# Tweaking Greenblatt's Magic Formula

We can depart from Greenblatt’s Magic Formula to develop a very simple investment strategy, which can be applied by any individual investor with relative ease. The original Magic Formula is explained in Joel Greenblatt’s books The Little Book That Beats The Market [1] and The Little Book That Still Beats The Market [2].

Greenblatt’s Magic Formula is a value strategy aimed at capturing quality companies at cheap prices. The beauty of the strategy comes from its reliance on just two accounting ratios, which makes it easily replicable by any inexperienced investor and free from human judgement. In The Little Book That Beats The Market, Greenblatt not only provides evidence on the outperformance of the Magic Formula strategy but also on its discriminatory power.

In a study for the period 1988-2009, Greenblatt ranks 2,500 US stocks from highest to lowest using the Magic Formula and groups them in deciles. When moving from the highest Magic Formula decile to the lowest, the annualised returns also decline , as depicted in the table presented below.
Group Annualised Returns (1998-2009)
1 15.2%
2 12.7%
3 12.1%
4 11.5%
5 10.7%
6 10.2%
7 8.8%
8 7.1%
9 4.1%
10 -0.2%

Source: ‘The Little Book That Still Beats The Market’

The Magic Formula presents itself as a good discriminating ratio to select stocks for a value portfolio.

## What is the Aim of the Magic Formula

The Magic Formula attempts to filter quality stocks that are selling for cheap from some universe of stocks. It ranks companies based on two factors: return on capital and earnings yield. The first ratio filters quality companies that make the best use of their employed resources while the second ratio filters the cheapest companies.

Buying quality for cheap is at the heart of every single value strategy. But Greenblatt’s strategy differentiates from others because it relies on a simpler methodology and it doesn’t suffer from common pitfalls found in strategies relying on return ratios and price ratios. Any investor with access to a simple stock screener can compute a Magic Formula and filter a list of stocks with relative ease, which is rarely the case with other investment strategies. With most investment strategies, an investor needs to simplify its methodology due to lack of available data or he needs to make assumptions that require subjective judgement. But, unlike what it may seem, complexity doesn’t add accuracy. The simplicity of the Magic Formula overcomes many of the drawbacks associated with the use of ratios like return-on-equity, return-on-assets, price-to-earnings and others. These ratios are widely used for investment purposes but highly inaccurate in valuing a business.

## Measuring Quality – Return on Tangible Capital Employed

The first ratio used by Greenblatt, aimed at determining quality, is the Return on Tangible Capital Employed (ROTC). It is calculated as the the ratio of Operating Profits (EBIT) to Tangible Capital Employed:

$ROTC=\frac{\text{EBIT}}{\text{Working Capital}+\text{Net Fixed Assets}}$

Greenblatt justifies the selection by stating that operating profit isn’t distorted by tax rates and debt levels. A highly indebted business corresponds to a geared bet on some fundamentals.

A business with high leverage would then appear more valuable when it is growing due to a more favourable phase of the business cycle, but should be worth the same as an unlevered business for someone willing to purchase the whole enterprise.

The return on capital used in the Magic Formula attempts to measure how much in operating profits is the company generating with the tangible assets it employs in the business. Its is a measure of return on tangible capital employed.

## Measuring Cheapness – EBIT Yield

Greenblatt uses operating profits as a proxy for corporate earnings because taxes and debt structure do have a huge influence in the final earnings per share attributable to shareholders. For someone willing to purchase the whole enterprise, what does matter is how much profits the company is generating before paying any interest. The potential buyer will not pay any interest because there won’t remain any interest-bearing debt. Regarding taxes, it is true the potential buyer will still have to pay them, but taxes are so volatile that considering after-tax profits is a distorting figure as a proxy for any profitability. For someone willing to consider an after-tax profit figure, it would be preferable to calculate operating profits and subtract potential taxes at a statutory rate rather than using after-tax figures.

The aim of using operating profits is to put companies with different levels of debt and different tax rates on an equal footing, for them to be comparable. For the purposes of portfolio selection, comparability is key.

The earnings yield considered by Greenblatt uses EBIT (earnings before interest and taxes), which is a measure of operating profits. Additionally, instead of using the market value of equity, it uses enterprise value. The resulting earnings yield ratio is a tweaked inverted price ratio, which corrects for different debt and tax structures and considers the whole enterprise value instead of just the market value of equity:

$\text{EBIT Yield}=\frac{\text{EBIT}}{\text{Enterprise Value}}$

Enterprise value is equal to the total market value of equity plus net interest-bearing debt:

$\text{Enterprise Value}=\text{Market Value of Equity}-\text{Net Interest-Bearing Debt}$

## Selecting Stocks With the Magic Formula

After calculating the ROTC and the EBIT Yield for each stock from some predefined universe of stocks, an investor must determine the Magic Formula, which is no more than a ranking number assigned to each stock, depending on their rank for ROTC and for EBIT Yield.

The first step involves sorting stocks by ROTC from highest to lowest. In order to keep track of each rank, a number from 1 to N is assigned to each. A number of 45 means that the stocks ranks in the 45th position.

The second step involves applying the same sorting procedure to EBIT Yield. Stocks are sorted by EBIT Yield from highest to lowest. A number is then assigned to keep track of rank. A number of 1, means the stock stands at the top of the list in terms of EBIT Yield.

The third step involves summing up the ROTC and EBIT Yield rank numbers, to sort stocks once again, but this time from lowest to highest. A stock ranking 2nd on ROTC and 24th on EBIT Yield, will be assigned the number 26. This final number is what is known by Magic Formula.

The fourth step involves selecting stocks based on the rankings given by the Magic Formula, with the lowest numbers representing the highest rankings. Additionally, Greenblatt believes that the best is to build a portfolio with 20 to 30 stocks, for the sake of diversification. It is important to remember that this selection process selects outperforming stocks, on average. The problem with averages is that they always come with standard deviation, which in terms of investment is a source of risk. To reduce the risk that comes with each selected stock, Greenblatt advises building a portfolio with 20 to 30 stocks. Such portfolio is expected to on average beat the market.

In order to optimise the selection and management of the Magic Formula portfolio, Greenblatt additionally advises to:

• Exclude Financials and Utilities, as they need a different valuation approach;
• Exclude stocks with a very small market capitalisation to avoid the price risk resulting from infrequent trading;
• Hold stocks for a period of one year, after which they should be sold and replaced by another stocks;
• Sell winners a few days after one year and losers a few days before to optimise for taxes;
• Start the portfolio by selecting 5 to 7 stocks each three-month period until the portfolio is full.

## Improving on How Quality is Measured

Greenblatt excludes intangible assets from its measure of quality. The return on the capital employed is then a measure of how much operating profits is the company able to generate by unit of fixed assets employed. But, not all businesses grow from expanding their fixed asset base. Some, just opt to acquire other businesses. When that happens, the difference between the acquisition price and the accounting value of the acquired business is recorded as goodwill, which is an intangible asset. The acquirer pays this extra because he believes there’s more value on what it just acquired than what is reflected in balance sheets. Ignoring goodwill from the calculation will make some businesses appear of better quality than they should. Part of the profit generating ability of a business is intangible and, of course, worth money, which should always be accounted for. From the exposed we believe there is a good reason to bring intangibles back to the calculation of return on capital employed.

Another important issue, pointed by Phil Oakley[^3] is the fact that some companies acquire assets through operating leases. An airliner may lease its planes instead of buying them, like a retailer may rent stores instead of purchasing them. When that happens, there is a long-term commitment from the lessee, which isn’t recorded in the books. This is a kind of off-balance sheet financing. An airliner that purchases planes may look a lot worse in terms of Greenblatt’s measure for quality than another airliner that leases them. But it shouldn’t. We will follow Phil Oakley’s suggestion to add operating leases back to capital employed. The annual reported value of the operating leases is multiplied by 7 and then multiplied by 7% to get a rough estimate of lease interest.

Finally, I believe quality is an attribute built over the years and not the result of just a single year. We then want to select companies that on average give the highest returns to the capital employed. Because of the business cycle and many factors that are internal to a company, we believe that the proper return on capital employed is a long-term average. We shouldn’t penalise a company just because it invested heavily last year. To overcome the issue, we use ROCE average for the last 10 years, instead of last year’s figures.

## Improving How Cheapness is Measured

Greenblatt defines enterprise value as the market value of equity plus net interest-bearing debt. Basically, it should mean that, to acquire the whole company, an investor would have to pay for the market value of equity plus the market value of debt less any cash left. But, it would still have more to pay. Minority shareholders must also be paid as do preference shareholders. We need to add these values back to enterprise value.

Phil Oakley[^phil1] claims that pension funds deficits should also be add to enterprise value, as this represents a claim on corporate assets, like debt. At some point, the deficit must be funded. For someone purchasing the whole business, this amount must be considered, as any other debt. When we take all claims into consideration, the final enterprise value figure will often be larger than what is considered in Greenblatt’s Magic Formula, which means that the real EBIT Yield is often lower.

Finally, the problem of operating leases also applies to the cheapness measure, because of EBIT. We then should calculate the estimated capitalised value of operating leases to have an idea on how much interest would the company pay if opting for acquiring the assets instead of leasing them. In general, the lease-adjusted EBIT figure should be higher than the reported EBIT figure.

## Adding a Relative Strength Measure

While not willing to distort the Magic Formula‘s original spirit, we may add a relative strength filter to it. One of the biggest problems associated with value investing is timing. It is not unusual for, battered down businesses to continue to underperform the market for long periods, before recovering. To avoid entering too soon in a long position, we may require the price performance of a stock to be greater than the price performance of a relevant stock index proxy, during the last three months, for example.

## Macro Investor Magic Formula Screener

Based on the above considerations, we may apply the following screener to build a Magic Formula Portfolio:

1. Choose the universe of stocks: LSE listings.
2. Filter stocks by market capitalisation: Market Capitalisation > £150m.
3. Filter stocks by industries: Industry is not Utilities and Industry is not Financials.
4. Filter stocks by relative strength: Stock price Relative to Index 3m > 0.
5. Sort stocks from highest to lowest by: Lease-Adjusted ROCE Average 10y and assign each a rank number from 1 to N.
6. Sort stocks from highest to lowest by: Lease-Adjusted Ebit Yield TTM and assign each a rank number from 1 to N.
7. Sum the two ranks previously obtained and sort stocks from lowest to highest to obtain a new rank, corresponding to the: Magic Formula.

## Selection Process

1. On the portfolio creation date, 7 stocks are selected using the Magic Formula Screener, as explained above.
2. Every 3 months, another 7 stocks are added to the portfolio using the Magic Formula screener, until the portfolio reaches 28 stocks, which happens 9 months after the inception date.
3. Every 3 months, starting 12 months after inception, the 7 stocks that are held for 12 months are sold and the proceeds used to buy another 7 stocks, using the Magic Formula screener.

Greenblatt, J. (2006). The little book that beats the market. John Wiley & Sons. ↩︎

Greenblatt, J. (2010). The little book that still beats the market (Vol. 29). John Wiley & Sons. ↩︎