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John Emerson
John Emerson
Articles (106) 

Towards Creating a Better Magic Formula

July 19, 2011 | About:

"In theory there is no difference between theory and practice. In practice there is."

— Yogi Berra

On a theoretical basis, the Magic Formula is difficult to challenge. The philosophy involves identifying companies with high pretax earnings yields which reinvest their earnings at a high rate of return (ROIC). There is nothing very magical about that concept, if I own a highly profitable hamburger stand and I employ the majority of my profits producing other highly profitable hamburger stands; I am going to become rich in a relatively short period of time. Unfortunately, Ray Kroc beat me to the punch on that brain storm.

Of course relatively few publicly-traded companies possess the aforementioned attributes at any particular point in time. Generally, stocks which fit the formula are either recognized by the market as values and soon rise in price, or suffer substantial forward declines in earnings and/or returns on capital which justify their depressed price (value traps). In other words, very few stocks remain on the "bargain list" year after year; although holders of King Pharmaceutics (KG) prior to being bought out by Pfizer (NYSE:PFE) last fall, might dispute that claim. Either the market is correct or the formula is correct and the dispute is generally settled in a relatively short period of time. It seems that more often the formula is correct; there in lies the beauty of the system.

The Magic Formula possesses several other favorable attributes. It factors out tax rates by comparing companies on a pretax basis, and it incorporates the value of cash versus the liability of debt by using enterprise value, instead of market capitalization.

The formula also recognizes that depreciation is a true business cost, therefore it relies upon Earnings Before Interest and Taxes (EBIT) rather than Earnings Before Interest, Taxes, Depreciation, and Amortization (EBITDA) as the numerator in its earnings yield multiple.

Problems with the Magic Formula: Accrual Earnings vs. Cash Earnings

Robert Olstein has pointed out on numerous occasions; "earnings are opinions, cash is fact." Mr. Olstein is quite accurate in pointing out that various corporations display a wide variation in the "quality” of their earnings.

Olstein, originally borrowed that notion from his former partner Thornton O'Glove. O'Glove is well known for writing the investment classic "Quality of Earnings, The Investor's Guide to How Much Money a Company Is Really Making,” in the mid 1980s. It remains one of best books on the market pertaining to a comprehensive evaluation of accrual earnings. In future articles I intend to cover the specifics of the classic in greater detail.

O'Glove was among the first to point out that analyst projections are generally garbage, auditor accreditations are not always synonymous with proper accounting and veracity, in addition to revealing specific accounting tricks that companies use to enhance their earnings. In other words, certain companies embellish earnings sufficiently enough that the actual cash which is available for business reinvestment, dividends or stock buybacks is not nearly as great as the accrual earnings would suggest.

It would seem that the objections of Olstein and O'Glove strike at the heart of Magic Formula theory. The old adage "garbage in garbage out" would apply to at least some of the "value stocks" which the formula identifies. Since the Magic Formula relies on EBIT and ROIC (accrual not cash figures) to evaluate whether a company qualifies as a buy; it becomes imperative that accrual figures accurately reflect the true profitability of a company. The accurate rate of profitability will also directly determine the "real" rate of return for the business.

Let's say Company A has a pretax earnings yield of 20% and a pretax ROIC of 40%. Not only does the company appear inexpensive on a price to earnings basis, it also seems to be doing an excellent job of redeploying its earnings to grow the business. The business appears to a worthy of an investment, correct — in the immortal words of Lee Corso — "not so fast.”

What if the company is only yielding pretax cash returns amounting to 50% of its EBIT? Not only does that affect the "real" earnings yield of the business but it also belies the ROIC since the calculation of that figure is based upon EBIT. In other words, any method of calculating a return on investment relies upon some type of earnings figure as the numerator in the fraction. If the earnings figure is inaccurate then the rate of return is inaccurate as well.

It is exactly such problems that drove the likes of Walter Schloss towards investments based upon the value of the assets that a business holds rather than the value of their future cash flows.

Problems with the Magic Formula: Cyclical Adjustment of Earnings

A second major problem with the Magic Formula is the cyclicality of earnings for some of the companies which it tends to identify. Home building stocks frequently turned up on the list of Magic Formula stocks prior to the credit crisis along with other highly cyclical businesses, such as energy, energy-related companies as well numerous stocks. Had the formula used an average EBIT dating back 5 to 10 years then many of these highly cyclical businesses would have been exposed.

It has occurred to me since the inception of Magic Formula that numerous cyclical businesses would turn up as buy candidates, exactly at the peak of their earnings cycle. Indeed that is when their trailing EBIT and ROIC is at its highest point.

Highly cyclical stocks tend to act contrary to normal stocks, meaning they are usually acquired by savvy investors when they appear expensive in terms of price to earnings and sold when they still appear to be inexpensive.

Identifying and investing in highly cyclical entities when they are at or approaching their peak earnings, is a recipe for disaster. Of course some of the peril is diminished by the fact that "formula" investors diversify into 30 different stocks and they rebalance on an annual basis. However, I still believe that factoring out highly cyclical companies which are "approaching a cliff" would significantly magnify the overall results for "formula" investors.

Suggestions for Creating a Better Formula

I believe the Magic Formula could be improved by two relatively simple steps:

1) Using a pretax 5-year cyclically adjusted cash formula rather than EBIT as the earnings yield.

2) Using a pretax 5-year Cash Return on Invested Capital (CROIC) rather than ROIC to measure the rate of return.

The earnings yield would be calculated as follows: EY = Cash Flow From Operations (CFFO) + Income Tax (IT) - Depreciation and Amortization Expense (D&A) divided by Enterprise Value (EV).

One would use the five year average of CFFO+IT-D&A/EV as the earnings yield.

The return on capital rate would be calculated as follows: CROIC = CFFO+IT-D&A divided by Shareholder Equity (E) + Total Liabilities (TL) - Current Liabilities (CL)

One would use the five year average of CFFO+IT-D&A/E+TL-CL as the CROIC

Additional Thoughts on the Magic Formula

The Magic Formula can be an excellent lead generating source; although I question its utility as a systematic investment strategy. Despite its back testing which seems to have established that it has been successful in outperforming the overall market over a significant period, I suspect that it will eventually revert to producing a yield similar to the overall market averages.

The fact that it has become popular as an investment tool dooms the system to eventually revert to the mean. Whenever a statistically significant sample of investors pile into a limited group of stocks, the ultimate result is a decline on the return on investment for that specific group of stocks. Simply stated, the investors drive up the price of the chosen group and eliminate any hint of value.

I turn to the world of thoroughbred horse racing for just such an example. Many readers are probably familiar with Andrew Beyer and his handicapping innovation, "adjusted speed figures,” which are now universally referred to as "Beyers" in racetrack patois. Without going into the specifics of how the figures are calculated, the intention is to establish a "real" clocking of how fast a horse covered a certain distance of ground with regard to variables such as wind, track speed, etc. The angle is to establish "real" race times to compare between horses which ran on different days or on different race courses. The comparison is accomplished by producing a track variant which is added or subtracted from the final time with the goal of standardizing the performance of the animal. Thus a universal figure is assigned to every horse in every race, with the objective of establishing exactly how fast the animal ran. The figures are now calculated and published by the Daily Racing Form for every legitimate race track in the US and Canada.

Back in the 1970s before Beyer published his book on "speed figures,” he made a considerable amount of money by betting on horses which actually ran faster than their race time indicated. He was successful in betting on horses which appeared to be overmatched by their competition. At that time relatively few handicappers were privy to "speed figures" and the result was high odds on these seemingly overmatched animals.

All that changed quickly after Beyer published his popular book which explained in detail how to calculate the figures. The book was published well over a decade before the figures were listed on the past performances of the Daily Racing Form. Almost immediately after Beyer's book was released, the odds on horses jumping in class with competitive "adjusted speed figures" began to steadily plummet. The reason was simple, the betting community was now privy to a new source of information and they quickly adjusted the market price (paramutual odds) accordingly.


1) The improved formula utilizes the best ideas of the Magic Formula; specifically pretax comparisons, cash vs. debt considerations, and the assumption that depreciation represents an ongoing cost in any business.

2) The improved formula is superior in minimizing the effect of ambitious accounting and diminishing the effects of cyclicality on economically-sensitive businesses. By calculating five year averages, the temporary nature of earnings cycles in particular businesses, is factored into the formula.

3) It is likely that using cash rather than accrual means to establish the value of a Magical Formula stock has not yet been "priced" into the equities; therefore it is more likely to produce a higher investment return.

4) Any Magic Formula computation should be used merely as a lead source since virtually all investment systems are flawed and ultimately destined for failure, in the event they become popular with investors.

About the author:

John Emerson
I have been of student of value investing since the mid 1990s. I have continued to read and study value theory on an ongoing basis. My investment philosophy most closely resembles Walter Schloss although I employ considerably less diversification. I also pattern my style after Buffett's early investment career when he was able to purchase shares of tiny companies.

Rating: 4.4/5 (17 votes)


Cjmitchell86 - 6 years ago    Report SPAM

I would have to assume that Greenblat thought of these cavets while researching the formula and doing backtesting. Why do you think he chose his inputs opposed to your proposed adjustments?
John Emerson
John Emerson - 6 years ago    Report SPAM

Thank you for you comment and question.

Frankly, I do not know why he based the formula on an accrual rather than a cash basis but I think the success of the formula is largely attributed to the fact that it more of a trading strategy as opposed to an investing strategy. I view the formula as a one year trade, just long enough to minimize taxes.

Trading strategies rarely consider cash flow instead they hone in on accrual earnings. Traders like to buy when they see a turnaround and formula metrics often identify improvements in operational results. I suspect that using cash metrics and a five year cyclically-adjusted approach would identify longer term holds and higher quality companies; although it might not be as successful in acheiving intermediate term trades. I believe the adjustments would create a superior stock screen for longer term investors.
Adib Motiwala
Adib Motiwala - 6 years ago    Report SPAM
Good work and some valid points especially about cyclical companies showing up at peak EBIT and peak ROIC.

However, unless this recommended formula is back tested we cannot really compare this formula to the existing formula. Your point that since the MF is getting popular, the returns will diminish has yet to be proved. It will be interesting how many people follow the formula once the market goes south. GreenBlatt clearly said the formula under performs for many years in a full cycle and people eventually will give up on any strategy that does not work 100% of the time.

I like using it as a source of ideas and dont invest purely in a basket. However, you will find many of the value stocks Gurus are buying or being discussed on this site, are on the MF. In fact, one of the advantages of the MF is you can identify sectors that are cheap.

-Large tech, for profit education, Defense and Semi-conductor are some of the sectors that show up prominently in the MFI currently.


Adib Motiwala
Adib Motiwala - 6 years ago    Report SPAM
I don't consider it as a trading strategy. Yes one year is shorter than a few yeas of holding. However, its a lot longer than what 90% of stock investors hold stocks for. I think the average holding period for a stock is in few weeks or months...

You can always customize it and hold for longer if you want. He wanted to come up with something that investors could invest without a lot of due diligence on individual names as the basket of 20-30 names would protect the investor.

John Emerson
John Emerson - 6 years ago    Report SPAM
Excellent comments Adib,

I have used the formula as a lead generating source as well. I concur that it tends to identify out-of-favor sectors and many times those sectors offer value.

As far as backtesting the modified strategy, I will leave that to the more computer savvy crowd. My thesis was based entirely on a theoretical basis; however I would applaud anyone who took the time to backtest the modified assumptions.
John Emerson
John Emerson - 6 years ago    Report SPAM
"I don't consider it as a trading strategy. Yes one year is shorter than a few yeas of holding."

On this point I disagree, trading strategies are quite common among value investors. For instance the strategy of Schloss or Templeton is really one of trading in the immediate to long term.

A Schloss strategy involves identifying undervalued equities, purchasing them and then selling the equity when it approachs intrinsic value in terms of book value. That implies trading, after the a stock is sold the capital is redeployed in another undervalued equity. Contrast that to the current ideas of Buffett or Munger or Fisher for that matter. They do not generally exchange (trade) businesses for ones that are currently cheaper, unless some material change develops. In the case of Buffett he now prefers to buy the business outright and hold it through Berkshire perpetually.

The MF does basicly the same thing as Schloss or Templeton, they just use a different set of criteria, nevertheless the goal is the same buy undervalued, sell when fully valued, and reinvest. In my mind that amounts to trading although it is rooted in value philosophy.
Crastogi - 6 years ago    Report SPAM
Did you do any backtesting, with a point in time database? How do you know that your proposed changes will improve the formula?
Cjmitchell86 - 6 years ago    Report SPAM

Someone should really backtest this. I see this strategy as having a wider margin of safety, but the question is: Do the returns beat the market? If so, over what holding periods?

Cjmitchell86 - 6 years ago    Report SPAM
Also, something else to think about: As the MF considers management, I am curious to see the quality of management that cash metrics produce opposed to the accrual metrics the MF uses / the corporate governance of the MF stocks vs the authors "formula"
Adib Motiwala
Adib Motiwala - 6 years ago    Report SPAM

Value investing comes in many flavors from the asset based investing followed by Graham and Schloss as you pointed out, earnings and cashflow based investing , special situations, etc. Each has its own merits. I do not consider any of them to be 'trading' if they are based on sound principles.

Specifically, you state that buying an equity much below book and then selling at book value ( implied intrinsic value) is trading. I don't think that to be the case. I think that is one of the examples of value investing being practiced. I think you are confusing holding period ( or forever as in the case of Buffett) with Value Investing. In fact, I believe Value investing at its heart means buying at a large enough discount to one's estimate of intrinsic value and then selling at or close to intrinsic value. Buffett does things to defer capital taxes and his positions are also very large. Also his cost basis is low in most of these positions. Also, its not fair to compare him buying out entire businesses with investors with 'average' means. We can also buy a few shares in these businesses.

I know several investors currently buying banks / insurance companies at a large discount to tangible book value. That is not trading.

Thats my 2 cents.

Paulwitt - 6 years ago    Report SPAM
Here's a current strategy I'm using (mainly to protect my call options). Feel free to use it!

Thesis: The financial sector is the worst performing sector over the last 10 years, and is undervalued.

The XLF is currently at 15.00 and the peak was 37.90 in 2007. Except for March 2009, the 10 year low was 21.05 in 2003. We are currently in a trading range.

Strategy: Dollar cost average the XLF. Every down day buy a set amount of XLF ($100 or $1,000). On up days do nothing. Buy until the XLF hits 20.00 and then stop.

Note: This strategy may not work with levered funds like FAS or UYG because assets may erode with volatility.

John Emerson
John Emerson - 6 years ago    Report SPAM

I really think we are the same page Adib, I believe what we are debating used to be called "arguing semantics" when I was in college 30 plus years ago.

I believe that you assume my use of the term "trading" to be consummate to Graham's definition of speculation. I must admit I sometimes use the words interchangably but speculation is much different than purchasing equities well under their intrinsic value with the intention of selling them for capital appreciation. I consider that approach to be intelligent trading or value trading.

Contrast that approach with buying a stock with the intent of drawing a lifetime dividend yield which continues to increase steadily as a company grows. Or in the case of purchasing Berkshire stock, buying a group of businesses with the intent of watching the intrinsic book value of the stock increase with no intention of selling the stock in the forseeable future.

You could argue that both methods are forms of value investing but one involves trading (whether it involves one day or five years) and the other does not. There in lies my distinction.

Graham defined speculation as an attempt to predict the movement of a market or an individual equity without a sufficient margin of safety so as to insure a fair return plus a reasonable assurance of a return of principle.

Clearly, purchasing a stock well below its intrinsic value with the intent to sell it for a profit at a later date when reaches its intrinsic value is not speculation and it offers a reasonable assurance of a return of principle. However, it represents a different philosophy of value investing than purchasing an undervalued stock with the intent of holding it indefinitely for its dividend yield or its equity growth.

By the way I completely agree with your comment about finding value in financials. I have systematically avoided them until recently. I now own substantial positions in BERK and TCHC, a tiny bank and a tiny Florida P&C insurer. However, unlike Buffett I am prone to errors of commission not omission.
Paulwitt - 6 years ago    Report SPAM

Investing Philosophy:

Using value investing approach, Leucadia buys distressed companies at discount prices, revives them and sells them for profits. They buy assets that are out of favor, and therefore cheap or disheveled. They then improve their performance until they are the most efficient and productive in their market segment.The above information is from Ian Cumming's profile

*I have both net-net (Graham) and garp (Buffett) stocks in my portfolio - but no cyclicals. I prefer garp stocks.

*Peter Lynch did well with cyclicals. He got a couple of 5 and 10 baggers that way!

*Note: John Templeton sometimes used an actuarial approach to investing i.e sector bets. In fact he started out with an actuarial approach.

Hollems - 6 years ago    Report SPAM
John --

Thank you for such an informative article.

I would be interested in seeing the results of a screen like one that you describe. Any thoughts on a screening program or other tool capable of making the calculations you describe?

Haoafu - 6 years ago    Report SPAM
Magic formula's idea is to buy good company at cheap price. Cash flow and earnings both have their merits and drawbacks in terms of valuing the company. It varies between industries and businesses.

If you pick a basket of 5-20 stocks, MF should only be used as a resource with further research needed. If you go indexing or have a much bigger 'basket' of stocks in the portfolio, it maybe easier to get earnings data than cashflow data from established databases.

John Emerson
John Emerson - 6 years ago    Report SPAM

Creating a screen and backtesting is above my pay grade but it should not be any more difficult that the traditional MF since all the information is in the published financials. Maybe some young enterprising student could take on the task.
Augustabound - 6 years ago    Report SPAM
Is the AAII.com data customizable in that way? I think you can customize screens, but I'm not sure about back testing.
Fkattan - 6 years ago    Report SPAM
John, thank you very much for the article.

I have one doubt though. If you are trying to use a cash basis rather than an accrual one, why instead of depreciation and amortization, don´t you use maintenance capex?

That is, you could add to cash from operations the depreciation and amortization figure and then substract the manteinance capex. Because the depreciation figure is taken on an accrual basis and that´s what you are trying to correct.

Best regards,
John Emerson
John Emerson - 6 years ago    Report SPAM
Good question, I believe that best way to analyze "real" earnings is to attempt to approximate maintence capex; however when analyzing data in masses from financial sheets it is impossible to estimate. Frequently depreciation approximates maintance capex spending and I threw in amortization to make the formula more conservative since many times the value of intangibles also have a limited duration eg. patents or any kind of licensing agreement.

You are correct is assuming that in some cases maintanence capex would be overstated or understanded. A valid concern for the formula.

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