## Thoughts on Margin of Safety

February 5th, 2014 | Posted by in InvestingWarren Buffett has said that the three most important words in investing are “margin of safety”. The term is quite common, and anyone who has done even a modicum of investment reading is familiar with it. But what does it mean? What *should* it mean?

The common understanding of the term is simple: an investor should seek opportunities in which an asset’s undervaluation is large enough to provide a buffer against analytical mistakes and market misjudgments. In other words, the asset should be so cheap that even if you’re wrong, you make money—or at least you don’t lose money.

Easy enough. But is it really that simple? And what does “margin of safety” mean when applied to real world investing? I have two examples—excuses really—that I want to use to offer a few of my thoughts on margin of safety.

The first example revolves around a typical scenario analysis in which an analyst presents the bear, base, and bull cases for an investment, and then assigns expected IRRs and probability weightings to each scenario. Here is one such scenario analysis:

The analyst will likely argue that with a probability-weighted expected return of 32%, this is a good investment. And from that perspective, it is indeed a good investment, if we can safely assume that the estimated returns and probability weightings are accurate.

But I think there is more to consider. Does this investment *actually* provide a margin of safety? Let’s focus on the bear case and try to approach it realistically. The bear case here represents a loss of capital and the probability of the bear case occurring—20%—is considerable. One in five to be exact. If we add in the likelihood that the analyst is overconfident in his or her estimations, then perhaps the actual loss, if incurred, turns out to be 30%, or 40%, rather of the originally posited 20%.

A 40% loss on an investment originally expected to return 30%+ is a major mistake. Then, consider the math of losses: a 40% loss requires a subsequent 67% gain just to make oneself whole, never mind turn a profit. Once these nasty real world complications get in the way, sometimes what looks like a good investment can turn out to be a very bad one.

I think it is also crucial to point out here that *even if* the analyst had correctly estimated the bear case, *the investment would still have appeared to be attractive* from a probability-weighted perspective:

One reasonable counter argument is that in a diversified portfolio, these things will even out. The bear cases are understated, but maybe the bull cases are too; the losses don’t matter too much because there will be big gains as well.

Obviously there is some truth to this counter argument. The problem I have with this solution is that it creates a paradox. By increasing the number of investments in the portfolio, you decrease the time you can devote to analyzing each one individually, and you thereby increase the size of your forecasting errors. So I’m not sure that wide diversification is really a sound solution the problem.

I think the better solution is to require that “margin of safety” mean more than just margin of undervaluation. The concept must also encompass the range of reasonable outcomes and the impacts those outcomes will have on the capital invested. I am sure there are many smart speculative investors out there capable of making nice livings investing in situations that involve high expected returns but also very real probabilities of loss. But, if you desire total—or close to total—protection of your capital, it might be wise to approach investments with probable negative outcomes cautiously. To go back to Buffett again, a long stream of impressive numbers multiplied by a single zero always equals zero.

The better investments—if you can find them—are those in which the worst reasonable outcome still involves a gain. I think it is important to keep in mind that when Benjamin Graham introduced the concept of margin of safety in *The Intelligent Investor*, the examples he discussed did not involve probability-weighted expected values—they involved *much greater* degrees of certainty, as they consisted mostly of companies trading at substantial discounts to the cash in the bank, or the inventory in the warehouse, or the capital expenditures made in the previous year, or some other tangible or indisputable value.

Personally I feel I have found an investment with a true margin of safety only when the question is not *whether* I will make money, but *how much *I will make*.* These investments are rare, but they exist, in the sorts of situations described above, as well as, often, in situations that involve recurring revenue or contracted future cash flows of some sort.

* * *

The second point I’d like to make about margin of safety involves another margin: margin of error. I recently read an investment pitch that argued investment XYZ offered 20% upside *and* a margin of safety.

This is a contradiction of terms. No investment with 20% upside can possibly offer a margin of safety. Why not? Because the margin of error inherent in analytical judgments, market forecasts, and so on, is greater—probably *much* greater—than 20%.

David Dreman’s book *Contrarian Investment Strategies: The Next Generation* references a study of analysts’ annual EPS estimates from 1973 to 1996 that found a 42% median error/variance between the analysts’ annual EPS estimates and the actual EPS figures reported by the companies.

42%! The study, which included 94,000 individual estimates, also found that fewer than half of the individual estimates proved to be accurate within a range of ±10% (20% in total) of the actual reported EPS figure. And that margin of error *includes *the accounting gymnastics so many companies perform to try to meet estimates.

I cannot speak for others. For myself and for Monte Sol, however, I can say that I only feel I am truly protected by a margin of safety when A) the valuation gap is large enough to protect against empirically demonstrated margins of error (and then some), *and *B) the probability of permanent capital impairment is remote.

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