The Magic Formula: An In-Depth Look At The Mechanics And A Potential Improvement

Includes: AAPL
by: Ryan Telford


Joel Greenblatt’s Magic Formula method of investing has outperformed the S&P500 over time.

Understanding the metrics used in the Magic Formula can be instructive when investing in individual stocks.

Recent research has suggested that returns from the Magic Formula can be improved with less volatility.

The Magic Formula (MF) is a quantitative investing method devised by famed value investor, Joel Greenblatt. Greenblatt described the Magic Formula in the 2004 book "The Little Book that Beats the Market". He updated the book in 2010 with updated portfolio performance in "The Little Book that Still Beats the Market".

The Magic Formula screen essentially ranks stocks on two metrics, low relative cost ("cheap") and high returns on capital ("quality" or "good"). Greenblatt has said that he wanted to marry the investment philosophies of Ben Graham ("cheap") and Warren Buffet ("quality"). One could also say that the screen finds high quality firms that are on sale. Greenblatt posts the results of his screen for free at

Magic Formula investing is a mechanical method of investing in stocks (also known as quantitative investing), which essentially removes all subjective bias on the part of the investor. A typical mechanical investing philosophy consists of purchasing a portfolio of stocks (20 or 30 is common), as specified by the given screen criteria, and held for a period of time. 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. A year holding period is common. The Magic Formula is just one such mechanical investing method.

The reported performance of the Magic Formula from the period 1988 to 2010 is illustrated below (as backtested by Greenblatt).

MF Performance

Source: Data from Greenblatt's book & Author Calculations

Impressive returns are reported in the hypothetical portfolios charted (practically 20 or 30 stocks are included in an investor's portfolio at any time, not 3,500 or 1,000). An investment of $1,000 in 1988 would result in a portfolio worth approximately $110,000 in 2009 (over a 100 fold increase in 21 years). Over the period, this equates to compounded annual growth rates of 19.7% and 23.8% for the largest 1,000 and largest 3,500 stocks respectively.

The portfolio can experience significant downward volatility for extended periods, which can test the staying power of the investor. The method requires that the investor hold on during the tough times. Note the nearly 50% drop in the 3,500 stock portfolio value from 2006 to 2008. The volatility of this method is discussed below.

All of this said, several investors have been unable to obtain the same results through backtesting as published by Greenblatt (more on this below). Over time, however, several independent backtests do confirm that the system does outperform the S&P500 over time.

While an investor may or may not choose to use the Magic Formula, the basis for the formula can be very instructive for understanding the multitude of value metrics when investing in individual stocks.

The Cheap Factor

Price to earnings (P/E) is a very common metric for determining how much the market values a stock based on its earnings (or E/P, or earnings yield). The "price" numerator is based on market value of the equity (current market price x shares outstanding), and the "earnings" denominator is the reported earnings per share, either on a trailing basis, or on forecast future earnings.

While a metric that is easily calculated and readily available on finance sites, the P/E ratio does have its limitations. The ratio is based on the market value of the firm's equity only, and does not consider the total capital structure of the firm. Equity makes up only a portion of the total value of a firm (more on this below). Firms often have varying amounts of debt to finance their operations. If managed prudently, debt can be advantageous to amplify returns. If not, the opposite can occur, and the firm may be unable to make its interest payments and risk credit rating de-ratings, or worse.

Another option for the "price" component of the P/E ratio is to use the firm's enterprise value, or EV. The enterprise value represents the total value that the firm could be purchased for. A purchaser (private equity or larger firm) would be required to pay for the equity, but would also need to take on the debt of the firm, any preferred equity and minority interests. Any cash of the books would be acquired by the acquirer firm, so cash and equivalents of the acquiree would reduce the cash outlay of the acquirer. In formula form:

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

The "earnings" portion of your standard P/E ratio is the earnings per share, or EPS. Earnings per share is based on the reported net income of the firm. Net income can include several non-cash charges such as depreciation and amortization, and any tax breaks the firm would receive from paying interest on debt obligations. E arnings b efore i nterest and t axes (EBIT) essentially looks at earnings without the benefit of tax shields. In Greenblatt's words, using EBIT "allows us to put companies with different levels of debt and different tax rates on an equal footing when comparing earnings yields." (p 169).

Greenblatt's metric for cheap firms (or high earnings yield) is:


P/E (or E/P) can be influenced by debt and tax rates, where as EBIT/EV cannot.

Consider the following example to illustrate the impact of debt on a firm (adapted from Greenblatt). Firm 'A' and Firm 'B' are the same, except their capital structure differs (Firm 'B' carries $50/share of debt).

Source: Data from Greenblatt, p 171

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

Another variation of EBIT is EBITDA, or E arnings b efore i nterest, t axes, d epreciation and a mortization. As stated above, several adjustments to gross income from non-cash charges of depreciation and amortization can distort the actual operating earnings of the firm.

For simplicity purposes, Greenblatt uses EBIT in his formula. He assumes that the non-cash depreciation and amortization expense (charged against earnings) is equivalent to the actual cash outlay required for maintenance capital spending requirements, which are actual cash outlays reported on the cash flow statement (and thus not charged against earnings).

The Quality Factor

Return on capital is a favourite metric of Warren Buffett's, and was Greenblatt's inspiration for including it in the Magic Formula model. Buffett counsels that companies who are able to sustain high returns on capital may have a competitive edge, or moat.

Like many accounting metrics, Return on Capital can be determined in several different ways. The basic formula is:

Operating Income / Capital

A simple formula in theory, however results can vary widely depending on which values are used for each of the "operating" and "capital" components.

"Operating Income" could be taken as EBIT, EBITDA, NOPAT (Net Operating Income after Tax), 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, it may or may not include intangible assets.

For the Magic Formula, Greenblatt identifies "good" companies by using "Return on Tangible Capital Employed":

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.

"Excess cash" is not specifically defined by Greenblatt; as a concept it is a loose term. Another well respected value investor, Bruce Greenwald, estimates that most firms require approximately 1% of revenue to run their operations (from his book, "Value Investing, From Graham to Buffett and Beyond", p 92).

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).

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

A Note on Different Versions of Return on Capital

Morningstar provides a value for "Return on Invested Capital" (or ROIC), however its value is significantly different than the Return on Tangible Capital Employed as used in the Magic Formula.

Morningstar does not explain how their ROIC is calculated on their website, however while Pat Dorsey was working at Morningstar, he wrote the book "The Five Rules for Successful Stock Investing". He defined ROIC as follows (page 95):

ROIC = Net Operating Profit after taxes (NOPAT) / Invested Capital


NOPAT = Operating profit - (Operating profit * tax rate)

Invested Capital = Total Assets - Non-interest bearing current liabilities - Excess cash

As an example, consider Apple (NASDAQ:AAPL), which is currently on the Magic Formula screen. The two versions of return on capital have values that vary by nearly a factor of 12.

Source: Morningstar Financials & Author Calculations

This example illustrates that when comparing stocks on a "return on capital" basis, it is important to ensure the criteria for the metric is the same. This caveat can be applied to any metric or ratio when comparing firms.

Optimizing the Magic Formula

Returns to the Magic Formula have been backtested by many investors, and in general few have been able to report the CAGR that Greenblatt claims in his book.

Most notably of these investors are Gray & Carlisle in their book "Quantitative Value", and further in Carlisle's book "Deep Value".

Gray & Carlisle backtested over a longer period, and came up with the following results:


While a lower return than the reported 23.8% by Greenblatt, Gray and Carlisle's independent backtesting confirmed that the MF did outperform the S&P500.

Suffice it to say, for a "passive" strategy these results are still impressive.

Over a smaller period than Carlisle and Gray (but longer than Greenblatt's), noted quantitative and academic value investor James Montier also had similar results.


Greenblatt's study was conducted in the US only. As you can see in the table above, Montier backtested in markets outside of the US, and found that outperformance of the respective market was still possible.

Cheap vs. Quality

Several investors and authors have made attempts to tweak the MF system to either achieve better returns, or to reduce the potential drawdown, or both.

Gray and Carlisle looked at this as well. They found that a portfolio based only on high earnings yield (EBIT/EV) actually outperforms a portfolio based only on high ROIC. This implies that the Magic Formula portfolio return is limited by the ROIC component. See the table below.


Their research suggests that EBIT/EV metric outperforms on an absolute CAGR (compounded annual growth rate) basis.

A portfolio's volatility (or "risk adjusted" return) can be measured by both the Sharpe ratio and the Sortino ratio. The higher the value of these ratios, the less volatile the portfolio. The Sharpe Ratio measures overall volatility (upside and downside), while the Sortino focuses on downside volatility. Technically speaking, per unit of risk, these ratios measure average return of the portfolio earned in excess of the risk-free rate (say US treasury bills).

Isolating the EBIT/EV portfolio outperforms the S&P500, MF and standalone ROIC portfolios on all measures in this study.

Cheap Wins Over Quality

Gray and Carlisle attribute the above results largely to mean reversion. One of the important concepts/phenomenon that apply in business (and in life in general) is that of cycles. The economy, different industries, and individual businesses operate in cycles, a series of peaks and troughs (prosperity vs difficult times). As much as we would like prosperity to last indefinitely, history tells us that this is not the case. On the flipside, states of depression or recession eventually find their way back to the status quo, or "revert to the mean". At a macro level, one can see the various peaks and valleys in the North American economy of the last 100 years. Roaring 1920s, 1930s Depression, Post World War II Boom, etc. The same happens for individual firms. It is rare for a firm to stay "on top"; if high returns on capital are being achieved, then competition will be attracted to get a piece of the pie. While these high achieving firms do their best to fend off competition, there are many factors at play that eventually work to erode these returns.

It could be said that firms that are "cheap" are in the trough of their cycle, while those high quality firms are at the peak of their cycle. When mean reversion occurs, equity of the cheap firms will improve in price, and the high quality firms will eventually revert to achieving average returns, and likely a corresponding decrease in market price. Thinking in terms of cycles and mean reversion, it can be seen how the quality component and the cheap components work against each other in the Magic Formula portfolio, thus limiting returns.


Selecting high quality stocks for investment that are on sale makes intuitive sense to a value investor. The Magic Formula does just this through a mechanical, passive investing method.

While the original returns of 23.8% per year claimed by Greenblatt have not yet been verified by independent backtesting, the returns of backtesting have still outperformed the S&P500 over time.

Even if one does not choose to invest using the Magic Formula method, the "cheap" and "quality" metrics used by the system can be very instructive and aid in understanding key concepts in business and accounting in valuing businesses for investment.

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, the Magic Formula, or any of the authors and researchers mentioned. While I do not currently hold AAPL, I do hold some of the stocks currently listed in the Magic Formula screen.

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