# Investing Thoughts and Wisdom (mostly from others) – Part 3

I have a file full of notes and excerpts from investors that I’ve collected over the years. I’ve been meaning to organize it for a while, and now that this newsletter is started, I’ll use it as a reason to gradually do so (in several parts). Part 1 can be found HERE. Part 2 can be found HERE.

I used to read through this file a lot, but it got to be pretty long, which led me to summarize the key parts of my own philosophy (as of the present time) in a blog post titled Final Decision Checklist last year.

Please note: Nothing here should be considered investment advice or the best way to invest. These are things I’ve saved as reminders and notes to myself that I’ve found helpful in the past, and think they are worth sharing in case any of you happen to get an insight from any of it.

Like many games of chance, investing is a game of probabilities, upside, and downside. But with investing—especially if one is investing in equities—we usually don’t know the precise odds or payoffs. If one did, the Kelly Criterion (or Kelly Formula) could be used to size positions in a way that would maximize one’s expected return over time, similar to what Ed Thorp did counting cards at blackjack back in the day.

And unlike games of chance, there are more things that can happen to change the odds while one is playing, and you may not know whether or not you can keep playing the game.

So the Kelly Criterion can be used to help us think about how concentrated one may want to be, but it can’t be used with precision. And because individual ability, emotion, and circumstances can determine the way one acts and reacts to positions over time, there is no one-size-fits-all answer to the questions around concentration and diversification. But many of the truly wealthy people over time (e.g. Warren Buffett, Bill Gates, Jeff Bezos, Sam Walton, etc.) achieved that wealth through concentration, either in their investments or businesses, and so it’s worth thinking through in helping to develop one’s own comfort level with concentration (and the volatility that usually comes with it).

For a book on the topic, see: *Concentrated Investing: Strategies of the World's Greatest Concentrated Value Investors*

**Kelly Criterion:**

F = Pw - (Pl / ($W/$L))

The amount to bet equals the probability of winning, minus (the probability of losing over (the amount you win if you win over the amount you lose if you lose).

This is only a good betting strategy if you can repeat the bet a large enough number of times.

If you over bet, you will go broke.

A better strategy, especially psychologically, is to bet half-Kelly, where you get three quarters of the return with half the volatility.

Generalized to investing, you need to find situations where the odds of winning are larger than the odds of losing, and where you make more money if you are right than you lose if you are wrong. And you have to make sure not to make your position sizes too big.....which may happen as a result of having too much confidence when you put in a lot of work to understand something, or from not doing enough work and thus not understanding the odds and payoffs well enough....so either from overconfidence or lack of effort.

**More on position sizing…**

*From Warren Buffett, in 1966:*

This year in the material which went out in November, I specifically called your attention to a new Ground Rule reading, "7. We diversify substantially less than most investment operations. We might invest up to 40% of our net worth in a single security under conditions coupling an extremely high probability that our facts and reasoning are correct with a very low probability that anything could drastically change the underlying value of the investment."

We are obviously following a policy regarding diversification which differs markedly from that of practically all public investment operations. Frankly, there is nothing I would like better than to have 50 different investment opportunities, all of which have a mathematical expectation (this term reflects the range of all possible relative performances, including negative ones, adjusted for the probability of each - no yawning, please) of achieving performance surpassing the Dow by, say, fifteen percentage points per annum. If the fifty individual expectations were not intercorrelated (what happens to one is associated with what happens to the other) I could put 2% of our capital into each one and sit back with a very high degree of certainty that our overall results would be very close to such a fifteen percentage point advantage.

It doesn't work that way.

We have to work extremely hard to find just a very few attractive investment situations. Such a situation by definition is one where my expectation (defined as above) of performance is at least ten percentage points per annum superior to the Dow. Among the few we do find, the expectations vary substantially. The question always is, “How much do I put in number one (ranked by expectation of relative performance) and how much do I put in number eight?" This depends to a great degree on the wideness of the spread between the mathematical expectation of number one versus number eight.” It also depends upon the probability that number one could turn in a really poor relative performance. Two securities could have equal mathematical expectations, but one might have .05 chance of performing fifteen percentage points or more worse than the Dow, and the second might have only .01 chance of such performance. The wider range of expectation in the first case reduces the desirability of heavy concentration in it.

The above may make the whole operation sound very precise. It isn't. Nevertheless, our business is that of ascertaining facts and then applying experience and reason to such facts to reach expectations. Imprecise and emotionally influenced as our attempts may be, that is what the business is all about. The results of many years of decision-making in securities will demonstrate how well you are doing on making such calculations - whether you consciously realize you are making the calculations or not. I believe the investor operates at a distinct advantage when he is aware of what path his thought process is following.

There is one thing of which I can assure you. If good performance of the fund is even a minor objective, any portfolio encompassing one hundred stocks (whether the manager is handling one thousand dollars or one billion dollars) is not being operated logically. The addition of the one hundredth stock simply can't reduce the potential variance in portfolio performance sufficiently to compensate for the negative effect its inclusion has on the overall portfolio expectation.

Anyone owning such numbers of securities after presumably studying their investment merit (and I don't care how prestigious their labels) is following what I call the Noah School of Investing - two of everything. Such investors should be piloting arks. While Noah may have been acting in accord with certain time-tested biological principles, the investors have left the track regarding mathematical principles. (I only made it through plane geometry, but with one exception, I have carefully screened out the mathematicians from our Partnership.)

Of course, the fact that someone else is behaving illogically in owning one hundred securities doesn't prove our case. While they may be wrong in overdiversifying, we have to affirmatively reason through a proper diversification policy in terms of our objectives.

The optimum portfolio depends on the various expectations of choices available and the degree of variance in performance which is tolerable. The greater the number of selections, the less will be the average year-to-year variation in actual versus expected results. Also, the lower will be the expected results, assuming different choices have different expectations of performance.

I am willing to give up quite a bit in terms of leveling of year-to-year results (remember when I talk of “results,” I am talking of performance relative to the Dow) in order to achieve better overall long-term performance. Simply stated, this means I am willing to concentrate quite heavily in what I believe to be the best investment opportunities recognizing very well that this may cause an occasional very sour year - one somewhat more sour, probably, than if I had diversified more. While this means our results will bounce around more, I think it also means that our long-term margin of superiority should be greater.

I was reminded of Buffett's thoughts as I was once again thinking about optimal portfolio size for the "know something" investor. If you can consistently find ideas where you make 50% more when you are right than you lose when you are wrong, then even if you are right only 50% of the time, the Kelly Formula would say that you should be making 16.67% position sizes, or a total portfolio of 6 positions.

While I think those odds and payouts are pretty conservative for the investor that really puts in the work and has a developed a good process, even being more conservative and betting 1/2 Kelly would yield an optimal portfolio of just 12 positions. Considering most of us are looking for traits that give us better than 50/50 odds of being right, and potential upside vs. downside ratios much higher than the above example, I think a portfolio composed of 6-12 core positions also adds some protection for the difficulty, or impossibility, of estimating odds and precise payouts.

Of course, the odds and payouts change as prices change, and certain things may be being bought or sold over time, which could lead to one having a few more positions. But if you are fully invested in things that meet the general purchase criteria for most value investors, and if you are willing to put in the significant effort required to deeply understand each investment, then a portfolio of 6-12 core holdings seems about right to me.

And I think the most common danger area with having this kind of concentration—among the things that one has some control over—is being wrong about the downside risk in each investment, and so that analysis is probably especially important. As Alice Schroeder wrote about Buffett: "He will pass on huge upside opportunities if he can't get downside protection..." Or as Howard Marks often says, if you avoid the losers the winners will take care of themselves.

What you really want is a 3x upside vs. downside ratio. So if you’re looking at something that you think can double, then you need the worst case scenario to be a decline of just 1/3 (33.33%). At 50/50 odds, a 3-to-1 upside versus downside scenario would equate to a 33.33% position size. So 1/2 Kelly would be 16.67%. That 16.67% (6 position portfolio) is also full Kelly if you are 1/2 wrong on upside and there's only 1.5x upside vs. downside.

And it is ideal—though not always possible because businesses growing at a competitive advantages are rarely at great prices (and even Buffett made big positions from profitable net-nets in his partnership days, though not nearly the 40% American Express sized position)—to find something where the upside over your holding period is 150% or more, since even the best companies can decline by 50%, and if the downside ends up being a full loss of capital (-100%), then you still have 1.5x upside vs. downside. The ideal investments would also have all of the 4G’s:

1. *Good business* with high returns on capital, competitive advantages, the ability to reinvest at those high returns, and the ability to mostly control its own destiny (i.e. it controls investment and the widening of its moats, instead of being beholden to large customers, commodity prices, etc. etc.)

2. *Good balance sheet* that is conservative and that also allows the company to control its own destiny (i.e. not subject to having to rollover debt at any point, and not having its balance sheet keep it from taking advantage of opportunities and/or market dislocations.)

3. *Good management* who understand capital allocation and whose interests are aligned with shareholders because they are owner-operators. And where, for the most part, they bought their shares in the open market (or by founding the company) instead of just getting their ownership and exposure through options, where they have the upside without sufficient downside risk.

4. *Good price* with a proper and significant margin of safety.

**A few more thoughts…**

Warren Buffett: “I believe that the chance of permanent capital loss for patient Berkshire shareholders is as low as can be found among single-company investments. That’s because our per-share *intrinsic business value* is almost certain to advance over time.”

This drove home the point to me of how much big position sizes are favored by good businesses that grow their per-share intrinsic business value over time. I mentioned I thought 6-12 position sizes is probably a good number of core positions for the value investor who puts significant effort in choosing his or her investments. Now, at the concentrated end of that, you'd have 16.67% position sizes if fully invested equally. If you're leaving some margin of safety for error, the unknown unknowns, or because of opportunity costs, maybe you're only "betting" 1/2 Kelly on a given position. Which means that you'd need a fully Kelly position to tell you that you should be putting 1/3 of your portfolio in something before committing 16.67% to it at 1/2 Kelly.

What upside vs. downside gives you that output? If you're assuming 50/50 odds of being right (which is hopefully conservative), then you'd need a 3x upside vs. downside ratio over your investing timeframe before investing. As we've seen and as Buffett and Munger stressed, even Berkshire has been about halved three times since 1965. And while that wasn't permanent of course, if you assume your downside on a given investment is around 50%, then you'd need 150% of upside (i.e. more than a double) in order for that bet to be worth taking. And it's hard to find that kind of potential in a company that isn't growing its value over time. And if you take the potential downside to be complete loss of capital (i.e. 100% downside), then 150% of upside would give you a full Kelly position size equal to the 16.67% number, and a 1/2 Kelly position size then at 8.33%.

And the key to that growth being growth in per-share *intrinsic business value* because not all growth creates value.

…..

So I want something that I think has a decent chance of doubling over a 3-year period (~26% IRR), without a whole lot of downside. And something that I think can be worth 2.5x (150%) of the price at which I’m buying it, over a 4-7 year period (2.5x over 4 years ~26% , 5 years ~20% IRR; over 6 years ~16.5% IRR; over 7 years ~14% IRR).

And in the search for the elusive 100-bagger, a 100x over 20 years is ~26% IRR, over 25 years ~20% IRR; over 30 years ~16.5% IRR; over 35 years ~14% IRR. (i.e. The return you’re looking for to achieve a 2.5x in 4-7 years can lead to a 100-bagger if it can continue for 5 times as long.)

“My largest positions are not the ones I think I’m going to make the most money from. My largest positions are the ones I don’t think I’m going to lose money in.” —Joel Greenblatt

“The businesses at the top of my portfolio are not necessarily going to be the ones that perform the best over the long term but are the ones I know will perform.” —Chris Bloomstran

**Nick Sleep on Portfolio Concentration:**

As the cash is invested, portfolio concentration will rise. In theory, if we could find fifty ideas at equal discounts to value, with equal probability (conviction) of value being realized, then they could all be equally weighted in the Partnership. We could all then look forward to a nice smooth rise in the value of our shares in Nomad, free from the swings a more concentrated portfolio might create. But life is not like that. In reality opportunities in which we are comfortable to deploy capital are rare, and the highest conviction ideas the rarest of them all. The issue then is how much to invest in each idea? Bill Miller, who has run the Legg Mason Value Trust so brilliantly for many years, suggests the use of a system devised in 1956 by J. L. Kelly. A simplified version of the Kelly criterion is that investors should bet a proportion of the portfolio equal to 2.1 x p - 1.1, where p is the probability of being right. The common sense outcome of this equation is that if one is certain of being right, one should invest the entire portfolio in that idea. Even if one is say 75% certain of being right the correct weighting remains high at 47.5% ((2.1 x 0.75) – 1.1). But does anyone do that? As far as we are aware, only the early Buffett Partnership portfolios had anywhere near this level of concentration, and then mainly in companies in which Buffett was a controlling shareholder. But is this not the right way to think? If you know you are right, why would you not bet a high proportion of the portfolio in that idea? The logical extension of this line of thought is that Nomad’s portfolio concentration has at times been too low. And if it has been too low at Nomad, what has been going on at the large mutual fund complexes with many hundred stocks in a single country portfolio? Apply the Kelly criterion, and the average fund manager would appear to have almost no clue as to the likely success of any one idea. In our opinion, the massive over-diversification that is commonplace in the industry has more to do with marketing, making the clients feel comfortable, and the smoothing of results than it does with investment excellence. At Nomad we would rather results were more volatile year to year, but maximized our rolling five-year outcome. If you do not share this view, think long and hard about your investment in Nomad.

**Seth Klarman on concentration and diversification (i.e. He’s more diversified than the likes of Buffett and Munger.)…**

“It seems to me that, as we know, you diversify most of the diversifiable risk away from a portfolio by owning 20 or 25 positions, and that if one is able to tell a good investment from a bad, one should be able to tell a great investment from a good. So I see no sense in having the same size position with your best idea and your hundredth best idea to round out a 1% idea type of portfolio. When we take a concentrated position, I’d say a dozen times over 26 years, we have had a 10% or so position. It also depends on the definition: Is a position in a type of investment a position or is it only a particular issuer? So a little definitional clarity might also be needed. But in general, in one particular company’s securities, every 2 years or so we have a 10% position. Most of the time, we have 3, and 5, and 6 percent positions as our most favorite ideas. We will take them higher when a cheap position becomes much, much better a bargain or when there’s a catalyst for the realization of underlying value. We favor catalysts because it gives you a much shorter duration on the investment and greater predictability that you will in fact make money on that investment and aren’t subject to the vagaries of the market and the economy and business over a longer period of time. So we would not own a 10% position in a common stock that was just plain cheap unless we had a seat on the board and control, because too many bad things can happen. But we’d own a 10% position in a senior, distressed debt investment where there was a plan in place, where the assets were very safe – either cash or receivables or something where we could count on getting our money back, and where we saw almost no chance of principal loss over a couple of years and a chance of a very high, meaning 20% plus, type of return. So that’s how we think about it. I think when people make mistakes, it often is on both sides of diversification. Occasionally, new managers especially, that aren’t that experienced in the business, will have a 20% position or perhaps even two in one portfolio. And those two might even be correlated – [i.e.] same industry, [or] the same exact kind of bet in two different names. That’s absurdly concentrated; maybe not if you have enormous confidence and it’s your own money, but if you have clients, that’s just not a good idea. But 1% positions also are too small to take advantage of what are usually the relatively few great mispricings that you can find. When you find them, you do need to step in and take advantage.”

Warren Buffett in 1998 (University of Florida lecture):

“If you can identify six wonderful businesses, that is all the diversification you need. And you will make a lot of money. And I can guarantee that going into the seventh one instead of putting more money into your first one is [going to] be a terrible mistake. Very few people have gotten rich on their seventh best idea. So I would say for anyone working with normal capital who really knows the businesses they have gone into, six is plenty, and I [would] probably have half of [it in] what I like best.”

Warren Buffett in 2008:

“If you are a professional and have confidence, then I would advocate lots of concentration. For everyone else, if it’s not your game, participate in total diversification. If it’s your game, diversification doesn’t make sense. It’s crazy to put money in your twentieth choice rather than your first choice. . . . [Berkshire vice-chairman] Charlie [Munger] and I operated mostly with five positions. If I were running $50, $100, $200 million, I would have 80 percent in five positions, with 25 percent for the largest.”

Whatever the level of diversification you end up being comfortable with, it’s important to remember that *extremely *unexpected things can happen. I think this is best illustrated by a story from Howard Marks.

From Peter Bevelin's book *All I Want To Know Is Where I'm Going To Die So I'll Never Go There*:

“It can always get worse than you think. I love this story from Howard Marks: ‘I tell my father’s story of the gambler who lost regularly. One day he heard about a race with only one horse in it, so he bet the rent money. Halfway around the track, the horse jumped over the fence and ran away. Invariably things can get worse than people expect. Maybe ‘worst-case’ means ‘the worst we’ve seen in the past.’ But that doesn’t mean things can’t be worse in the future.’”