How can Graham and Greenblatt both be right? Some thoughts on Mark Carter's algebraic illustration of Geoff Gannon's 'value investing paradox'.

Profitability as it concerns shareholders is determined by dividing earnings, the profit remaining for shareholders once all other costs have been deducted, by book value, the value of the company's assets less everything it owes external parties (liabilities). The remainder belongs to shareholders, and their annual profit divided by their equity is the Return on Equity.

The relationship between profitability, and the price investors pay in relation to earnings (profit) and book value (equity) is:

Where B = Book value, E = earnings and P = price. To keep things simple, I'll refer to these fractions by their ratio names from now on, so:

Where ROE = Return on Equity, PBV = Price to book value and PE = Price Earnings Ratio.

Here's the conundrum.

Ben Graham, the original value investor, favoured companies on low multiples of earnings (low PERs) and book values (low Price to Book) and from the above equation, you can see that if a company with a low PER is to have a low PBV it will also have low ROE (profitability).

Joel Greenblatt, one of Graham's f''ted successors, favours companies on low multiples of earnings with high levels of profitability. If we use the same ratios to illustrate the principle (Greenblatt uses alternative measures of profitability and value) and assume the PE is relatively low and the ROE is relatively high then our equation:

Is going to give us a middling PBV. How can both strategies work?

Relatively unprofitable companies can be good investments if:

1. Low profitability is temporary, and in future they will be more profitable
2. The price investors are paying is so low they will still get a good return.

Graham found that on average, over long periods of time, the gains made by the very cheapest shares when they recover more than outweigh the losses from companies in the same pool of shares that don't recover. This, he believed, was because in general the market underrates the prospects of companies that are currently doing badly, and that companies gradually work out how to improve profitability and erode that of their competitors.

Highly profitable companies can be good investments if:

1. High profitability is persistent, and in future they will still be highly profitable
2. The price investors are paying is low enough for them still to get a good return.

Greenblatt found that on average, over long periods of time, the gains made by shares in companies that have the best combination of profitability and value and remain highly profitable more than outweigh the losses from companies in the same pool of shares that don't. This, he believes, is because some companies can withstand competition from rivals and defend their high levels of profitability for long periods of time.

The two rationales seem contradictory, but they're not necessarily.

Though he's not particularly keen on Greenblatt's approach, Geoff says this isn't a paradox. Though profitability does generally revert towards the mean some companies are special, and Greenblatt's formula may find enough of them to beat the market.

I think it's critical to recognise which camp you're in, especially if, like me, you're in both. My Thrifty screen attempts to improve on the Graham strategy, and my Nifty screen attempts to improve on the Greenblatt one.

Sometimes, when I go from looking at a Nifty company to a Thrifty company I'm put off by the Thrifty company's dismal profitability.  That's ludicrous. The Thrifty companies are potential bargains and, as I hope I have demonstrated, I should be expecting low ROE. Poor results, albeit temporarily so, present the opportunity to profit.

Thrifty companies, or the environments they operate in, must change, so the following are positive signs because they might lead to higher ROE in the future:

1. New management, especially if they're buying shares
2. Restructuring, asset sales, write offs
3. Talk of cost control and organic growth
4. An improvement in business performance (indicated by the F_Score).

Nifty companies, those special companies that remain highly profitable, must stay the same. The past is our guide to the future and change increase risk. The following are positive signs because they are signs of stability:

1. Consistently high ROE at a consistent level of leverage over a long period of time
2. A management team responsible for the company's past success, that owns a significant stake in the business
3. Talk of cost control, organic growth, and extending a successful business model gradually into closely related markets.