ROA, earnings/assets) for several reasons.EBIT (or earnings before interest and taxes) was used inplace of reported earnings because companies operatewith different levels of debt and differing tax rates. Usingoperating earnings before interest and taxes, or EBIT,allowed us to view and compare the operating earnings ofdifferent companies without the distortions arising fromdifferences in tax rates and debt levels. For each company,it was then possible to compare actual earnings from operations (EBIT) to the cost of the assets used to producethose earnings (tangible capital employed).*Net Working Capital + Net Fixed Assets (or tangiblecapital employed) was used in place of total assets (used in anROA calculation) or equity (used in an ROE calculation).The idea here was to figure out how much capital is actuallyneeded to conduct the company’s business. Net workingcapital was used because a company has to fund its receivables and inventory (excess cash not needed to conduct thebusiness was excluded from this calculation) but does not*For purposes of the study and in the interest of simplicity, it was assumedthat depreciation and amortization expense (noncash charges against earnings) were roughly equal to maintenance capital spending requirements(cash expenses not charged against earnings). It was, therefore, assumedthat EBITDA − Maintenance Cap/Expenditures = EBIT.
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have to lay out money for its payables, as these are effectively an interest-free loan (short-term interest-bearing debtwas excluded from current liabili-ties for this calculation). Inaddition to working capital requirements, a company mustalso fund the purchase of fixed assets necessary to conductits business, such as real estate, plant, and equipment. TheNOTE: Intangible assets, specifically goodwill, wereexcluded from the tangible capital employed calculations. Goodwill usually arises as a result of an acquisition of another company. The cost of an acquisitionin excess of the tangible assets acquired is usuallyassigned to a goodwill account. In order to conductits future business, the acquiring company usuallyonly has to replace tangible assets, such as plant andequipment. Goodwill is a historical cost that does nothave to be constantly replaced. Therefore, in mostcases, return on tangible capital alone (excludinggoodwill) will be a more accurate reflection of a business’s return on capital going forward. The ROE andROA calculations used by many investment analystsare therefore often distorted by ignoring the difference between reported equity and assets and tangibleequity and assets in addition to distortions due to differing tax rates and debt levels.
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depreciated net cost of these fixed assets was then added tothe net working capital requirements already calculated toarrive at an estimate for tangible capital employed.
2. Earnings Yield
EBIT/Enterprise ValueEarnings yield was measured by calculating the ratio ofpre-tax operating earnings (EBIT) to enterprise value (market value of equity* + net interest-bearing debt). This ratiowas used rather than the more commonly used P/E ratio(price/earnings ratio) or E/P ratio (earnings/price ratio) forseveral reasons. The basic idea behind the concept of earnings yield is simply to figure out how much a businessearns relative to the purchase price of the business.Enterprise value was used instead of merely the price ofequity (i.e., total market capitalization, share price multipliedby shares outstanding) because enterprise value takes intoaccount both the price paid for an equity stake in a businessas well as the debt financing used by a company to help generate operating earnings. By using EBIT (which looks atactual operating earnings before interest expense and taxes)and comparing it to enterprise value, we can calculate the*Including preferred equity.
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pre-tax earnings yield on the full purchase price of a business (i.e., pre-tax operating earnings relative to the price ofequity plus any debt assumed). This allows us to put companies with different levels of debt and different tax rates onan equal footing when comparing earnings yields.For example, in the case of an office building purchasedfor $1 million with an $800,000 mortgage and $200,000 inequity, the price of equity is $200,000 but the enterprisevalue is $1 million. If the building generates EBIT (earningsbefore interest and taxes) of $100,000, then EBIT/EV orthe pre-tax earnings yield would be 10 percent ($100,000/$1,000,000). However, the use of debt can greatly skewapparent returns from the purchase of these same assetswhen only the price of equity is considered. Assuming aninterest rate of 6 percent on an $800,000 mortgage and a 40percent corporate tax rate, the pre-tax earnings yield on ourequity purchase price of $200,000 would appear to be 26percent.* As debt levels change, this pre-tax earnings yield*$100,000 in EBIT less $48,000 in interest expense equals $52,000 in pretaxincome. $52,000/$200,000 equals 26 percent. The E/P (earnings/price), orafter-tax earnings yield, would be 15.6 percent ($100,000 in EBIT less$48,000 in interest less $20,800 in income tax equals $31,200 in after-taxincome; $31,200/$200,000 equals 15.6 percent). This 15.6 percent returnwould be more comparable to looking at an EBIT/EV after-tax yield of 6 percent (i.e., looking at EBIT as if fully taxed, or net operating profit after taxdivided by EV; it is important to note that the fully taxed EBIT to enterprise value of6 percent would be the earnings yield ratio used to measure investment alternatives versus the risk-free 10-year government bond yield, not the EBIT/EV ratio of 10 percent).
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on equity would keep changing, yet the $1 million cost ofthe building and the $100,000 EBIT generated by thatbuilding would remain unchanged. In other words, P/E andE/P are greatly influenced by changes in debt levels and taxrates, while EBIT/EV is not.
Consider two companies, Company A and CompanyB. They are actually the same company (i.e., thesame sales, the same operating earnings, the sameeverything) except that Company A has no debt andCompany B has $50 in debt (at a 10 percent interestrate). All information is per share.Company A
Company B
Sales
$100
$100
EBIT
10
10
Interest exp.
0
5
Pre-tax income
10
5
Taxes (@40%)
4
2
Net income
$6
$3
The price of Company A is $60 per share. Theprice of Company B is $10 per share. Which ischeaper?
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Let’s see. The P/E of Company A is 10 ($60/6 =10). The P/E of Company B is 3.33 ($10/3). The E/P,or earnings yield, of Company A is 10 percent (6/60),while the earnings yield of Company B is 30 percent(3/10). So which is cheaper? The answer is obvious.Company B has a P/E of only 3.33 and an earningsyield of 30 percent. That looks much cheaper thanCompany A’s P/E of 10 and earnings yield of only 10percent. So Company B is clearly cheaper, right?Not so fast. Let’s look at EBIT/EV for bothcompanies. They are the same! To a buyer of thewhole company, would it matter whether you paid $10per share for the company and owed another $50 per shareor you paid $60 and owed nothing? It is the samething! You would be buying $10 worth of EBIT for $60,either way!*
Enterprise value
Company A
Company B
60 + 0 = $60
10 + 50 = $60
10
10
(price + debt)EBIT
*For example, whether you pay $200,000 for a building and assume an$800,000 mortgage or pay $1 million up front, it should be the same to you.The building costs $1 million either way!
A Random Walk Spoiled
For many years, academics have debated whether it ispossible to find bargain-priced stocks other than bychance. This notion, sometimes loosely referred to asthe random walk or efficient market theory, suggests thatfor the most part, the stock market is very efficient attaking in all publicly available information and settingstock prices. That is, through the interaction of knowledgeable buyers and sellers, the market does a prettygood job of pricing stocks at “fair” value. This theory,along with the failure of most professional managers tobeat the market averages over the long term,* hasunderstandably led to the movement toward indexing, acost-effective strategy designed to merely match themarket’s return.Of course, over the years, many studies have attemptedto identify strategies that can beat the market. But thesestudies have often been criticized on numerous grounds.*Both before and after management fees and expenses.
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These include:1. The study beat the market because the data used toselect stocks weren’t really available to investors atthe time the selections took place (a.k.a. look-aheadbias).2. The study was biased because the database used inthe study had been “cleaned up” and excludedcompanies that later went bankrupt, making thestudy results look better than they really were(a.k.a. survivorship bias).3. The study included very small companies thatcouldn’t have been purchased at the prices listed inthe database and uncovered companies too smallfor professionals to buy.4. The study did not outperform the market by asignificant amount after factoring in transactioncosts.5. The study picked stocks that were in some way“riskier” than the market, and that’s why performance was better.6. The stock selection strategy was based on backtesting many different stock selection strategiesuntil one was found that worked (a.k.a. data mining).7. The stock selection strategies used to beat the market included knowledge gained from previous“market-beating” studies that was not available at
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magic formula study was conducted. In sum, despite itsobvious simplicity and the usual objections, the magic formula appears to work. It works well even when comparedto much more sophisticated strategies used in some of thebest market-beating research completed to date.Yet, in one sense, the success of the magic formulastrategy should not be a surprise. Simple methods for beating the market have been well known for quite some time.Many studies over the years have confirmed that valueoriented strategies beat the market over longer time horizons. Several different measures of value have been shownto work. These strategies include, but are not limited to,selecting stocks based upon low ratios of price to bookvalue, price to earnings, price to cash flow, price to sales,and/or price to dividends. Similar to the results found in themagic formula study, these simple value strategies do notalways work. However, measured over longer periods, theydo. Though these strategies have been well documentedover many years, most individual and professional investorsdo not have the patience to use them. Apparently, the longperiods of underperformance make them difficult—and, forsome professionals, impractical—to implement.Another problem with these simple methods is that,though they work well, they work far better with smallerand medium-capitalization stocks than with larger stocks.This should not be surprising, either. Companies that are
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too small for professionals to buy and that are not largeenough to generate sufficient commission revenue to justify analyst coverage are more likely to be ignored or misunderstood. As a result, they are more likely to presentopportunities to find bargain-priced stocks. This was thecase in the magic formula study. The formula achievedthe greatest performance with the smallest-capitalizationstocks studied.However, this good performance cannot be reasonably attributed to a small-cap effect because smallcapitalization stocks did not appreciably outperform largecaps during the study period. Dividing our universe ofstocks into deciles by market capitalization during the 17year study period, the smallest 10 percent of stocks provided returns of 12.1 percent, while the largest 10 percentof stocks returned 11.9 percent. The next deciles weresimilarly close: 12.2 percent for the next smallest and 11.9percent for the next largest.But the whole issue of whether small-capitalizationstocks outperform large-capitalization stocks is not particularly relevant. It seems clear that there is a greateropportunity to find bargains (and overpriced stocks, forthat matter) in the small-cap arena both because there aremore stocks to choose from and because smaller stocksare more likely to be lightly analyzed and, as a result,more likely to be mispriced. In a sense, it is just easier for
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simple methods like price/book screens and the magicformula to find bargain stocks among these smallercapitalization stocks.However, where the magic formula parts ways withprevious market-beating studies, whether simple or sophisticated, is that for larger stocks (market caps over $1 billion) the results for the magic formula remain incrediblyrobust. Other methods do not fare nearly as well. Forexample, during our study period, the most widely usedmeasure to identify value and growth stocks, price tobook value, did not discriminate particularly stronglybetween winners and losers for these larger stocks. Thebest-ranked decile of low price/book stocks (cheapest 10percent) beat the worst-ranked decile of high price/bookstocks (most expensive 10 percent) by only 2 percent peryear.*In comparison, the magic formula strategy did muchbetter. The best-ranked decile of magic formula stocks(cheapest 10 percent) beat the worst-ranked decile (mostexpensive 10 percent) by over 14 percent per year on average during the 17-year study. The best decile returned18.88 percent, the worst returned 4.66 percent, while themarket average for this universe of over $1 billion stocks*This is 13.72 percent for the lowest price/book decile to 11.51 percent forthe highest price/book decile. The market average for this group was 11.64percent.
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was 11.7 percent. In truth, this is not surprising. Whilehaving a low price relative to the historical cost of assetsmay be an indication that a stock is cheap, high earnings relative to price and to the historical cost of assets are muchmore direct measures of cheapness and should work better. Of course, these two factors are the ones used in themagic formula study.One of the most significant recent studies, conducted by Joseph Piotroski at the University ofChicago,* took price/book analysis one step further.Piotroski observed that while low price/book stocks beatthe market on average, less than half of the stocksselected following this strategy actually outperformedthe market. By using simple and readily availableaccounting metrics, Piotroski wondered whether hecould improve the results of a generic price/book strategy. Piotroski rated the top quintile of low price/bookstocks (i.e., the cheapest 20 percent) using nine different measures of financial health. These included measures of profitability, operating efficiency, and balancesheet strength. The results over the 21-year study werespectacular . . . with one exception.For larger stocks, it didn’t really work. For the largest*Piotroski, J. “Value Investing: The Use of Historical Financial Statements to Separate Winners from Losers,” Journal of Accounting Research,vol. 38, supplement, 2000.
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one-third of stocks by market capitalization,* the highestranked stocks on Piotroski’s nine-point scale did not significantly outperform the average low price/book stock.†This is not surprising, either. As already mentioned, it’sjust easier to find mispriced stocks among smaller- andmid-capitalization issues.But this relative inability for market-beating methodsto work with larger-cap stocks is not unique. Even verysophisticated market-beating strategies, while showingexcellent results in general, do not fare nearly as well asthe relatively simple magic formula in the large-cap universe.‡ For example, some of the best work done to dateon sophisticated factor models was completed by RobertHaugen and Nardin Baker.§ Professor Haugen actuallystarted an advisory business based on the excellent resultsachieved in this groundbreaking paper.Essentially, instead of the two factors used in themagic formula strategy, Haugen developed a sophisticated model using 71 factors that supposedly help predict*This is equivalent in the magic formula study to stocks with market capitalizations over approximately $700 million.†Though Piotroski’s “lowest”-ranked large-cap stocks did do poorly relativeto other low price/book stocks, his ranking system selected a total of only34 low-ranked stocks over 21 years.‡Or in the small-cap universe.§Haugen, R., and N. Baker, “Commonality in the Determinants ofExpected Stock Returns,” Journal of Financial Economics, Summer 1996.
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how stocks will do in the future. These 71 factors evaluatestocks based on “risk, liquidity, financial structure, profitability, price history and analysts’ estimates.” Based on acomplicated weighting of all of these different factors,Haugen’s model predicts future returns for each stock.Historical “expected returns” for the stocks in the 3,000+stock universe evaluated by Haugen’s model have beenposted on his web site, covering the period from February1994 through November 2004. We decided to testHaugen’s model to see whether it worked for largecapitalization stocks (those with a market capitalizationover $1 billion in 2004 dollars).It did. The results were quite spectacular. Over this10+-year period, the market average for the large-cap universe tested returned 9.38 percent. But buying the highestranked stocks (best-ranked decile) based on Haugen’s71-factor model returned +22.98 percent. The lowestranked stocks (worst-ranked decile) actually lost 6.91 percent. This amounts to a spread of almost 30 percentbetween best and worst! This assumed that stocks wereheld for only one month and then reranked at the end ofeach month. Of course, though these results were great,the magic formula did better!Over the same 10+-year period, the highest-rankedstocks (best-ranked decile) based on the magic formulatwo-factor model returned +24.25 percent. The worstranked stocks (worst-ranked decile) lost 7.91 percent.
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This amounts to a spread from best to worst of over 32percent! Though the results from the magic formulastrategy were somewhat better (and easier to achieve)than the results from the 71-factor model used by Haugen, the performance of both methods was excellentand quite comparable. But here’s the thing. Most people don’t (and shouldn’t) invest by buying stocks andholding them for only one month. Besides the hugeamount of time, transaction costs, and tax expenseinvolved, this is essentially a trading strategy, not reallya practical long-term investment strategy. So what happens if we change our test and hold each portfolio forone year?*Actually, something very interesting occurs. Haugen’s 71-factor model still does well: the best-rankeddecile returns +12.55 percent (versus 9.38 percent forthe market) and the worst-ranked decile returns +6.92percent. The spread from high to low is down to 5.63percent. If we hadn’t just seen the one-month returns,this would still look pretty good. But what happens withthe magic formula? The best-ranked decile returns+18.43 percent and the worst-ranked decile returns*Portfolios were purchased every month during the 10-year period, andeach portfolio was held for 1 year, so more than 120 separate portfolioswere tested for each strategy.
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+1.49 percent—a spread of almost 17 percent betweenbest and worst! That’s pretty good no matter how youlook at it. Here’s something else that’s interesting. Theworst return during those 10+ years for following theHaugen strategy for 36 months straight (with annualturnover) was −43.1 percent. The worst 36-monthperiod for the magic formula was +14.3 percent. Notonly that, the magic formula used 69 fewer factors and alot less math!*So, here’s the point. The magic formula appears toperform very well. I think and hope it will continue to perform well in the future. I also hope that, just as MarkTwain aptly referred to golf as “a good walk spoiled,” perhaps someday the random walk will finally be consideredspoiled as well.†
*Professor Haugen does not suggest buying the top 10% of his highestrated stocks in one portfolio or holding stocks for one year. Also, the lossesfor the worst 36 month return for the theoretical “top 10%” Haugen portfolio were similar to the overall market’s loss during that period. The statistics listed were compiled for comparison purposes with the magic formulaportfolio using only those stocks that were included in both the Haugen andmagic formula over $1 billion universe.†On second thought, who am I kidding? I hope it lives forever!
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