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The Multiplication Rule of Investing

1 March, 2016 by Ben O'Brien in Commentary

When it comes to looking for good investments simplicity is a great virtue. One way of measuring the simplicity or complexity of a business is by using a fairly elementary but powerful statistical concept called the multiplication rule.

According to the multiplication rule, to get the probability of a series of independent events turning out a certain way, you simply multiply the probability of each of the individual events.

It is a simple but powerful idea. When you flip a coin, the probability of getting heads is .5 or 50%. The probability of getting heads twice in a row is .5 X .5 which .25 or 25%. The probability of getting heads ten times in a row is .5 to the tenth power which is .001 or .1%. The point is that if a certain outcome depends on a large number of scenarios, even if each of those scenarios is highly likely, the probability of the ultimate outcome becomes surprisingly unlikely.

I first came across this idea in a great article published last year by the Indian investor and professor Sanjay Bakshi. Ever since then it has been one of my favorite tools for evaluating potential investments.

Though these probabilities, of course, are not exact when you apply them to an investment, they help to roughly quantify and weight the moving parts involved in an investment situation.

You can apply this concept by comparing a complex business, say, a large pharmaceutical company, such as Merck, with a relatively simple one such as Dunkin Donuts.

First let’s think about Merck. Perhaps there are ten scenarios that have to go right for a big pharma stock such as Merck to do really well over time:

1) They have to do a lot of expensive R&D—sometimes in the billions of dollars—to come up with a new drug.

2) They have to keep the cash flow going in their existing business in order to finance billions of dollars in R&D.

3) They have to attract and retain the top talent in the industry capable of discovering blockbuster drugs.

4) Once they develop the drug, they have to get it approved by regulators.

5) They have to get a patent to protect their new drug from copycats or generics.

6) They have to advertise widely and convince doctors to prescribe the drug.

7) They have to get Medicare/Medicaid and pharmacy benefit management companies and private insurers to agree to pay a high enough price to recoup the large R&D and other costs.

8) They need enough blockbuster drugs to cover the cost of R&D for all the drugs that never worked out.

You get the idea, and there’s no need to list the rest.

Even if there is a 90% chance that each scenario individually goes your way, to get the likelihood of all of them turning out favorably you must multiply .9 to the tenth power. Despite that fact that your chance of success in each scenario was extremely high, when you multiply them all, your chance of success drops to 35%. And in reality the probability of success in each of those individual scenarios is probably less than 90%.

This does not mean that you should never invest in a big pharma stock. It does mean, though, that the business has some substantial built-in handicaps and a real lack of transparency that you should take into consideration in your research and valuation. All else equal you might want to go with a company with less complexity and fewer moving parts. Or require a substantial discount for the uncertain and opaque business.

Now let’s think about Dunkin Donuts, a much simpler business. How many scenarios are there that need to go right for Dunkin to succeed? Given that it seems likely that people will continue to love coffee and ice cream (Baskin Robbins is part of Dunkin Donuts), the core business seems a lot more certain.

What are the independent scenarios involved?

1) Will people continue buying lots of coffee and donuts and ice cream?

2) Will DD be able to continue adding new stores in the US and abroad?

3) Will people still want to get their coffee and ice cream from DD and Baskin Robbins, which is to say will the brand maintain its appeal?

I’m sure you could come up with a few more scenarios, but it seems pretty clear that the business model is structurally a lot more stable and reliable than a business like pharmaceuticals.

All of the scenarios for DD, which involve serving coffee and donuts and ice cream and licensing new franchises, appear to me to be more certain than those for Merck which involves massive R&D expense with armies of PhDs and MDs as well as significant regulatory and reimbursement risk that no one can reliably predict.

Most importantly though for the multiplication rule, there are only three scenarios. If we assign a 90% probability to each scenario, that’s .9 X .9 X .9 = 73%. And given that coffee is basically addictive, ice cream is perhaps the single most beloved food item, and DD invests lots and lots of cash into enhancing its brand–90% for each scenario is more conservative than it was for Merck.

Of course the business model, or what you might call the narrative behind the business, is not the only consideration. In addition to the business model, the company’s valuation is critical.  In fact, the quantitative side of producing a valuation and the qualitative business narrative go hand in hand.

In the case of Dunkin Donuts, I ultimately decided against investing for valuation and balance sheet reasons, even though I like the underlying business a lot. I put the stock on my watch list in the hopes that it will some day approach a better entry point.

Investing is ultimately a game of probabilities where you never have total certainty but try to tilt the odds in your favor through research and analysis. The multiplication rule helps to clarify the underlying drivers of growth on which the valuation and the investment decision depend. If you have a lot of trouble identifying the underlying scenarios or the total probability of success is a lot lower than a 50% coin flip, it’s usually a good idea to pass on the stock and look for a simpler and more transparent one.