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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.

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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 volatil-

ity 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 in-

clude 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

1Bridgewater launched the first investment product based on risk parity called the “All Weather” fundin 1996, and the term “risk parity”was originally coined by Edward Qian in 2005.

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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

2Specifically, Greenblatt rank the largest 3,500 stocks on the U.S. stock exchanges from 1 to 3,500 basedon their return on capital and earnings yield, respectively. The stock with the highest return on capital isassigned a rank of 1, and the stock with the lowest return on capital receives a rank of 3,500. Similarly, thestocks are ranked by the earnings yield as well, assigning number 1 to the one with the highest earning yieldand number 3,500 to the one with the lowest. Then, the two rankings are added. The stocks with the smalltotal ranks have a combination of high return on capital and high earnings yield. Getting excellent rankingsin both categories would be better than being the top-ranked in one category but being the bottom-rankedin the other under this system. Portfolios are formed based on the total ranking and rebalanced once a year.

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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 1998-2008 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

3Greenblatt’s book has become a bestseller since its initial publication. Several websites have beenbuilt for investors to employ the magic formula investing, including www.magicformulainvesting.com andwww.smartmoney.com.

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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 time-

series 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 time-

series 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

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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

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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 justi-

fications 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, re-

spectively. 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 supe-

rior 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.

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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.

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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, 2014. Table 3.1

reports the numbers and the total market capitalization of firms listed on the MB and GEM

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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$23780.2 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

4999. 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$11516.8

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

Returnt =(

PRCCDt/AJEXDIt × TRFDtPRCCDt−1/AJEXDIt−1 × TRFDt−1

− 1)× 100

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

4The number of listed firms and their total market capitalization data for year 2000 to 2013 are obtainedfrom the HKEx Fact Books released annually in the website of the Hong Kong Stock Exchange. The datafor 2014Q2 is obtained from the HKEx Securities and Derivatives Markets Quarterly Report.

5See http://wrds-web.wharton.upenn.edu/wrds/6The 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 StockExchange. We collect the closing price of HSI adjusted for dividends and splits at the end of each monthfrom January, 2000 to June, 2014. During the sample period, HSI began from 17057.7 and increased to the20,000 point milestone on December 28, 2006. In less than 10 months, it passed the 30,000 point milestoneon October 18, 2007. Its all-time high, set on October 30, 2007, was 31,958.41 points during trading and31,638.22 points at closing. From October 30, 2007 to October 27, 2008, the index fell nearly two-thirdsfrom its all-time peak to 10,676.29 points. But it rebounded to the 20,000 point milestone on 24 July, 2009.At the end of our sample period, HSI closed at 23,190.72 on June 30, 2014.

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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

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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 2014. 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 perfor-

mance. 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

7The historical exchange rate data is obtained from the website http://www.ozforex.com.au/forex-tools/historical-rate-tools/historical-exchange-rates.

8We use the variable definitions of French’s data library as ref-erence to calculate size and book-to-market ratio measures. Seehttp://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/variable_definitions.html

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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-to-

market 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 loga-

rithm of the market capitalization. Decile 1 contains the bottom 10% of stocks with smallest

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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,

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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.

3.2. 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 port-

folios on one of the other factors. We use the median of the size measure as the breakpoints

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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

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× (RSHH +RSHL +RSLH +RSLL)− 1/4× (RBHH +RBHL +RBLH +RBLL)

BM_HML = 1/4× (RSHH +RSHL +RBHH +RBHL)− 1/4× (RSLH +RSLL +RBLH +RBLL)

MF_HML = 1/4× (RSHH +RSLH +RBHH +RBLH)− 1/4× (RSHL +RSLL +RBHL +RBLL)

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

9We weight the returns using the natural logarithm of market capitalization to avoid the portfolio returnsto be dominated by the performance of a few very large firms in the portfolio.

17

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.

4.2. 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 value-

weighted 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. Size Portfolio

1 refers to the group of the smallest 20% stocks and Size 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

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.

4.3. 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 3.10. 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

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 2007. Hence, to make a robustness test of our analysis, we estimate the risk

premium again using the sample period from July 2007 to June 2014. The results are shown

in Table 3.11. 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

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 0.19.

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

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23

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. Size 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 (%) 134601 1.54 20.90 -99.94 110.53 78109 1.71 19.65 -96.58 110.53

Value-weighted Return (%) 134568 3.07 48.55 -99.94 110.53 78109 3.33 56.22 -96.58 110.53

Beta 135585 0.94 0.44 -1.11 3.35 78109 0.95 0.41 -0.91 2.92

Size 135495 6.71 1.79 -2.16 13.96 78109 7.03 1.76 1.48 13.96

Book-to-Market Ratio 125642 1.76 18.36 -347.70 1814.32 78109 1.37 2.11 -32.03 71.18

Return on Capital 73947 0.04 0.15 -0.71 0.54 68023 0.04 0.15 -0.71 0.54

Return on Capital (Revised) 83679 0.03 0.11 -0.60 0.36 76736 0.03 0.11 -0.60 0.36

Earnings Yields 81614 0.03 0.12 -0.44 0.68 75766 0.03 0.12 -0.44 0.68

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 2014.

All Decile 1 Decile 2 Decile 3 Decile 4 Decile 5 Decile 6 Decile 7 Decile 8 Decile 9 Decile 10 Panel A: Size Portfolios

Return 1.68 3.20 2.86 2.03 1.51 1.45 1.01 0.97 1.15 1.00 1.65 Beta 0.94 0.85 0.87 0.88 0.91 0.92 0.96 0.96 0.96 1.01 1.04 Size 6.48 3.98 4.83 5.31 5.71 6.09 6.51 6.97 7.50 8.25 9.73 B/M Ratio 1.59 2.34 2.01 2.04 1.87 1.65 1.51 1.25 1.20 1.00 1.03 ROC 0.04 -0.03 0.02 0.01 0.01 0.03 0.04 0.05 0.06 0.07 0.11 ROC (Revised) 0.03 -0.04 0.00 0.01 0.02 0.02 0.03 0.04 0.04 0.06 0.07 EY 0.04 0.01 0.03 0.04 0.04 0.07 0.05 0.06 0.05 0.04 0.03

Panel B: B/M Ratio Portfolios Return 1.64 0.52 1.00 1.02 1.15 1.60 1.92 2.17 2.40 2.36 2.27 Beta 0.93 0.92 0.94 0.94 0.93 0.93 0.93 0.93 0.92 0.91 0.98 Size 6.51 7.10 7.25 7.11 6.87 6.55 6.39 6.25 6.14 5.84 5.64 B/M Ratio 1.74 0.17 0.39 0.58 0.79 1.03 1.31 1.65 2.13 2.92 6.46 ROC 0.04 0.03 0.07 0.06 0.06 0.04 0.04 0.05 0.03 0.02 0.01 ROC (Revised) 0.03 0.01 0.05 0.05 0.05 0.03 0.03 0.04 0.03 0.02 0.01 EY 0.04 0.00 0.02 0.04 0.06 0.05 0.05 0.07 0.06 0.05 0.04

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 1.81 1.63 1.85 1.45 1.84 2.11 1.61 1.77 2.02 1.85 2.01 Beta 0.93 0.91 0.91 0.93 0.92 0.94 0.95 0.91 0.92 0.93 0.95 Size 7.06 6.38 6.65 6.73 7.00 7.16 7.14 7.41 7.47 7.55 7.28 B/M Ratio 1.46 2.31 2.09 1.82 1.65 1.39 1.28 1.00 0.97 0.83 1.03 ROC 0.10 0.01 0.02 0.04 0.05 0.07 0.08 0.10 0.13 0.17 0.32 ROC (Revised) 0.08 0.01 0.02 0.03 0.05 0.06 0.07 0.09 0.11 0.14 0.21 EY 0.08 0.02 0.04 0.06 0.06 0.08 0.08 0.08 0.09 0.11 0.15

Panel D: ROC (Revised) Portfolios Return 1.93 1.54 1.91 2.06 1.56 2.12 1.83 1.80 2.18 1.90 2.38 Beta 0.93 0.91 0.91 0.90 0.94 0.91 0.96 0.95 0.92 0.93 0.95 Size 7.11 6.57 6.93 7.00 7.10 7.06 7.16 7.29 7.44 7.47 7.19 B/M Ratio 1.50 2.13 2.21 1.95 1.99 1.48 1.28 1.08 0.94 0.89 0.64 ROC 0.10 0.01 0.03 0.04 0.06 0.07 0.09 0.10 0.13 0.17 0.28 ROC (Revised) 0.08 0.01 0.02 0.03 0.04 0.05 0.07 0.08 0.10 0.14 0.23 EY 0.07 0.02 0.03 0.05 0.06 0.07 0.08 0.08 0.08 0.11 0.15

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 1.96 1.34 1.69 2.18 1.85 2.00 1.74 1.77 2.30 2.32 2.62 Beta 0.93 0.90 0.94 0.93 0.94 0.97 0.94 0.93 0.94 0.89 0.89 Size 7.11 7.67 7.11 7.61 7.79 7.39 7.14 7.00 6.79 6.50 6.07 B/M Ratio 1.45 1.09 1.57 1.40 1.55 1.36 1.31 1.36 1.51 1.51 1.81 ROC 0.10 0.06 0.06 0.07 0.08 0.09 0.10 0.11 0.11 0.14 0.17 ROC (Revised) 0.07 0.04 0.04 0.05 0.06 0.07 0.08 0.09 0.09 0.11 0.13 EY 0.08 0.00 0.01 0.02 0.03 0.04 0.05 0.07 0.09 0.15 0.33

Panel F: MF1 Portfolios Return 1.79 2.53 2.36 1.69 1.45 1.51 2.05 1.99 2.00 1.09 1.30 Beta 0.92 0.90 0.94 0.93 0.92 0.92 0.92 0.91 0.94 0.94 0.93 Size 7.09 6.44 7.00 7.11 7.26 7.28 7.43 7.35 7.38 6.96 6.70 B/M Ratio 1.42 1.40 1.13 1.20 1.20 1.39 1.29 1.51 1.46 1.78 1.93 ROC 0.10 0.24 0.15 0.12 0.11 0.09 0.09 0.07 0.05 0.03 0.01 ROC (Revised) 0.08 0.18 0.12 0.10 0.09 0.08 0.07 0.05 0.04 0.02 0.01 EY 0.08 0.23 0.13 0.10 0.08 0.07 0.05 0.04 0.03 0.02 0.01

Panel G: MF2 Portfolios Return 1.92 2.91 2.15 2.06 1.37 1.90 1.72 1.93 2.16 1.84 1.10 Beta 0.93 0.89 0.95 0.93 0.93 0.93 0.94 0.93 0.89 0.94 0.93 Size 7.14 6.38 6.99 7.09 7.23 7.23 7.30 7.57 7.49 7.23 6.81 B/M Ratio 1.47 1.19 1.14 1.29 1.25 1.43 1.37 1.75 1.67 1.84 1.77 ROC 0.10 0.23 0.15 0.12 0.10 0.09 0.08 0.07 0.05 0.04 0.02 ROC (Revised) 0.07 0.18 0.12 0.10 0.08 0.08 0.07 0.05 0.04 0.02 0.01 EY 0.07 0.23 0.12 0.09 0.08 0.06 0.04 0.03 0.03 0.02 0.01

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: Size Portfolios

Return 4.11 8.39 6.32 6.92 4.71 4.13 3.50 3.06 3.11 2.55 4.36 Beta 1.00 0.91 0.90 0.90 0.94 0.93 0.97 0.98 0.98 1.00 1.00 Size 9.52 4.06 4.85 5.33 5.72 6.10 6.53 6.99 7.53 8.31 10.40 B/M Ratio 1.40 2.97 1.84 1.96 1.94 1.63 1.59 1.33 1.29 1.03 1.43 ROC 0.10 -0.03 0.03 0.01 0.02 0.05 0.04 0.07 0.07 0.09 0.12 ROC (Revised) 0.07 -0.03 0.01 0.01 0.03 0.03 0.03 0.05 0.05 0.07 0.08 EY 0.03 0.02 0.04 0.04 0.04 0.07 0.06 0.07 0.05 0.04 0.03

Panel B: B/M Ratio Portfolios Return 4.37 2.01 1.99 1.92 2.27 2.50 6.15 5.29 10.76 7.51 3.08 Beta 0.99 0.95 1.01 1.04 1.03 1.05 1.07 1.06 0.93 0.93 0.99 Size 9.50 10.01 9.44 9.10 8.81 8.46 8.83 8.66 9.12 8.73 9.66 B/M Ratio 1.42 0.16 0.39 0.57 0.78 1.02 1.30 1.68 2.13 2.94 6.28 ROC 0.10 0.19 0.12 0.08 0.08 0.06 0.06 0.05 0.05 0.04 0.03 ROC (Revised) 0.07 0.14 0.08 0.06 0.06 0.04 0.04 0.04 0.03 0.03 0.03 EY 0.03 0.02 0.03 0.03 0.05 0.04 0.05 0.04 0.04 0.05 0.03

Table 4. Decile Portfolios with Value-weighted Summary Statistics (Continued)


Panel C: ROC Portfolios

Return 2.60 2.91 4.87 2.22 2.28 2.18 2.01 2.14 2.83 2.18 2.57 Beta 1.03 1.06 1.00 1.14 1.08 1.05 1.01 0.98 1.02 1.00 1.00 Size 9.68 8.48 8.93 9.21 9.75 9.27 8.90 9.25 9.39 9.65 9.61 B/M Ratio 0.99 1.52 1.61 1.32 1.90 1.19 0.81 0.74 0.63 0.49 0.48 ROC 0.12 0.01 0.02 0.04 0.05 0.07 0.08 0.10 0.13 0.17 0.31 ROC (Revised) 0.09 0.01 0.02 0.03 0.04 0.06 0.07 0.08 0.10 0.14 0.20 EY 0.04 0.01 0.03 0.03 0.04 0.04 0.04 0.05 0.05 0.05 0.07

Panel D: ROC (Revised) Portfolios


Table 4. Decile Portfolios with Value-weighted Summary Statistics (Continued)


Panel E: EY Portfolios


Panel F: MF1 Portfolios


Panel G: MF2 Portfolios


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 30th and 70th 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

High Medium Low High Medium Low

Size Large 27.67 16.41 5.09 Size Large 26.08 13.09 1.30 Small 28.04 25.96 20.00 Small 26.45 24.12 15.62

ROC ROC High Medium Low High Medium Low


ROC (Revised) ROC (Revised) High Medium Low High Medium Low


EY EY High Medium Low High Medium Low


MF1 MF1 High Medium Low High Medium Low


MF2 MF2 High Medium Low High Medium Low


Table 5. Equal-weighted Average Returns on Double-sorted Portfolios (Continued)

Panel C: Standard Deviations Panel D: Sharpe Ratios

BM Ratio BM Ratio High Medium Low High Medium Low

Size Large 29.25 28.26 27.41

Size Large 0.89 0.46 0.05

Small 29.81 29.32 33.46 Small 0.89 0.82 0.47 ROC ROC


Size Large 27.12 28.63 28.51

Size Large 0.57 0.51 0.35

Small 28.98 28.10 28.09 Small 1.10 0.96 0.74 ROC (Revised) ROC (Revised)


Size Large 27.21 28.52 26.94

Size Large 0.65 0.46 0.80

Small 28.27 28.53 28.92 Small 1.23 0.97 0.65 EY EY


Size Large 28.83 27.11 26.77

Size Large 0.84 0.52 0.57

Small 27.97 28.84 28.99 Small 1.06 0.99 0.85 MF1 MF1


Size Large 29.88 26.23 28.87

Size Large 0.68 0.53 0.20

Small 27.53 28.90 28.84 Small 1.04 0.86 0.78 MF2 MF2


Size Large 29.39 27.31 26.74

Size Large 0.79 0.47 0.68

Small 27.63 29.45 28.34 Small 1.13 0.89 0.69

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 30th and 70th 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


Size Large 29.42 16.70 5.79

Size Large 28.47 13.41 2.07



Size Large 18.00 17.17 13.84

Size Large 15.32 13.86 10.29



Size Large 19.87 16.00 25.63

Size Large 17.44 12.56 24.56

Small 33.13 27.77 19.65 Small 33.41 26.50 16.90 EY EY


Size Large 25.81 17.39 18.77

Size Large 23.86 14.61 16.34

Small 28.86 28.52 23.89 Small 28.02 27.41 21.94 MF1 MF1


Size Large 23.10 16.03 9.96

Size Large 20.32 13.28 6.04

Small 28.01 25.23 23.03 Small 27.14 23.22 20.89 MF2 MF2


Size Large 25.37 15.75 22.00

Size Large 23.20 12.68 20.22

Small 30.27 26.72 19.85 Small 29.93 24.87 17.38

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


Size Large 28.69 28.28 27.19

Size Large 0.99 0.47 0.08



Size Large 26.87 28.59 28.34

Size Large 0.57 0.48 0.36



Size Large 27.03 28.44 26.44

Size Large 0.65 0.44 0.93

Small 28.34 28.45 28.33 Small 1.18 0.93 0.60 EY EY


Size Large 28.90 26.97 26.48

Size Large 0.83 0.54 0.62

Small 27.91 28.72 28.22 Small 1.00 0.95 0.78 MF1 MF1


Size Large 29.80 26.17 28.57

Size Large 0.68 0.51 0.21

Small 27.45 28.92 28.34 Small 0.99 0.80 0.74 MF2 MF2


Size Large 29.37 27.15 26.30

Size Large 0.79 0.47 0.77

Small 27.64 29.43 27.60 Small 1.08 0.85 0.63

Table 7. Summary Statistics of the Risk Factors

The factors are constructed by the value-weighted returns of the 2×2×2 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 0.44 6.14 0.90 1.00 -0.34 0.18 0.10 SMB 0.46 3.86 1.47 -0.34 1.00 -0.17 -0.18 BM_HML 1.17 2.53 5.76 *** 0.18 -0.17 1.00 0.20 ROC_HML 0.51 2.03 3.14 *** 0.10 -0.18 0.20 1.00

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 0.44 6.14 0.90 1.00 0.02 -0.26 -0.29 SMB 0.17 4.36 0.48 0.02 1.00 -0.42 -0.49 BM_HML 1.44 3.33 5.41 *** -0.26 -0.42 1.00 0.61 ROC_R_HML 0.49 3.20 1.92 * -0.29 -0.49 0.61 1.00

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 0.44 6.14 0.90 1.00 -0.24 0.12 -0.04 SMB 0.10 3.73 0.32 -0.24 1.00 -0.13 0.01 BM_HML 1.28 2.51 6.35 *** 0.12 -0.13 1.00 -0.02 EY_HML 0.00 2.15 0.02 -0.04 0.01 -0.02 1.00

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 MF1_HML MKT 0.44 6.14 0.90 1.00 -0.32 0.17 0.03 SMB 0.40 3.82 1.31 -0.32 1.00 -0.20 -0.07 BM_HML 1.05 2.66 4.92 *** 0.17 -0.20 1.00 -0.05 MF1_HML 0.28 2.25 1.54 0.03 -0.07 -0.05 1.00

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 MF2_HML MKT 0.44 6.14 0.90 1.00 -0.30 0.16 0.06 SMB 0.02 3.76 0.07 -0.30 1.00 -0.09 -0.08 BM_HML 1.43 2.49 7.17 *** 0.16 -0.09 1.00 0.05 MF2_HML 0.27 2.20 1.52 0.06 -0.08 0.05 1.00

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 MF1 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 MF2 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 0.6441 1.0466 *** 0.3937 ** 0.2785 0.6626 Std Err (0.5050) (0.0977) (0.1511) (0.1701) Coef 0.5101 1.0447 *** 0.4122 *** 0.3006 * 0.3753 *** 0.6728 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 0.7478 1.0296 *** 0.3573 ** 0.3391 ** 0.6700 Std Err (0.4901) (0.0964) (0.1509) (0.1543) Coef 0.6662 1.0241 *** 0.3707 ** 0.3269 ** 0.3782 *** 0.6800 Std Err (0.4813) (0.0898) (0.1591) (0.1501) (0.1254)

Table 9. Time-series Regressions of Size 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 Size Portfolio 1 0.9166 1.0812 *** 1.2936 *** 0.8325 *** 0.2824 * 0.5758

(0.6470) (0.1120) (0.2956) (0.3128) (0.1702) Size Portfolio 2 -0.0053 1.0489 *** 0.9489 *** 0.6883 *** 0.3335 ** 0.6059

(0.5899) (0.1035) (0.2233) (0.2216) (0.1374) Size Portfolio 3 -0.2391 1.0790 *** 0.7413 *** 0.4167 ** 0.4337 *** 0.6145

(0.5262) (0.1065) (0.1643) (0.1727) (0.1354) Size Portfolio 4 -0.1405 1.0590 *** 0.3768 ** 0.3387 * 0.4422 *** 0.5924

(0.5693) (0.1222) (0.1695) (0.1913) (0.1459) Size Portfolio 5 0.7897 ** 1.0910 *** -0.0444 0.0207 0.2690 ** 0.7324

(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

Size Portfolio 1 1.3640 ** 1.0743 *** 1.3076 *** 0.6781 ** 0.1082 0.5840 (0.6239) (0.1150) (0.2884) (0.2699) (0.2024)

Size Portfolio 2 0.2023 1.0362 *** 0.9510 *** 0.6308 *** 0.2656 * 0.6141 (0.5498) (0.1041) (0.2262) (0.1958) (0.1424)

Size Portfolio 3 -0.0112 1.0686 *** 0.7548 *** 0.3510 ** 0.4258 *** 0.6228 (0.5025) (0.1075) (0.1683) (0.1502) (0.1426)

Size Portfolio 4 -0.0899 1.0497 *** 0.3753 ** 0.3242 * 0.4159 *** 0.5942 (0.5489) (0.1223) (0.1707) (0.1782) (0.1364)

Size Portfolio 5 0.6870 * 1.0791 *** -0.0777 0.0870 0.2386 ** 0.7328 (0.4046) (0.0735) (0.1609) (0.1269) (0.1179)

Table 10. Estimated Risk Premiums with Fama-MacBeth Regressions (from 07/2002-06/2014)

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 2014. Panel A reports the estimates on risk factors of size, value and MF1 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 MF2 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 Size, B/M Ratio and MF1

Coef -0.0385 0.0752 -0.0586 Std Err (0.1718) (0.0759) (0.0596) Coef -0.0798 0.0509 -0.0804 0.1921 *** Std Err (0.1672) (0.0783) (0.06) (0.0495)

Panel B：Fama-MacBeth Estimates on Size, B/M Ratio and MF2

Coef -0.0191 0.0152 0.0088 Std Err (0.1655) (0.0629) (0.0488) Coef -0.0351 0.0312 -0.0391 0.1507 *** Std Err (0.1711) (0.0684) (0.0472) (0.0532)

Table 11. Estimated Risk Premiums with Fama MacBeth Regressions (from 07/2007-06/2014)

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 2014. 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 MF1, and Panel B shows the estimates on size, value and MF2 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 Size, B/M Ratio and MF1

Coef 0.1307 -0.0310 -0.0259 Std Err (0.2529) (0.0743) (0.0374) Coef 0.0784 -0.0344 -0.0314 0.1613 *** Std Err (0.2425) (0.0750) (0.0361) (0.0534)

Panel B：Fama-MacBeth Estimates on Size, B/M Ratio and MF2

Coef 0.1170 -0.0437 -0.0150 Std Err (0.2568) (0.0744) (0.0414) Coef 0.1594 -0.0559 -0.0229 0.1130 ** Std Err (0.2522) (0.0732) (0.0424) (0.0491)

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Appendix. Stocks in the Top MF1 Decile Portfolio

The table below lists 36 stocks in the top decile MF1 portfolio selected from our sample based on the rankings calculated from the magic formula in June, 2014. 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 1.28 1905.24 -2.15

HK1023 SITOY GROUP HOLDINGS LTD 4.73 4737.25 0.43

HK113 DICKSON CONCEPTS (INTL) LTD 4.72 1800.51 2.83

HK1146 CHINA OUTFITTERS HOLDINGS 1.12 3858.90 0.90

HK1149 ANXIN-CHINA HOLDINGS LTD 1.04 3183.43 -0.97

HK1240 SUNLEY HOLDINGS LTD 2.73 819.00 8.33

HK1300 TRIGIANT GROUP LTD 2.11 2352.65 3.99

HK1335 SHEEN TAI HLDGS GROUP CO LTD 1.73 719.11 12.79

HK1388 EMBRY HOLDINGS LTD 4.49 1870.81 -0.22

HK175 GEELY AUTOMOBILE HLDGS LTD 2.73 24027.95 -4.30

HK1830 PERFECT SHAPE (PRC) HLDG LTD 2.31 2617.23 16.08

HK2010 REAL NUTRICEUTICAL GRP LTD 1.75 1965.31 4.79

HK2200 HOSA INTERNATIONAL LTD 2.45 4053.69 -5.77

HK2300 AMVIG HOLDINGS LTD 2.73 2515.82 -3.51

HK2302 CNNC INTL LTD 2.17 1061.50 3.33

HK2623 CHINA ZHONGSHENG RESOURCES 1.37 987.59 -0.73

HK282 NEXT MEDIA 0.85 2066.36 2.41

HK336 HUABAO INTL HLDGS LTD 4.59 14235.05 27.15

HK3777 CHINA FIBER OPTIC NETWORK 1.79 2604.45 -3.72

HK426 ONE MEDIA GROUP 0.52 208.00 -5.46

HK477 AUPU GROUP HOLDING CO LTD 0.90 939.15 3.45

HK483 BAUHAUS INTL (HLDGS) LTD 2.57 937.56 7.53

HK540 SPEEDY GLOBAL HOLDINGS LTD 0.36 213.00 4.41

HK550 CINDERELLA MEDIA GRP LTD 1.13 377.01 -6.61

HK566 HANERGY SOLAR GROUP LTD 1.19 34277.51 5.31

HK609 TIANDE CHEMICAL HLDGS LTD 1.64 1388.88 -7.87

HK623 SINOMEDIA HOLDING LTD 5.99 3384.62 -5.13

HK6838 WINOX HOLDINGS LTD 0.66 330.00 0.00

HK703 FUTURE BRIGHT HOLDINGS LTD 3.70 2568.92 -1.60

HK8039 PEGASUS ENTERTAINMENT HLDGS 0.82 393.60 0.00

HK8058 SHANDONG LUOXIN PHARM STK CO 11.18 1839.78 8.34

HK8146 MASTERCRAFT INTL HOLDINGS 0.47 225.60 -14.55

HK833 ALLTRONICS HOLDINGS LTD 1.92 664.06 0.50

HK837 CARPENTER TAN HLDGS LTD 4.76 1190.00 3.03

HK85 CHINA ELECTRS HLDGS CO LTD 1.55 2621.92 -3.74

HK873 CHINA TAIFENG BEDDINGS HLDGS 0.94 940.00 25.33

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