Greenblatt Wizardry: A Quantitative Look At The Magic Formula

by: Ryan Telford


Magic Formula investing has outperformed over time.

While returns are not as impressive as some single factor value strategies, the Large Cap strategy of the Magic Formula has been a less volatile strategy with improved base rates.

The “quality companies on sale” criterion allows investors to invest in some household names.

Click to enlarge


The Magic Formula (MF) is a quantitative investing method devised by famed value investor Joel Greenblatt. Greenblatt outlined the Magic Formula in his 2004 book "The Little Book that Beats the Market." After a few years of market performance, he updated the book in 2010 with updated portfolio performance in "The Little Book that Still Beats the Market."

I have written previously on the Magic Formula, describing the method in detail. In this article I would like to continue that thought, but with my own independent backtesting of this strategy.

The Strategy

The Magic Formula screen essentially ranks stocks on two metrics, low relative cost ("cheap") and high returns on capital ("quality" or "good"). Greenblatt's desire was to combine the investment philosophies of both Benjamin Graham (the "cheap" component) and Warren Buffett (the "quality" component). This screen finds quality firms at a discount, in the true sense of value investing.

Greenblatt created the screening website to allow investors to screen for these types of stocks.

It is important to note here that the Magic Formula is a "multi-factor" strategy in quantitative investing-speak. In previous articles I have discussed the low EV/EBIT strategy, which ranks stocks on a "single factor," namely the EV/EBIT value. The Magic Formula ranks all stocks in the universe by "cheapness," and by "quality." Each is weighted equally and a composite score allows ranking of all stocks.

This is also a "buy and hold" strategy, where an investor purchases a portfolio of stocks, as specified by the given screen criteria, and holds (1 year is typical). At the end of the period, the portfolio is updated with the new screen results, i.e. sell those no longer appearing on the screen and replace with new issues.

Factor #1: Cheapness

The Benjamin Graham half of this strategy, this factor looks for firms selling at low valuations relative to their price. Greenblatt used low enterprise value to earnings before interest and taxes (EV/EBIT). Let's take a look at the rationale for using this value.

The price-to-earnings ratio (P/E) is a helpful value to see how the market values a company's stock based on its earnings. It is easily determined and commonly available on finance websites such as Yahoo or Morningstar.

Breaking the P/E ratio down, we have the

  • "Price" numerator, which is based on market value of the equity (current market price x shares outstanding), and the
  • "Earnings" denominator, the reported earnings per share (can be either trailing or forecast future/analyst consensus)

The Limits of "Price"

The "price" component of the P/E ratio only takes into account the market value of the firm's equity, and not the total capital structure of the firm. A firm's total value arguably also considers total debt, which can be used to finance their operations. Debt is of course a double-edged sword; if managed sensibly, it can be used to leverage profits and potentially stock returns. If not managed carefully however, it can lead to issues and complications such as missed interest payments, de-ratings in credit score, etc. Firms have different capital structures, so using only the equity value of the firm can be limiting.

An alternative to using only market cap for the "price" component is the enterprise value, EV. The enterprise value represents the total value that the firm could be purchased for by a private equity firm or a larger firm. This includes market cap, total debt, but also preferred equity (i.e. preferred shares, market cap only includes the value of common shares) and minority interests (stakes or holdings in other companies, stocks, etc.). Any cash holdings the target firm has on the books would reduce the total amount the acquiring firm would be required to outlay in the purchase/acquisition as well.

In summary:

Enterprise Value = Market Equity + Total Debt + Preferred Equity + Minority Interests - Cash and Eq

The Limits of "Earnings"

Earnings per share, EPS, is typically used as the denominator in the P/E ratio, which reports net income per share. Net income is an accounting value, and does not necessarily reflect the cash the firm has available as several non-cash charges are deducted from the gross revenue. Such non-cash charges include (but are not limited to):

  • depreciation and amortization, and
  • any tax breaks the firm would receive from interest payments on debt obligations.

An alternative to EPS is EBIT (or Earnings Before Interest and Taxes). EBIT allows investors to look at the earnings of a firm without the benefit of tax shields. The advantage of EBIT is that you can now compare different companies, even in different industries, with different capital structures with a more direct "apples to apples" comparison.

Putting it together, Greenblatt substitutes P/E with EV/EBIT.

Investors may use the inverse of P/E, or E/P, better known as "earnings yield." This is essentially how the firm generates earnings relative to its price. For a value investor, you would look for firms with low P/E ratios. Since earnings yield (E/P) is simply the inverse of P/E, the higher the earnings yield, the better.

For ranking purposes, Greenblatt uses his version of earnings yield to rank companies on their "cheap" factor, or EBIT/EV.


E/P can be influenced (and appear better) by debt and tax rates, whereas EBIT/EV cannot.

To illustrate the impact that debt can have on the capital structure and thus how it reports earnings, look at the two firms below. Firms 'A' and 'B' are identical except their capital structure is different (see the $50/share of debt that Firm 'B' carries).

(Source: Greenblatt p 171 and Author Table)

While a simple example, the impact of debt on a firm's balance sheet is not revealed through the E/P ratio, and illustrates how the EV/EBIT (or EBIT/EV) metric is superior in this regard.

Factor #2: The Quality Factor

Any discussion on quality usually revolves around the ability of a firm to generate returns on its capital, and if it can sustain high returns, may suggest that the firm has a competitive edge, or moat.

Return on Capital is the second half of the Magic Formula that attempts to emulate Buffett (where the "cheap" component attempts to mimic Benjamin Graham).

The basic formula for return on capital is:

Operating Income / Capital


  • "Operating Income" could be taken as EBIT, EBITDA, NOPAT (Net Operating Income after Tax), Operating Earnings, etc.
  • "Capital" can be "invested capital", "capital employed", or "assets." Capital includes various assets, such as basic working capital (current assets - current liabilities), or variations of it. Working capital may or may not include intangible assets.

For the Magic Formula, Greenblatt identifies "quality" companies by using "Return on Tangible Capital Employed" or EBIT / Tangible Capital Employed

Where Tangible Capital Employed = Net Working Capital + Net Fixed Assets

As we discussed in the earnings yield section, EBIT is used to remove any effects from tax shields or leverage from debt, to more easily compare firms in different industries and capital structures.

Tangible capital employed is defined as the actual capital required to operate the business. "Net Working Capital" is defined as current assets less current liabilities. Adjustments include the subtraction of both excess cash and short-term interest bearing debt.

Greenblatt's version of ROC excludes intangible assets such as goodwill, as they are not directly required for operation of the business.

"Net Fixed Assets" is simply the firm's Property, Plant and Equipment account, less accumulated depreciation (line item on the balance sheet).

Putting it all Together

To recap, Greenblatt uses "EBIT/EV" as his earnings yield factor, as "EBIT/Tangible Capital Employed" as his quality factor.

The Magic Formula is a ranking strategy. All stocks in the universe are ranked in terms of high EBIT/EV and given a score out of 100. The same stocks are ranked and scored in terms of high ROC. The two rank scores are summed and the overall score determines the stock's position in the overall strategy. Note that cheapness and quality factors both carry a weighting of 50% each.

The Universe

As versatile as EBIT and Enterprise value are, they do not suit utility companies or financial firms particularly well due to the structure of their financial reporting. For this reason both sectors are excluded from the strategy and the backtests.

Typical Stocks

Stocks selected by this Greenblatt strategy are typically known firms. While not all are household names, an investor should recognize many of these firms. Most high ROC firms are higher profile and may make an investor more comfortable knowing what s/he is buying.

The table below shows the 30 top-ranked stocks in the Large Cap US Magic Formula screen as of 01 Jan. of 2016. Note household names such as Apple, Gilead, Cisco, Oracle and Time Warner.

Ticker Name Market Cap ($M)
KING King Digital Entertainment plc 5646.61
GILD Gilead Sciences Inc 150087.44
AAPL Apple Inc 602672.69
VIAB Viacom Inc 16365.89
STRZA Starz 3433.73
HUM Humana Inc. 26428.34
KORS Michael Kors Holdings Ltd 7520.24
BRCD Brocade Communications Systems, Inc. 3750.14
QCOM QUALCOMM Inc. 75514.2
HLF Herbalife Ltd. 5126.34
DISCA Discovery Communications, Inc. 12694.37
CA CA, Inc. 12581.85
UTHR United Therapeutics Corp. 7334.76
TARO Taro Pharmaceutical Industries Ltd. 6681.13
AET Aetna Inc. 38227.98
CSCO Cisco Systems, Inc. 139145.14
ANTM Anthem, Inc. 36690.23
SNI Scripps Networks Interactive, Inc. 7116.13
TGNA TEGNA, Inc. 5748.5
ORCL Oracle Corp. 155738.08
AMSG AmSurg Corp. 3688.88
FFIV F5 Networks, Inc. 6834.25
SYNT Syntel, Inc 3811.78
PPC Pilgrim's Pride Corp. 5797.25
AMCX AMC Networks Inc. 5560.46
HRB H&R Block, Inc. 7864.18
LYB LyondellBasell Industries NV 39927.34
MOH Molina Healthcare, Inc. 3430.67
RHI Robert Half International Inc. 6254.54
TWX Time Warner Inc. 51705.18
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(Source: Portfolio123 data)

The Performance

Let's take a look at how the Magic Formula has performed since 1999.

For a refresher on backtesting and the key statistics and how they are determined, please read here and here.

Summary Statistics, Large Cap US Universe

(Source: Portfolio123 data and Author Calculations)

Returns are quite impressive compared to that of the benchmark Russell 1000 TR. An investor would experience increased volatility compared to investing in the Russell 1000 TR index, however with significantly better return. Drawdown is only a few percentage points greater as well.

Base Rates

Let's take a look to see how the Magic Formula has done over various rolling periods. Remember that the odds of a strategy beating its benchmark, BM, over a series of rolling periods are referred to as the base rate.

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(Source: Portfolio123 data and Author Calculations)

Note that an investor would have beaten the benchmark 78% of the time on all 1-year rolling periods, not bad. Not all one year periods in other strategies have such a high base rate.

The 5-, 7- and 10-year periods show good base rates as well, all greater than 85% of the time an investor would have beaten the BM in the periods.

It should not be a surprise that when the strategy outperformed the BM, it did so by at least 14.1%. This historical data shows us that while volatility exists (as it does in all strategies), in the end the final returns and odds of beating the BM has been quite high.

Rolling 5-Year Return Trend

An interesting piece of information to look at for any strategy is how the CAGR varies over rolling periods. We will find that most strategies are cyclical; when the 5-year strategy return begins to drop, over time it often returns to a higher position.

The graph below shows us how the rolling 5-year period has done, in terms of compounded rate per 5 years, in excess (or below) the benchmark.

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(Source: Portfolio123 data and Author Calculations & Graph)

You can see from this graph that there were some periods where the strategy failed to beat the benchmark over rolling 5-year periods. The most significant of these periods was 2011 and late 2012. That being said, after these troughs it returned to positive territory in a few months. This was particularly dramatic after late 2012; the 5-year difference between the strategy and the benchmark spiked to over 50% for the period ending 2013, but then dropped again.

Maximum and Minimum Compounded Annual Rates

The table below shows the best and worst rolling period of each of the time spans.

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(Source: Portfolio123 data and Author Calculations)

This is encouraging, as the Magic Formula has either performed better or lost less than the respective period of the benchmark for all minimum and maximum periods.

While every investor expects a positive return over longer periods, it is not always the case as the above table shows. Note that if an investor invested in the Russell 1000TR index in March of 1999, he/she would have experienced a CAGR of -2.6% over the next 10 years. While most of this poor return likely happened in 2008/2009, investing in the Magic Formula for 10 years would not only have put the investor in positive territory, but the worst 10-year period (8%) is only 1.5% within the benchmark's best 10-year period (9.5%). In other terms, the large cap strategy would have resulted in a minimum of doubling your investment (8% CAGR), or best case making 4.5X your initial investment, whereas worst case Russell 1000TR an investor would have lost money, best case more than doubling their money ($10,000 becomes $24,778).

For both Greenblatt and the BM, the worst periods ended in 2008 or 2009, which should not be a surprise.

Now let's see how the same strategy has performed with a larger universe.

The Performance, Large And Mid Cap

Let's see how the Magic Formula has fared in the large and mid-range market cap since 1999.

Summary Statistics:

(Source: Portfolio123 data and Author Calculations)

The benchmark in this case is the Russell 3000TR, which looks at stocks of mid to large size (whereas the R1000TR is only large cap).

While slightly less return than the Large Cap version, returns are still impressive compared to that of the benchmark Russell 3000 TR. An investor would have experienced increased volatility compared to investing in the Russell 3000 TR index, however with significantly better return. Comparing to the Large Cap strategy, volatility is higher as shown in the standard deviation and lower Sharpe and Sortino ratios. Drawdown is actually slightly less than that of the benchmark.

Base Rates

Return and volatility are important over the entire period; however, let's take a closer look at the strategy over smaller time periods, or the base rates (the odds of a strategy beating its benchmark, BM, over a series of rolling periods).

Click to enlarge

(Source: Portfolio123 data and Author Calculations)

Base rates are generally lower by 8-12% for each rolling period span, compared to the Large Cap strategy. Instead of beating the benchmark 78% of the time over a one year period, the odds drop to about 68%. Longer term an investor could have beaten the benchmark nearly 88% of the time over 10 years, however there also means that 12% of the time that he/she would not have. For comparison the Large Cap version has beaten its respective benchmark nearly 96% of the time over the same period.

Still, when the strategy beat the benchmark, it did so by at least 17% in any rolling period (actually higher than the Large Cap strategy).

Rolling 5-Year Return Trend

The graph below shows us how the rolling 5-year period has done, in terms of compounded rate per 5 years, in excess (or below) the benchmark.

Click to enlarge

(Source: Portfolio123 data and Author Calculations and Graph)

The strategy shows an overall decrease in performance above the benchmark over 5-year rolling periods from about 2004 to 2012. It stays in positive territory for most of that period until 2010, where it wavers back and forth around the 0% mark (remember that 0% simply means the strategy has not beaten the benchmark, and negative values indicate that the strategy has underperformed the benchmark over the periods). After dropping to about -10%, it then returns to positive territory and ends up reaching its second highest peak since 1999. This is another reminder that all strategies have times of underperformance, that is eventually followed by outperformance.

Maximum and Minimum Compounded Annual Rates

The table below shows the best and worst rolling period of each of the time spans.

Click to enlarge

(Source: Portfolio123 data and Author Calculations)

In all periods except the minimum 1 year, this strategy has either performed better, or lost less, than the respective period of the benchmark at the minimum and maximum periods.

As we saw with the Large Cap strategy, investing over long time periods in the Russell Indices does not always provide a positive return. This is evident with the Russell3000TR as well, as you can see the minimum return for all holding periods is negative, whereas an investor in the Magic Formula, Large & Mid Cap, would have made money after holding for 7 and 10 years.

Best case, the strategy had very high maximum returns over the periods, quite higher than the benchmark, and even higher than the Large Cap strategy over some periods.

Like the Large Cap strategy, both Greenblatt LC & MC and the Russell 3000TR, most of the worst periods ended in 2008 or 2009, which should not be a surprise.

To Conclude

Both classes of the Magic Formula have done quite well since 1999. In addition to experiencing very attractive returns, they boast of high base rates and attractive long-term rolling results. Generally Large Cap experienced higher returns with less volatility than its Large/Mid Cap cousin.

On a less statistical basis, the stocks in this screen are typically well-known stocks, many of which may be household names. For those investors who feel better knowing what they are purchasing, this strategy may have you covered in that department.

As was hinted in the introduction bullets, some single factor strategies have done better over time than the Magic Formula, but with more volatility. One such strategy is the low EV/EBIT strategy. Read about it here.

Follow me on Seeking Alpha for more articles on Quantitative Value Investing!

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

Additional disclosure: I have no affiliation with Joel Greenblatt or I am a user of Portfolio123, and have included affiliate links in the article.