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# What concept of margin of safey is the best?

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I find the concept of margin of safety fuzzy, it seems to be used in different ways:

1. Price relative to expected value.

Suppose there is a binary outcome bet: with 50% probability we get 200 and with 50% probability zero. Price is 90 so MoS is 10 (expected value minus price).

2. How much buffer do I have such that I do not make a loss?

This is more a scenario where I want to have a low price that provides buffer against risk. In the above example, there will never be a MoS then as with 50% everything will be lost.

3. Robustness to valuation assumptions:

Here the margin of safety provides a buffer against modelling mistakes. Suppose that the 200 in the above example is in estimated, and lies in fact anywhere between 190 and 210. Assuming the lower end (190) I could then arrive at a MoS of 5 if the price is 90.

Each concept underlies a different objective -- which one do you find the most attractive one? Does it matter in the first place (in practice) which one to use?

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I would say the second. 1 and 3 require repeated tries to reach expected value. You might hit zero in your first four tries and now are bankrupt and can't continue.

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Thanks -- appreciate your answer. I think I am in fact using all three aspects of MoS simultaneously, which leads of course to muddle thinking.

What I dont like about 2. is that it focuses exclusively on the downside of the individual investment. Suppose I choose between investments with high expected return and (low) risk of a considerable loss, and investments with lower expected return but zero risk of big loss. If through my investment life I tend to carry out investments of the first type repeatedly (and size them of course appropriately), my wealth outcome may effectively be safer because of the higher expected return (safer in terms of for example the likelihood of falling below a certain amount I need to retire). So the downside in my *portfolio* may be more protected than in the second case.

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The concept was originally for bonds, since the times were a little different then they are now when Graham was investing, you would buy bonds that were so well covered by cash flow as well as assets that even in a Great Depression-like event your money would be protected. Number 1 is just a bet, you have no margin of safety in that scenario because if your wrong your money isn't protected that scenario is just flipping a coin. Number 2 is the real concept, when you buy a stock buying it at a discount to assets by enough that your capital is protected no matter what. Number 3 is basically the same as 2 in that the price of a security makes it so that the margin of safety is so large that it doesn't matter if the intrinsic value is \$9 or 10\$ a share when the price is \$2 or \$3 now if the price of the security is \$7 or \$8 then it matters a whole lot if intrinsic value is \$9 or \$10.

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I'd say #2 with the understanding not to make a loss over time and defining a loss as not beating an index - for you could always buy an index otherwise. I consider not beating an index a loss - perhaps not of money but of time and effort.

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For #3 what is the number you are calculating? i.e. 190-200

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For #3 what is the number you are calculating? i.e. 190-200

The idea of #3 is to seek "margin of safety" within your modelling assumptions -- but still looking at the expected value in terms of fundamental risk (as opposed to #2). So in the example I do not know the exact value of the pay-off in the good state, and to be conservative I assume the worst (190). Thus expected value is 190/2=95 so MoS is 5 given that price is 90.

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On second thought I'd go with the first option. It's all about expected value, but I think your example is a bit extreme to illustrate it. 1) and 3) look like the same thing to me.

I'd also think about expected loss as a floor vs. expected value used as a ceiling.

The second option is how you run into value traps.

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I'd also think about expected loss as a floor vs. expected value used as a ceiling.

Could you elaborate?

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I think you are confusing margin of safety with expected value (EV). Suppose you can make the following bet:

75% chance: lose everything.

25% chance: quintuple your money.

If you bet \$100 you expect to make \$25 in the long run. So expected value is positive but it would (most of the time) be idiotic to stake your net worth in this scenario because there is no margin of safety as far as I am concerned. For me personally margin of safety is a fuzzy concept that could be summarized as: "how much do I lose in a reasonable worst case scenario". I use it mostly for position sizing. Large positions in binary bets are bad if you want to compound money (according to the Kelly criterion optimal bet sizing for the above bet is ~6%).

I do think that you raise an interesting point regarding 'robustness to valuation assumptions'. I think that that is a concept undervalued by many investors. As an example, compare Valeant and Berkshire in 2015. Berkshire was trading slightly above book at reasonable multiples and had a solid balance sheet. Valeant was heavily leveraged and trading at lofty multiples. If you invested \$100 in Berkshire and some of your assumptions were wrong you kinew that you'd probably end up owning something worth \$80 - \$120. If you did the same with Valeant it would be \$10 - \$ 190. Similar EV but much riskier bet.

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#2 is the closest, but its missing much of the point.

Yes, you're trying not to lose money; but the reality is that your handicapping will be off by quite a bit (model error) - simply because you're trying to compensate for irregular events that have inherent high standard deviation. The MOS you think you have, could well be a lot less than you thought - as for a time , the market is pricing at something other than the conventional metrics.

Once bought you're looking for both return to the mean, AND growth. The company that can grow its FCF 5x over the next 3 years, is currently losing \$, & just fell out of favor with the street. You bought because the negative sentiment distorted pricing, & are hoping you got the timing reasonably right (it does not crash another 20% the day after it was bought). Return to mean, means change in sentiment, & has nothing to do with conventional metrics.

Focusing only on low cost means that you will almost never buy a great business doing well, and will almost always be in clean up mode. There are a lot easier ways of making a dime.

SD

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I'd also think about expected loss as a floor vs. expected value used as a ceiling.

Could you elaborate?

Yeah, so usually the idea is saying, well OK I think the value of this company is \$100 (EV = 100), but I can buy it at P=75 and sell somewhere around \$100.

In this case the ceiling is 100, and you buy below that.

But take the same example. What's the worst case scenario, tail risk, etc.? Your \$100 EV is just the average of a bunch of probabilities. How does that distribution look?

In other words, the EV = 100 but P1=0 and P2=200 is much different investment than EV=100, P1=95, P2=105.

For the second, your floor is essentially 95. For the first, your floor is bankruptcy. But same EV.

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In other words, the EV = 100 but P1=0 and P2=200 is much different investment than EV=100, P1=95, P2=105.

For the second, your floor is essentially 95. For the first, your floor is bankruptcy. But same EV.

Which is why you would use Kelly's. 8)

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In other words, the EV = 100 but P1=0 and P2=200 is much different investment than EV=100, P1=95, P2=105.

For the second, your floor is essentially 95. For the first, your floor is bankruptcy. But same EV.

Which is why you would use Kelly's. 8)

I hate that damn formula! :D Just because it is precise, does not mean it is accurate. It fools people in that way. In reality, we are all probably not-so-great at determining exact probabilities and expected outcomes.

Take the common-sense lesson from the kelly formula: safer stocks with higher potential outcomes deserve more of your investment dollar than risky stocks with lower potential outcomes. But most people don't need a formula to tell them that...

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In other words, the EV = 100 but P1=0 and P2=200 is much different investment than EV=100, P1=95, P2=105.

For the second, your floor is essentially 95. For the first, your floor is bankruptcy. But same EV.

Which is why you would use Kelly's. 8)

I hate that damn formula! :D Just because it is precise, does not mean it is accurate. It fools people in that way. In reality, we are all probably not-so-great at determining exact probabilities and expected outcomes.

Take the common-sense lesson from the kelly formula: safer stocks with higher potential outcomes deserve more of your investment dollar than risky stocks with lower potential outcomes. But most people don't need a formula to tell them that...

I agree with you, but your summary can be made looser:

Safer stocks with same potential outcomes (EV) deserve more of your investment dollar than risky stocks with same potential outcomes.

8)

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The original question is interesting, as are the responses.  Both Sharper and Jurgis are spot on but there is really a fundamental analysis that is lacking here.

• You have to know the limits of a model before you use it.  To paraphrase Gerald Weinberg(Systems, excellent book), you need to know at least 3 examples of a tool's (model's) failure or misuse to begin to understand when and how to use it. Hence Sharper's point about missing excellent businesses.
• The concept of margin of safety in finance is a particular application of the structural engineering concept: don't put a 3 ton load on a bridge, structure, or rope rated for 500 pounds, in fact only put 250 on it! See Buffett's commentary.
• Margin of safety is generalizable to the portfolio itself, hence half Kelley, etc.  So on those low probablity, but positive EV positions your portfolio itself should have a margin of safety. To paraphrase Munger, you do not want to go back to go, i.e. zero.  Hence, the worst super cat will never threaten BRK. Or succinctly, unlike Godiva, don't put everything you have on a horse.
• The above imply that you can use all of the suggested tools in your MoS, but judiciously.
• All of the above also might imply then price substantially less than worst case, unless you are making low probability high return bets, in which case >1% type bets might be in order.

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Graham divided investors into two groups: aggressive and defensive. For both group a substantial underlying assumption was that any investment with a substantial chance of loss was completely excluded from consideration.

So the MOS never even enters into the picture because of the high probability of complete loss. Graham would not call this an investment...he would call it a speculation. Now after you met this first criterion then things are simple, you take your expected value and multiply by 2/3rds. You always expect to pay about one third less than the investment is worth as your MOS.

HOWEVER, right at the end of the Intelligent Investor Graham writes the following:

It is our argument that a sufficiently low price can turn a security of mediocre quality into a sound investment opportunity - provided a) the buyer is informed and experienced and b) that he practices adequate diversification.....To carry this discussion to a logical extreme, we might suggest that a defensible investment operation could be set up by buying such intangible values as are represented by a group of "common-stock option warrants" selling at historically low prices

I would argue that you can consider your definition of margin of safety as meaning 1). However appropriate portfolio sizing or equivalently diversification is important. You would never want to invest 100% of your lifetime opportunities into the opportunity that was described. But 1-2% might be quite ok provided the price is sufficiently low. Cornwall capital made a lot of money on bets exactly like this.

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I'd also think about expected loss as a floor vs. expected value used as a ceiling.

Could you elaborate?

Yeah, so usually the idea is saying, well OK I think the value of this company is \$100 (EV = 100), but I can buy it at P=75 and sell somewhere around \$100.

In this case the ceiling is 100, and you buy below that.

But take the same example. What's the worst case scenario, tail risk, etc.? Your \$100 EV is just the average of a bunch of probabilities. How does that distribution look?

In other words, the EV = 100 but P1=0 and P2=200 is much different investment than EV=100, P1=95, P2=105.

For the second, your floor is essentially 95. For the first, your floor is bankruptcy. But same EV.

The argument here depends critically on diversification. If you can get a large number of diversified opportunities that look like the first case than the first distribution will start narrowing and converge to the second at the portfolio level.

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