The Multiplication Rule – Investment Perspective

One of the topics we learnt in middle school was the multiplication rule.

Two events are independent in the sense that the outcome of one event has no influence on the outcome of the other, then the probability that they both occur is computed by multiplying the probabilities of the individual events.

While in school we used it to calculate solve inane problems such as the probability of flipping coins, drawing cards, it’ll be interesting to see how we can apply this rule for our investment purposes.


Benjamin Graham in his book “The Intelligent Investor” suggested principles utilizing the multiplication rule. He never directly spoke about it but talked about diversifying investments over independent risks.

An investment might be justified in a group of issues, which would not be sufficiently safe if made in any one of them singly. In other words, diversification might be necessary to reduce the risk involved in the separate issues to the minimum consonant with the requirements of investment.

There is a close connection between the concept of a safety margin and the principle of diversification. They have a mutual relationship. Even if the margin of safety is in our favor, an individual investment may not work out. This is because the margin of safety only says that we have a better chance of profit than loss, not that loss cannot occur.

But as the number of such commitments is increased the more certain does it become that the aggregate of the profits will exceed the aggregate of the losses. This is one of the fundamental principles used in the insurance underwriting business.

A margin of safety does not guarantee an investment against loss; it merely guarantees that the probabilities are against loss. The individual probabilities may be turned into a reasonable approximation of certainty by the well known practice of “spreading the risk.” This is the cornerstone of the insurance business, and it should be a cornerstone of sound investment.

This can be said in simple words– While some investments can go wrong at the same time, the chance that all our diversified investments will fail is very low, thanks to the multiplication rule.

“Don’t put all your eggs (portfolio positions) in one basket (one industry)”

Warren Buffet, one of the most famous investors of our time regarded Graham as his investment guru. He too, has spoken of this rule in one of his widely appraised letters.

They limit the business they accept in a manner that guarantees they will suffer no aggregation of losses from a single event or from related events that will threaten their solvency. They ceaselessly search for possible correlation among seemingly-unrelated risks.

The multiplication rule is used in designing ship vessels and oil rigs as well! It uses a term called “redundancy”. A system called Dynamic Positioning 3 (DP 3) is used which has a triple redundant controller. An error in one may then be out-voted by the other two. In a triply redundant system, the system has three sub components, all three of which must fail before the system fails. Since each one rarely fails, and the sub components are expected to fail independently, the probability of all three failing is calculated to be extremely small.

This is a powerful idea which can be utilized in various domains such as increased safety in planes, cars and nuclear plants.

I would like to conclude by quoting Warren Buffet yet again.

If only one variable is key to a decision, and the variable has a 90% chance of going your way, the chance for a successful outcome is obviously 90%. But if ten independent variables need to break favorably for a successful result, and each has a 90% probability of success, the likelihood of having a winner is only 35%. In one of our problematic ventures, we solved most of the problems. But one proved intractable, and that was one too many. Since a chain is no stronger than its weakest link, it makes sense to look for – if you’ll excuse an oxymoron – mono-linked chains.

For the investment to be successful, all of those risks must be mitigated. And given the way the multiplication rule works, that’s fairly low. Risky long term investments can sometimes be offset by windfall profits if success does occur, but that kind of investing is more in the nature of a venture capital operation than a value investing operation.

With inputs from Prof. Sanjay Bakshi of MDI Gurgaon

AadityaVikram Singh


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