization. The proportion of sample in terms of the market capitalization is less than that in terms of the number of firms, which is mainly because the excluded financial and utility firms tend to have large market capitalization. We collect monthly closing prices of the listed stocks from Compustat Global Security Daily dataset and calculate the monthly returns in percentage adjusted for dividends and stock split as follows, according to the guidance from WRDS: 5 Return t = ( ) PRCCDt /AJEXDI t TRFD t PRCCD t 1 /AJEXDI t 1 TRFD t 1 where PRCCD_t is the month closing price at the end of month t, AJEXDI_t and TRFD_t are the adjustment factors in WRDS database. We use the 1-month HIBOR as a proxy for the risk-free rate, and use monthly returns of the Hang Seng Index as a proxy for the market return. 6 4 The number of listed firms and their total market capitalization data for year 2000 to 2013 are obtained from the HKEx Fact Books released annually in the website of the Hong Kong Stock Exchange. The data for 2014Q2 is obtained from the HKEx Securities and Derivatives Markets Quarterly Report. 5 See 6 The Hang Seng Index (HSI) is a freefloat-adjusted market capitalization-weighted Hong Kong stock market index, which is used as the main indicator of the overall market performance in Hong Kong. Now, it contains 48 large companies representing about 60% of the total capitalization of the Hong Kong Stock Exchange. We collect the closing price of HSI adjusted for dividends and splits at the end of each month from January, 2000 to June, During the sample period, HSI began from and increased to the 20,000 point milestone on December 28, In less than 10 months, it passed the 30,000 point milestone on October 18, Its all-time high, set on October 30, 2007, was 31, points during trading and 31, points at closing. From October 30, 2007 to October 27, 2008, the index fell nearly two-thirds from its all-time peak to 10, points. But it rebounded to the 20,000 point milestone on 24 July, At the end of our sample period, HSI closed at 23, on June 30,

11 According to the magic formula introduced by Greenblatt, the return on capital employed is calculated as EBIT divided by capital employed, which equals to the sum of the net working capital and the net fixed assets. Return on Capital (ROC) = EBIT/Capital Employed (CE) = EBIT/ (Net Working Capital (NWC) + Net Fixed Assets (NFA)) The earnings yield is calculated as EBIT divided by the enterprise value of firm. Earnings Yield (EY) = EBIT/Enterprise Value (EV) Considering the alternative approach to measure the capital employed with intangible asset included, we calculate an alternative measure of return on capital as the difference of total asset and current liability. This alternative measure is denoted as the return on capital (revised) in the following analysis: Return on Capital_revised (ROC_revised) = EBIT/Capital Employed_revised (CER) = EBIT/ (Total Asset (TA) Current Liability (CL)) To calculate the above measures, we collect semi-annual data of earnings before interest and tax (EBIT), net working capital (NWC), net fixed asset (NFA), total asset (TA), current liability (CL) and enterprise value (EV) from Bloomberg. All the measures are lagged for 6 months to ensure that the data is available and no look-ahead bias is involved. Fama and French (1993, 1996) are the pioneer studies building up a standard framework to explore the risk factors in asset pricing. The size and value factors in their studies have strong and robust explanation power to the stock returns. In our study, we first calculate the size and value factors with the data of Hong Kong stock markets following Fama and French s approach, and take these analyses as the benchmark. We compare performance of the portfolios formed on the size and value factors and that of the portfolios formed following the magic formula, and examine whether the new factor created following the magic formula 11

12 has extra power to explain the stock returns in addition to the size and value factors. We collect the annual data from Compustat to calculate the size and book-to-market ratio of the firms. All the accounting data in currency other than the Hong Kong Dollar are transferred using the historical exchange rates provided on the OzForex website. 7 The firm size is calculated as the natural logarithm of the market capitalization in million HKD at the end of each calendar year. The book-to-market ratio is the book value of equity at the previous fiscal year end divided by market value at the end of previous year. The market value of equity equals to the stock price times common shares outstanding, and the book value of equity is calculated as the total book value of common equity, plus deferred taxes and investment tax credit, and minus the book value of preferred stock. When the deferred taxes and investment tax credit are not available, we use the balance sheet deferred taxes instead. The redemption value and par value of the preferred stocks are used in order to estimate the book value of them. 8 Table 2 describes the distribution statistics of the returns and the risk measures. Panel A summarizes the collected whole sample. The average stock return of our sample is 1.54% per month during the period from January 2000 to June The return has a value-weighted mean of 3.07% per month and a standard deviation of 48.55% per month. They are both higher than the equal-weighted ones as they concentrate on a few very large stocks. The value-weighted return moves much when some of the large stocks have extraordinary performance. As there are some missing values of the firm fundamentals, we further summarize a subsample that we will use to form portfolios and calculate the risk factors in Panel B. This subsample only contains stocks with size, book-to-market ratio and one of the return on capital measures or the earnings yield measure available. We find that the sample with non-missing measures has slightly higher returns, large firm sizes and smaller book-to-market 7 The historical exchange rate data is obtained from the website 8 We use the variable definitions of French s data library as reference to calculate size and book-to-market ratio measures. See 12

13 ratios. Following Greenblatt, we rank the sample stocks according to ROC, ROC (revised) and EY, respectively. The stock with the highest value of each measure is ranked number 1, and the rank number increases as the measure values decrease. Then, we add the rank on ROC and the rank on EY together to obtain the first magic formula measure, denoted as MF1. MF1 is calculated in the exactly same way as Greenblatt does. As we introduce an alternative return on capital measure denoted as ROC (revised), we also calculate an alternative magic formula measure MF2 as the sum of ranks on ROC (revised) and EY. Similarly for MF1 and MF2, a low value indicates a stock has high return on capital and high earnings yield as the stock is ranked on top. 3. Portfolio Performance 3.1. Single-sorted Portfolios Fama and French (1993, 1996) document the size and value effects with the U.S. stock market evidence. Even with the data up to date, the size and book-to-market ratio are still being the two major risk factors in explaining the variation in stock returns. The small firms tend to have higher stock returns than the big firms and the firms with high book-tomarket ratio tend to have higher returns than those with lower book-to-market ratio. The portfolio analysis used by Fama and French provides a direct way to identify how a factor may influence the investment performance. Hence, we follow Fama and French s approach in our analysis. First, we analyze whether the size and value effects present in the Hong Kong stock markets as well. Then, we examine whether the new risk factors we construct following the magic formula contributes to explaining the cross-sectional variations of the stock performance. We construct 10 size portfolios according to the decile breakpoints of the natural logarithm of the market capitalization. Decile 1 contains the bottom 10% of stocks with smallest 13

14 firm size and Decile 10 contains the top 10% of stocks with largest firm size. Panel A of Table 3.3 summarizes the equal-weighted averages of the 10 size portfolios. For the Hong Kong listed stocks, we also observe the size effect as average portfolio return tends to decrease as the firm size increases, except that the last portfolio of the largest stocks has slightly higher return. On average, Decile 1 has a monthly return of 3.2% while that for Decile 10 is about 1.65% per month. Panel A of Table 3.4 summarizes the portfolios weighted by the market capitalization of firms. The value-weighted portfolio returns have even larger dispersion. As the firm size increase, the portfolio return tends to decrease as well. With the stocks having positive book-to-market ratios, we apply similar portfolio analysis separating the sample into 10 decile portfolios. Decile 1 refers to the stock portfolio with lowest B/M ratio and Decile 10 is the portfolio with highest B/M ratio. We find that the equal-weighted average of portfolio returns are monotonically increasing with the B/M ratios, except for the top two portfolios with returns slightly lower returns than the 3rd top portfolio, shown in Panel B of Table 3. Regarding the value-weighted portfolio returns, the top 5 portfolios have large returns than the bottom 5 portfolios, though they are not monotonically increasing with the B/M ratio. Panel B of Table 3.4 shows that the top 5 portfolios have about 6% monthly average value-weighted portfolio returns, while the bottom 5 portfolios have about 2% on average. According to Greenblatt, the magic formula evaluates stocks based on their returns on capital combining with their earnings yields. High return on capital is proxy for that the firm have strong profitability, and high earnings yield is used as an indicator showing that they re traded at bargain prices. In our analysis, we first examine the factors separately by forming portfolios according to one of measures, ROC, ROC (revised) or EY. We restrict our sample with positive ROC, ROC (revised) and EY measures, and calculate the equal-weighted and value-weighted average returns of 10 decile portfolios shown in Table 3.3 and Table 3.4. We find that the equal-weighted average returns of the 10 portfolios formed on ROC and ROC (revised) do not demonstrate a monotonic pattern as those of size or B/M ratio portfolios, 14

15 although the top decile portfolio formed with the ROC measure has an average return about 0.5% higher than the bottom decile per month. The average value-weighted ROC and ROC (revised) portfolio returns do not monotonically increase with the return on capital measures, neither. The portfolio with high EY tends to have higher returns than the portfolio with low EY. The top decile portfolios formed with the EY measure has a 1% higher average return compared with the bottom decile. We add the rank on ROC and the rank on EY together to obtain the first magic formula measure MF1, and alternatively, use rank on ROC (revised) instead of ROC to calculate MF2. 10 decile portfolios are formed on MF1 and MF2 each. As the portfolios with smaller ranks calculated from the magic formula refers to firms with high return on capital and with bargain prices, we expect that the portfolio returns should decline from Decile 1 to Decile 10 if the magic formula claim is valid. Our evidence in the last two panels of Table 3.3 and Table 3.4 support the argument. We find that the top 2 decile portfolios formed on MF1 and MF2 have the largest portfolios returns and the bottom 2 portfolios have the smallest average returns. However, the average returns of portfolios in the middle do not monotonically decrease. Figure 1 and Figure 2 show the equal-weighted and value-weighted average returns of portfolios formed on the measures together. First, we confirm the effect of firm size and book-to-market ratio as risk measures on the Hong Kong stock markets. Second, considering return on capital or earnings yield alone, we find that the returns on capital of the firms do not lead to much of the difference in returns, while firms with high earnings yield tends to have higher returns Double-sorted Portfolios To analyze the possible different influence of factors in large and small firms, we construct six double-sorted portfolios with the intersections of 2 portfolios formed on size and 3 portfolios on one of the other factors. We use the median of the size measure as the breakpoints 15

16 to separate the stocks into big and small stock groups. We use the 30th and 70th percentile values of the other measures as the breakpoints to categorize stocks into the high, medium and low portfolios of the specific measure. The analysis of double-sorted portfolio enables us to observe how the factors influence the big and small stocks, respectively. Table 5 reports the equal-weighted means of returns, standard deviations and Sharpe ratios of the double-sorted portfolios. The returns are annualized and reported in percentage value. We find that the B/M ratio influences more on the returns of large firms. The difference of returns between the high and low B/M portfolios is 24.78% annually for large firms while it is 10.83% for small firms. Regarding the small stocks, we find that they are more sensitive to the ROC and ROC (revised) measures. The geometric mean of the small-high portfolio returns sorted on size and ROC is 31.98% per year and that of the small-low portfolio is 20.84%. Similarly for ROC (revised), the mean of small-high portfolio returns is 34.84% while the small-low portfolio has an average return of 18.78%. The difference between the high and low portfolios on ROC and ROC (revised) are both over 10% per year for the small stocks. However, the return of the large-high portfolio on size and ROC minus that of the large-low portfolio is 5.55% only, and the return of the large-high portfolio on size and ROC (revised) is even lower than that of the large-low portfolio. When we consider ROC and EY together as the magic formula, we find that the both the large and small stocks with high MF1 have significantly higher return than the portfolios with low MF1. For the large stock group, the difference of the high and low portfolios is 14.61% annually, and for the small stock group, the difference is 6.04%. As we consider ROC or EY alone, they tend to explain more variation in returns of small stocks. But when we consider them together, it distinguishes the returns more on large stocks. We also examine the MF2 computed using the ROC (revised) and find that the influence of MF2 on large stocks is weaker than the original MF1 measure. In Table 6, we summarized the value-weighted returns of the double-sorted portfolios. 16

17 The stock returns are weighted by the natural logarithm of market capitalization and we find similar results as the equal-weighted ones. 9 Panel C of Table 6 summarizes the standard deviations of the portfolios and Panel D reports the Sharpe ratios of the portfolios calculated as the geometric means of portfolio returns divided by the standard deviations. The standard deviations of portfolios are similar and hence the Sharpe ratio is high when the average return is large. 4. Regressions on Risk Factors 4.1. Construct Risk Factors We construct 2?? portfolios with median breakpoints of size, B/M ratio and one of the magic formula measures and separate the stocks into 8 portfolios labelled with three letters. A stock with label BHL means it is a big stock with high B/M ratio and low magic formula measure. Then, we calculate the risk factors as follows. SMB = 1/4 (R SHH + R SHL + R SLH + R SLL ) 1/4 (R BHH + R BHL + R BLH + R BLL ) BM_HML = 1/4 (R SHH + R SHL + R BHH + R BHL ) 1/4 (R SLH + R SLL + R BLH + R BLL ) MF _HML = 1/4 (R SHH + R SLH + R BHH + R BLH ) 1/4 (R SHL + R SLL + R BHL + R BLL ) To construct the risk factors with each magic formula measures, including ROC, ROC (revised), EY, MF1 calculated from rankings of ROC and EY, and MF2 calculated from rankings of ROC (revised) and EY, we restrict our sample to have positive firm size, B/M ratio and the target magic formula measure to ensure that every stock is allocated into one of the portfolios. Hence, we have a distinct subsample to construct each set of the risk factors, but the subsamples have great overlap. Table 3.7 shows the summary statistics and the correlations of each set of risk factors 9 We weight the returns using the natural logarithm of market capitalization to avoid the portfolio returns to be dominated by the performance of a few very large firms in the portfolio. 17

18 in one panel. The value factor has a very significant return which is over 1% on average. Besides, the factors of ROC and ROC (revised) also have statistically significant returns but smaller in magnitude. The correlations among the factors are low Time-Series Regressions In this subsection, we aim to analyze how much time-series variations in stock returns can be explained by the risk factors of the market, size and value, additionally with the factor constructed from the magic formula. First, we run time-series regressions of the valueweighted portfolio return of our whole sample on the proposed risk factors. Table 3.8 shows the regression results. Panel A compares the estimates of regressions on the constructed Fama-French three factors with and without the magic formula factor MF1. We find that the magic formula measure is statistically significant, and when added, the adjusted R-square increases about 1% as it contributes to explain the time-series variation in the stock returns slightly. As the correlation of magic formula factors and the Fama-French factors are low, we find that the estimated coeffi cients of the Fama-French factors do not change much when we add the magic formula to the regression. The interception term, known as alpha, is not significant, and all the factors together explain about 67% of time-series variation in returns of the whole sample. Panel B reports the estimates of regressions on the Fama-French three factors and the MF2, and we find the results are quite similar as we use MF1. This indicates that whether to include the intangible asset in the calculation of return on capital does not change the performance of the magic formula dramatically. In Table 3.9, we separate the sample stocks into 5 quantile portfolios on size, and take the value-weighted portfolio returns as the dependent variables for the regression. Portfolio 1 refers to the group of the smallest 20% stocks and Portfolio 5 includes the largest 20% stocks. First, we find over 70% of the time-series variation of the portfolio of the largest stocks can be explained by the factors, while for the smaller stock groups, the explanatory power is weaker. Second, the market and the magic formula factors are significant in all the 18

19 size portfolio regressions, shown in Panel A of the table. But the size and the value factor are not significant for the largest stock portfolio and the alpha is significant. From Panel B, we also find that the explanatory power of the size and value factors for large stocks is weak. MF2, however, more significantly influences the returns of large stocks Fama-MacBeth Regressions We estimate of the risk premium of the Fama-French three factors and the magic formula factor we newly construct with the Fama-MacBeth regressions. We first regress the individual stock returns in excess of the risk-free rate on the factors to estimate the beta of each asset for the factor. We run the time-series regressions with the rolling window of 12 months. In the second stage, we run cross-sectional regressions of the stock excess returns on the estimated betas and estimate the risk premium for each factor in each month. Then, we calculate the time-series average of the risk premium on each factor for the whole sample period and report the estimation results in Table The average is calculated based on estimates of 144 months. We use the Newey-West standard errors to correct for the potential autocorrelations. Based on the results, we find that only the MF1 factor has a significant and positive risk premium of 0.19, and the MF2 factor has a positive risk premium of 0.15 at the 1% significant level. However, the risk premiums of the Fama-French three factors are not significantly different from zero. We examine the estimated risk premium in months and find that the risk price of magic formula factors tends to be positive for most of the months, but the risk prices of the size and value factors are not always positive. The time-series variation of the estimates is a possible reason for that we do not observe statistically significant risk premium of the size and value factors. Comparing the magic formula factors and the Fama- French value factor, rankings calculated from the magic formula tend to provide a more comprehensive measure to evaluate both the profitability of a firm and its market valuation together. Hence, the magic formula seems to be a stricter criterion to select stocks. This may be another reason for that we observe more stable risk premium estimates on the magic 19

20 formula factors. During our sample period, the Hong Kong stock market experienced a quite important structural change. Since the year of 2005 to 2006, there are some large stocks from Mainland China listed on the Hong Kong stock exchange. The total market capitalization increase dramatically. Besides, in 2007, the Exchange adopted an electronic system to publish the announcements of listed firms. For our sample, we observe that more data is available since the year of Hence, to make a robustness test of our analysis, we estimate the risk premium again using the sample period from July 2007 to June The results are shown in Table We find similar estimated risk premium of the MF1 and MF2 factors. MF1 has a significant and positive risk premium of 0.16 at the 1% significant level, and MF2 has a positive risk premium of 0.11 significant at 5% level. The Fama-French three factors still do not bear significant risk premium. 5. Conclusion Motivated by the recent trend that academic researchers start to examine the investment strategies either pioneered or advocated by practitioners in asset management industry, we investigate the effectiveness of the magic formula investing on Hong Kong stock market in the standard asset pricing framework. We find that, if we invest in the top 10% of the sample stocks with a combination of high return on capital and high earnings yield, a 2.53% monthly return can be achieved for the sample period. Comparatively, the portfolio of the bottom 10% stocks with low return on capital and low earnings yield has an average monthly return of 1.30% per month. As we separate the stocks in half according to their market capitalization, we find the top 30% of the large stocks with high magic formula rankings would earn an annualized return of 20.26% while the bottom 30% with low magic formula rankings would earn only 5.65% annually. Similarly for the small stocks, the portfolio of stocks with high magic formula rankings has 6.04% more return annually than the portfolio with low magic 20

21 formula rankings. We examine whether the new factor created following the magic formula has extra power to explain the time-series variation in stock returns in addition to the Fama-French three factors. We find that the adjusted R-squares of the regressions increase about 1% as the factor MF1 is added to the Fama-French three factor model, and the coeffi cient estimates of MF1 is significant different from zero. The Fama-MacBeth regressions show that MF1 has a significant and positive risk premium of Our next research agenda is to refine the magic formula investing and extend our work to mainland Chinese stock market. By 2013, over 80% of the total market capitalization of the Hong Kong Stock Exchange consists of companies from mainland China. It is well known that on the one hand, the Chinese economy has performed extraordinarily well in the past thirty years with an annual growth rate of over 9 percent, one the other hand, the performance of the Chinese stock market has been notoriously disappointing, especially compared to the growth of GDP. The question we want to address in our future research is whether the magic formula strategy can be applied to the Chinese stock market, given its effectiveness in the Hong Kong stock market. If the answer is yes, we should ask why investors missed the opportunity. If the answer is no, we should find out what unique features of Chinese stock market lie behind the scene. 21

22 Alpert, B. (2006). The Little Book s Little Flaw, Barron s, March 27, Ang, A., R. J. Hodrick, Y. Xing, and X. Zhang (2006). The Cross-Section of Volatility and Expected Returns, Journal of Finance, 61, pp Asness, C., A. Frazzini, and L. H. Pedersen (2012). Leverage Aversion and Risk Parity, Financial Analysts Journal, 68, pp Black, F. and R. B. Litterman (1992). Global Portfolio Optimization, Financial Analysts Journal, 48, pp Black, F. and M. Scholes (1973). The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 81, pp Campbell, J. Y., J. Hilscher, and J. Szilagyi (2008). In Search of Distress Risk, Journal of Finance 63, pp Carhart, M. M. (1997). On Persistence in Mutual Fund Performance, Journal of Finance, 52, pp Chan, L., J. Lakonishok, and T. Sougiannis (2001). The Stock Market Valuation of Research and Development Expenditures. Journal of Finance, 56, pp Chang E. C., J. W. Cheng, and Y. Yu (2007). Short-Sales Constraints and Price Discovery: Evidence from the Hong Kong Market. Journal of Finance, 62, pp Choueifaty, Y. and Y. Coignard (2008). Towards Maximum Diversification, Journal of Portfolio Management 34, pp Cooper, M. J., H. Gulen, and M. J. Schill (2008). Asset Growth and the Cross-Section of Stock Returns, Journal of Finance 63, pp Fama, E. F. and K. R. French (1992). The Cross-Section of Expected Stock Returns, Journal of Finance, 47, pp Fama, E. F. and K. R. French (1993). Common Risk Factors in the Returns on Stocks and Bonds, Journal of Financial Economics, 33, pp Fama, E. F., and K. R. French (1996). Multifactor Explanation of Asset Pricing Anomalies, Journal of Finance 51, pp Fama, E. F., and K. R. French (2006). Profitability, Investment, and Average Returns, Journal of Financial Economics 82, pp Greenblatt, J., The Little Book That Beats the Market, John Wiley & Sons, Haugen, R. A. and A. J. Heins (1975). Risk and the Rate of Return on Financial Assets: Some Old Wine in New Bottles, Journal of Financial and Quantitative Analysis 10, pp Hurst, R., B. W. Johnson, and Y. W. Ooi (2010). Understanding Risk Parity, AQR Capital Management. Jegadeesh, N. and S. Titman (1993). Returns to Buying Winners and Selling Losers: Implications for Stock Market Effi ciency, Journal of Finance, 48, pp Li, E. and L. Liu (2012). Intangible Assets and Cross-Sectional Stock Returns: Evidence from Structural Estimation. Mimeo. Cheung Kong Graduate School of Business and Hong Kong University of Science and Technology. Markowitz, H. (1952). Portfolio Selection, Journal of Finance, 7, pp Martellini, L. (2008). Toward the Design of Better Equity Benchmarks, Journal of Portfolio Management 34, pp Merton, R. C. (1973), Theory of Rational Option Pricing, Bell Journal of Economics and Management Science, 4, pp

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24 Table 2. Summary Statistics of Returns and Fundamental Measure This table reports the summary statistics of the sample. Panel A describes the whole sample with all available data, and Panel B summarizes the statistics of the sample stocks we use for further analysis which have the return, the size proxy, the book-to-market ratio and one of the return on capital and earnings yield measures available. The returns are weighted equally and weighted by the market capitalization of each stock. The market beta of each stock is estimated using the stock excess returns and the market return in excess of the risk-free rate for the whole sample period. is calculated as the natural logarithm of market capitalization. Book-to-market ratio is calculated as the book value of equity at the previous fiscal yearend divided by market value at the end of previous year. Return on capital is calculated as EBIT divided by capital employed, which equals to the sum of the net working capital and the net fixed assets. A revised version of return on capital is calculated using the difference of total asset and current liability as the proxy for capital employed. Earnings yields are calculated as EBIT divided by the enterprise value of firm. Panel A: Whole sample Panel B: Sample with Non-missing Measures N Mean Std Min Max N Mean Std Min Max Equal-weighted Return (%) Value-weighted Return (%) Beta Book-to-Market Ratio Return on Capital Return on Capital (Revised) Earnings Yields

25 Table 3. Decile Portfolios with Equal-weighted Summary Statistics This table reports the equal-weighted means of monthly returns, market betas and risk proxies of the decile portfolios formed by each measure. The first column summarizes the subsample which has non-missing values of the measure used to form portfolios. For each measure, we exclude the stocks with missing or negative values, then separate the remaining stocks into 10 decile portfolios according to the decile breakpoints. Decile 1 includes the stocks with lowest values of the risk measure and Decile 10 includes the stocks with highest values of the risk measure. We report the equal-weighted means of the monthly stock returns, market betas estimated using the whole sample period, firm sizes, book-to-market ratios, measures of return on capital employed (ROC and ROC (Revised)) and earnings yields (EY), winsorized at 1% and 99% level to avoid the influence of the extreme values. The sample period includes 162 months, from January 2001 to June All Decile 1 Decile 2 Decile 3 Decile 4 Decile 5 Decile 6 Decile 7 Decile 8 Decile 9 Decile 10 Panel A: Portfolios Return Beta B/M Ratio ROC ROC (Revised) EY Panel B: B/M Ratio Portfolios Return Beta B/M Ratio ROC ROC (Revised) EY

26 Table 3. Decile Portfolios with Equal-weighted Summary Statistics (Continued) All Decile 1 Decile 2 Decile 3 Decile 4 Decile 5 Decile 6 Decile 7 Decile 8 Decile 9 Decile 10 Panel C: ROC Portfolios Return Beta B/M Ratio ROC ROC (Revised) EY Panel D: ROC (Revised) Portfolios Return Beta B/M Ratio ROC ROC (Revised) EY

27 Table 3. Decile Portfolios with Equal-weighted Summary Statistics (Continued) All Decile 1 Decile 2 Decile 3 Decile 4 Decile 5 Decile 6 Decile 7 Decile 8 Decile 9 Decile 10 Panel E: EY Portfolios Return Beta B/M Ratio ROC ROC (Revised) EY Panel F: MF 1 Portfolios Return Beta B/M Ratio ROC ROC (Revised) EY Panel G: MF 2 Portfolios Return Beta B/M Ratio ROC ROC (Revised) EY

28 Table 4. Decile Portfolios with Value-weighted Summary Statistics The monthly portfolio returns and risk measure are calculated as the means weighted by the market capitalization of each stock. The first column summarizes the subsample which has non-missing and non-negative values of the risk measure used to form portfolios. The samples are separated into 10 portfolios according to the decile breakpoints of each risk measure. The measures and the market capitalization used as the weights are both winsorized at 1% and 99% level to avoid the influence of the extreme values. All Decile_1 Decile_2 Decile_3 Decile_4 Decile_5 Decile_6 Decile_7 Decile_8 Decile_9 Decile_10 Panel A: Portfolios Return Beta B/M Ratio ROC ROC (Revised) EY Panel B: B/M Ratio Portfolios Return Beta B/M Ratio ROC ROC (Revised) EY

29 Table 4. Decile Portfolios with Value-weighted Summary Statistics (Continued) All Decile 1 Decile 2 Decile 3 Decile 4 Decile 5 Decile 6 Decile 7 Decile 8 Decile 9 Decile 10 Panel C: ROC Portfolios Return Beta B/M Ratio ROC ROC (Revised) EY Panel D: ROC (Revised) Portfolios Return Beta B/M Ratio ROC ROC (Revised) EY

30 Table 4. Decile Portfolios with Value-weighted Summary Statistics (Continued) All Decile 1 Decile 2 Decile 3 Decile 4 Decile 5 Decile 6 Decile 7 Decile 8 Decile 9 Decile 10 Panel E: EY Portfolios Return Beta B/M Ratio ROC ROC (Revised) EY Panel F: MF 1 Portfolios Return Beta B/M Ratio ROC ROC (Revised) EY Panel G: MF 2 Portfolios Return Beta B/M Ratio ROC ROC (Revised) EY

31 Table 5. Equal-weighted Average Returns on Double-sorted Portfolios The stocks are separated into 6 portfolios by size and one of the other risk measures. We use the median value of the size measure and the 30 th and 70 th percentile value of the other factor as the breakpoints. The portfolio returns of each month are calculated as the equal-weighted average of the stock returns in each portfolio. The table reports the means and standard deviations of the time-series of portfolio returns in annualized percentage value. The Sharpe ratios are calculated as the geometric means of returns divided by the standard deviations. Panel A: Arithmetic Means Panel B: Geometric Means B/M Ratio B/M Ratio Large Large Small Small ROC ROC Large Large Small Small ROC (Revised) ROC (Revised) Large Large Small Small EY EY Large Large Small Small MF 1 MF 1 Large Large Small Small MF 2 MF 2 Large Large Small Small

32 Table 5. Equal-weighted Average Returns on Double-sorted Portfolios (Continued) Panel C: Standard Deviations Panel D: Sharpe Ratios BM Ratio BM Ratio Large Large Small Small ROC ROC Large Large Small Small ROC (Revised) ROC (Revised) Large Large Small Small EY EY Large Large Small Small MF 1 MF 1 Large Large Small Small MF 2 MF 2 Large Large Small Small

33 Table 6. Value-weighted Average Returns on Double-sorted Portfolios The stocks are separated into 6 portfolios by size and one of the other risk measures. We use the median value of the size measure and the 30 th and 70 th percentile value of the other factor as the breakpoints. The portfolio returns of each month are calculated as the value-weighted average of the stock returns in each portfolio, using the natural logarithm of market capitalization as the weight. The table reports the means and standard deviations of the time-series of portfolio returns in annualized percentage value. The Sharpe ratios are calculated as the geometric means of returns divided by the standard deviations. Panel A: Arithmetic Means of Portfolio Returns Panel B: Geometric Means of Portfolio Returns BM Ratio BM Ratio Large Large Small Small ROC ROC Large Large Small Small ROC (Revised) ROC (Revised) Large Large Small Small EY EY Large Large Small Small MF 1 MF 1 Large Large Small Small MF 2 MF 2 Large Large Small Small

34 Table 6. Value-weighted Average Returns on Double-sorted Portfolios (Continued) Panel C: Standard Deviations of Portfolio Returns Panel D: Sharpe Ratios of Portfolio Returns BM Ratio BM Ratio Large Large Small Small ROC ROC Large Large Small Small ROC (Revised) ROC (Revised) Large Large Small Small EY EY Large Large Small Small MF 1 MF 1 Large Large Small Small MF 2 MF 2 Large Large Small Small

35 Table 7. Summary Statistics of the Risk Factors The factors are constructed by the value-weighted returns of the portfolios formed by the size, value and one of measures from the magic formula. For each measure, we use the median value as the breakpoints and separate the stocks into two categories. We use three letters to denote the categorization of a stock. For example, a stock in the "BHL" portfolio means it is a big stock with high book-to-market ratio and low magic formula measure. The market factor is calculated as the monthly Hang Seng Index return minus the 1-month HIBOR rate. Other factors are computed as the average return of the four portfolios with high value of the target measure minus the average return of the four portfolios with low value of the measure. We report the means, standard deviations and the t-statistics of the monthly factor values. *, **, ** are used to indicate the 10%, 5% and 1% significant level of the two-tail t-test. Panel A: Subsample 1 of stocks with positive size, book-to-market ratio and return on capital measures Summary Statistics Correlations Mean Std t-value sig. MKT SMB BM_HML ROC_HML MKT SMB BM_HML *** ROC_HML *** Panel B: Subsample 2 of stocks with positive size, book-to-market ratio and return on capital (revised) measures Summary Statistics Correlations Mean Std t-value sig. MKT SMB BM_HML ROC_R_HML MKT SMB BM_HML *** ROC_R_HML * Panel C: Subsample 3 of stocks with positive size, book-to-market ratio and earning yields measures Summary Statistics Correlations Mean Std t-value sig. MKT SMB BM_HML EY_HML MKT SMB BM_HML *** EY_HML

36 Table 7. Summary Statistics of the Risk Factors (Continued) Panel D: Subsample 4 of stocks with positive size, book-to-market ratio and magic formula measures Summary Statistics Correlations Mean Std t-value sig. MKT SMB BM_HML MF 1 _HML MKT SMB BM_HML *** MF 1 _HML Panel E: Subsample 5 of stocks with positive size, book-to-market ratio and magic formula (revised) measures Summary Statistics Correlations Mean Std t-value sig. MKT SMB BM_HML MF 2 _HML MKT SMB BM_HML *** MF 2 _HML

37 Table 8. Time-series Regressions of Excess Stock Returns on the Risk Factors The dependent variable of the regression is the value-weighted average monthly return of the sample stocks in excess of the 1-month HIBOR. We report the estimated coefficients and the Newey-West standard errors. There are 156 months. Panel A reports the estimates of the subsample 1 containing stocks with the factor MF 1 which is calculated following the magic formula from the sum of the rank of ROC and the rank of EY. Panel B shows the estimates of the subsample 2 containing stocks with the factor MF 2 which is computed from the revised magic formula measure using ROC (revised) instead of ROC. *, **, and *** are used to indicate the significance level of 10%, 5% and 1%. Intercept MKT SIZE_SMB BM_HML MF_HML Adj R-Square Panel A: Subsample 1 of stocks with positive size, book-to-market ratio and magic formula measure Coef *** ** Std Err (0.5050) (0.0977) (0.1511) (0.1701) Coef *** *** * *** Std Err (0.4933) (0.0915) (0.1526) (0.1609) (0.1127) Panel B: Subsample 2 of stocks with positive size, book-to-market ratio and magic formula (revised) measure Coef *** ** ** Std Err (0.4901) (0.0964) (0.1509) (0.1543) Coef *** ** ** *** Std Err (0.4813) (0.0898) (0.1591) (0.1501) (0.1254)

38 Table 9. Time-series Regressions of Portfolio Returns on the Risk Factors The dependent variable of the regression is the value-weighted return of 5 size portfolios formed on the quantile breakpoints of the size measure. We use the natural logarithm of the market capitalization as the weights. We report the estimated coefficients and the Newey-West standard errors in brackets. There are 156 months. Panel A reports the estimates on the market, size, value and magic formula measures, and Panel B shows the estimates using the ROC (revised) instead of ROC when we compute the magic formula measure. *, **, and *** are used to indicate the significance level of 10%, 5% and 1%. Intercept MKT SIZE_SMB BM_HML MF_HML Adj R-Square Panel A: Subsample 1 of stocks with positive size, book-to-market ratio and magic formula measure Portfolio *** *** *** * (0.6470) (0.1120) (0.2956) (0.3128) (0.1702) Portfolio *** *** *** ** (0.5899) (0.1035) (0.2233) (0.2216) (0.1374) Portfolio *** *** ** *** (0.5262) (0.1065) (0.1643) (0.1727) (0.1354) Portfolio *** ** * *** (0.5693) (0.1222) (0.1695) (0.1913) (0.1459) Portfolio ** *** ** (0.4280) (0.0729) (0.1564) (0.1428) (0.1178) Panel B: Subsample 2 of stocks with positive size, book-to-market ratio and magic formula (revised) measure Portfolio ** *** *** ** (0.6239) (0.1150) (0.2884) (0.2699) (0.2024) Portfolio *** *** *** * (0.5498) (0.1041) (0.2262) (0.1958) (0.1424) Portfolio *** *** ** *** (0.5025) (0.1075) (0.1683) (0.1502) (0.1426) Portfolio *** ** * *** (0.5489) (0.1223) (0.1707) (0.1782) (0.1364) Portfolio * *** ** (0.4046) (0.0735) (0.1609) (0.1269) (0.1179)

39 Table 10. Estimated Risk Premiums with Fama-MacBeth Regressions (from 07/ /2014) This table shows the risk premiums estimated from the Fama-Macbeth regressions. We first regress the excess returns of stocks against the risk factors for rolling windows of 12 months and estimate the beta for each risk factor and each stock. In the second stage, we run cross-sectional regressions of the stock excess returns on the estimated betas of risk factors for each month. The risk premiums of factors are determined as the time-series average of the estimated coefficients of the cross-sectional regression. In the table below, we report the time-series average of estimated coefficients and the Newey-West standard errors. There are 144 months of estimates from July 2002 to June Panel A reports the estimates on risk factors of size, value and MF 1 which is calculated from the magic formula as the sum of the rank of ROC and the rank of EY. Panel B shows the estimates on size, value and MF 2 factors where magic formula is revised using ROC (revised) instead of ROC in the calculation. *, **, and *** are used to indicate the significance level of 10%, 5% and 1%. MKT SIZE_SMB BM_HML MF_HML Panel A:Fama-MacBeth Estimates on, B/M Ratio and MF 1 Coef Std Err (0.1718) (0.0759) (0.0596) Coef *** Std Err (0.1672) (0.0783) (0.06) (0.0495) Panel B:Fama-MacBeth Estimates on, B/M Ratio and MF 2 Coef Std Err (0.1655) (0.0629) (0.0488) Coef *** Std Err (0.1711) (0.0684) (0.0472) (0.0532)

40 Table 11. Estimated Risk Premiums with Fama MacBeth Regressions (from 07/ /2014) This tables report the estimated risk premiums of the risk factors following the Fama-MacBeth regressions for a sub-period of the sample from July 2007 to June There are 84 months included. The time-series average of estimated risk premiums and the Newey-West standard errors are reported. Panel A shows the estimates on risk factors of size, value and MF 1, and Panel B shows the estimates on size, value and MF 2 factors where magic formula measure is revised using ROC (revised) instead of ROC in the calculation. *, **, and *** are used to indicate the significance level of 10%, 5% and 1%. MKT SIZE_SMB BM_HML MF_HML Panel A:Fama-MacBeth Estimates on, B/M Ratio and MF 1 Coef Std Err (0.2529) (0.0743) (0.0374) Coef *** Std Err (0.2425) (0.0750) (0.0361) (0.0534) Panel B:Fama-MacBeth Estimates on, B/M Ratio and MF 2 Coef Std Err (0.2568) (0.0744) (0.0414) Coef ** Std Err (0.2522) (0.0732) (0.0424) (0.0491)

41 Figure 1. Equal-weighted Monthly Portfolio Returns The stocks are sorted into 10 portfolios accordingg to the risk measures, i.e. size, book-to-market formula. The return on capital ratio, return on capital, earnings yield and the rankings calculated according to the magic employed is calculated in two ways, denoted as ROC and ROC (revised), and MF 1 and MF 2 refer to thee rankings computed with ROC and ROC (revised), respectively. We calculate the portfolio returnss as the equal-weighted means of the monthly returns of the stocks in each portfolio and report the average portfolio returnss over the sample period in the figures below Portfolios B/M Ratio R Portfolios Return (%) Return (%) Decile Decile ROC Portfolios ROC (revised) Portfolios Return (%) Return (%) Decile Decile EY Portfolios MFF 1 Portfolios Return (%) Return (%) Decile Decile MF 2 Portfolios Return (%) Decile

42 Figure 2. Value-weighted Monthly Portfolio Returns The stocks are sorted into 10 portfolios accordingg to the risk measures, i.e. size, book-to-market formula. The return on capital ratio, return on capital, earnings yield and the rankings calculated according to the magic employed is calculated in two ways, denoted as ROC and ROC (revised), and MF 1 and MF 2 refer to thee rankings computed with ROC and ROC (revise),( respectively. The portfolio returns are weighted by the market capitalization of the stocks in each month. Thee figures below shows thee average portfolio returnss over the sample period. Return (%) Portfolios Decile Return (%) B/M Ratio R Portfolios Decile Return (%) ROC Portfolios Decile Return (%) ROC (revised) Portfolios Decile Return (%) EY Portfolios Decile Return (%) MF 1 Portfolios Decilee 10 Return (%) MF 2 Portfolios Decile

43 Figure 3. Equal-weighted Averagee Returns on Double-sorted Portfolios We construct six portfolios with size and one of risk factors, and calculated the equal-weighted geometric means of the portfolio returns. The returns are annualized and reported in percentage level. We use the median value of the size measure to separatee the stocks into Big and Small group. For other measures, the stocks with the measure larger than the 70 th percentile breakpoint are categorized as the High group. Stocks with the measure smaller than the 30 th percentile breakpoint are categorized as the Low group. The rest are in the Middle group. Annualized Return (%) and B/M Ratio (2 3) Portfolios 0.00 High Medium Low S B Annualized Return (%) and ROC (2 3) PortfoliosP High Medium Low S B Annualized Return (%) and ROC (Revised) (2 3) Portfolios High Medium Low S B and EY (2 3) Portfolios and MF1 (2 3) Portfolios and MF2 (2 3) Portfolios Annualized Return (%) High Medium Low S B Annualized Return (%) High Medium Low S B Annualized Return (%) High Medium Low S B

44 Figure 4. Value-weighted Averagee Returns on Double-sorted Portfolios We construct six portfolios with size and one of risk factors, and calculated the annualized portfolio returns value-weighted by the natural logarithm of market capitalization. We use the median value of the size measure to separate the stocks into Big and Small group. For other measures, the stocks with the measure larger than the 70th percentile breakpoint are categorized as the High group. Stocks with the measure smaller than the 30th percentile breakpoint are categorized as the Low group. The rest are in the Middle group. Annualized Return (%) and B/M Ratio (2 3) Portfolios 0.00 High Medium Low S B Annualized Return (%) and ROC (2 3) Portfolios High Medium Low S B Annualized Return (%) and ROC (Revised) (2 3) Portfolios High Medium Low S B and EY(2 3) Portfolios and MF1 (2 3) Portfolios and MF2 (2 3) Portfolios Annualized Return (%) High Medium Low S B Annualized Return (%) High Medium Low S B Annualized Return (%) High Medium Low S B

45 Appendix. Stocks in the Top MF 1 Decile Portfolio The table below lists 36 stocks in the top decile MF 1 portfolio selected from our sample based on the rankings calculated from the magic formula in June, We reports the closing price of each stock at the end of the month, the market capitalization calculated as the closing price times the common shares outstanding, and the monthly return in percentage. Code Company Name Closing Price Market Capitalization (Million) Return (%) HK1008 BRILLIANT CIRCLE HLDGS INTL HK1023 SITOY GROUP HOLDINGS LTD HK113 DICKSON CONCEPTS (INTL) LTD HK1146 CHINA OUTFITTERS HOLDINGS HK1149 ANXIN-CHINA HOLDINGS LTD HK1240 SUNLEY HOLDINGS LTD HK1300 TRIGIANT GROUP LTD HK1335 SHEEN TAI HLDGS GROUP CO LTD HK1388 EMBRY HOLDINGS LTD HK175 GEELY AUTOMOBILE HLDGS LTD HK1830 PERFECT SHAPE (PRC) HLDG LTD HK2010 REAL NUTRICEUTICAL GRP LTD HK2200 HOSA INTERNATIONAL LTD HK2300 AMVIG HOLDINGS LTD HK2302 CNNC INTL LTD

46 HK2623 CHINA ZHONGSHENG RESOURCES HK282 NEXT MEDIA HK336 HUABAO INTL HLDGS LTD HK3777 CHINA FIBER OPTIC NETWORK HK426 ONE MEDIA GROUP HK477 AUPU GROUP HOLDING CO LTD HK483 BAUHAUS INTL (HLDGS) LTD HK540 SPEEDY GLOBAL HOLDINGS LTD HK550 CINDERELLA MEDIA GRP LTD HK566 HANERGY SOLAR GROUP LTD HK609 TIANDE CHEMICAL HLDGS LTD HK623 SINOMEDIA HOLDING LTD HK6838 WINOX HOLDINGS LTD HK703 FUTURE BRIGHT HOLDINGS LTD HK8039 PEGASUS ENTERTAINMENT HLDGS HK8058 SHANDONG LUOXIN PHARM STK CO HK8146 MASTERCRAFT INTL HOLDINGS HK833 ALLTRONICS HOLDINGS LTD HK837 CARPENTER TAN HLDGS LTD HK85 CHINA ELECTRS HLDGS CO LTD HK873 CHINA TAIFENG BEDDINGS HLDGS