Brookfield, Kelly, and Lindy (2024)

“For whosoever hath, to him shall be given, and he shall have more abundance: but whosoever hath not, from him shall be taken away even that he hath.”

— Matthew 13:12 (King James translation).1

Since it’s Father’s Day this weekend, I thought I would get something out earlier in the week. Enjoy. ~15 min read

We added to our Brookfield position and trimmed some stuff. We’re going to swing wide around that topic today. We’ll cover more of the thought process, frameworks, and foundation behind making the decision. We’ll talk less about the facts and reasoning, since we already thought out loud about that.

Safe harbor statement and huge (yuuuuuuge) disclaimer:

I’ll remind you all again. There are stocks below. May the God of Abraham2 and securities regulators bear witness, I am not your fiduciary or financial advisor! You own your decisions, good or bad! Do your own homework! I may or may not own all these in a month. Maybe I changed my mind about an idea. Maybe we found something better than what we own and didn’t get around to writing about it yet. Maybe I need some cash. And so on. If some crazy news comes out and one of these is up or down 20%, I have no obligation to immediately update you!

I know some of you are already copy-catting. I’m flattered. But remember I have no fiduciary responsibility for what you do with your money!

Not to mention, stock market investing is like chainsaw juggling: It’s completely safe!…

…

…if you catch them by the handles!

That takes serious practice if you don’t want your digits hacked off. If you want to start with the sharp things and fire rather than first going to juggling school then working on the oranges and the bowling pins, there are other places for that. Like r/WallStreetBets. We don’t do crazy stuff here. Keep your fingers intact.

I am now almost 15 years into juggling, and only recently did I start doing the chainsaws and the fire sticks, okay? I still don’t even do the broken wine bottles.

Good. Moving on.

Story Time

Warren Buffett once said there are a few businesses he’d be comfortable putting his whole net worth into, at the right price and with the right characteristics.3

Obviously, one was Berkshire, which for much of his life has been 99% of his net worth, now being donated to the Gates Foundation. Berkshire rose to 95% of his partner Charlie Munger’s wealth, at least until the 2000s when he decided he also liked Costco. The two stocks were then most or nearly all his personal wealth until his death last year.

Another “I’d put my whole net worth into it” bet was American bank Wells Fargo.

From the 90s to the mid-10s, as far as I know, Berkshire’s dynamic duo often considered Wells their bogey, the hurdle other opportunities had to surmount. Munger used to think: is this new investment better, or is it better to own more of this wonderful company we’ve already got? Which is the better risk/reward?

In practice, though, I believe Buffett never had more than ~half his partnerships’ (subsequently Berkshire’s) portfolio in a single stock. He put half the partnerships’ capital into American Express once. Later, in the 80s and 90s, GEICO then Coca-Cola, were at times about half Berkshire’s stock portfolio.

Charlie Munger did take the big bet at least once.

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Munger managed a portfolio at the Daily Journal Corp. I believe he did it at no cost other than his board director’s fee. Actually, I just thought: I wouldn’t be surprised if Munger also sat on the DJCO board for free, so I checked. He did:

In March 2009, in the aftermath of the ‘08 financial crisis, Munger nearly bottom-ticked the market. The Daily Journal bought Wells Fargo… for $7 or $10 per share (my memory’s foggy, sorry!). In 2011, it bought Bank of America for $7. Both prices represented a very large discount of up to ~50% vs. each bank’s tangible capital, in an industry where Buffett and Munger believed the leading players would earn excess returns (say, 13-20% ROEs) “forever”. Both companies were well-managed, and there was no longer anything fundamentally wrong with their business models. Both had been following the banking industry at least 30 years by then.

When the crisis passed, Wells had $20 per share in tangible equity capital, and continued to earn attractive returns on capital. Because of its lending discipline and industry position, it had preserved and even grown the bank’s capital at a time when many lenders’ bad mortgage bets left their shareholders with worthless stock. BofA took longer to work through its issues but has since grown its capital base, market share, and earning power considerably, earning around 20% compounded its first 8 years in the Daily Journal’s portfolio.

After these actions, the Daily Journal owned 3 or 4 stocks. But it was really two: Wells and BofA represented >90% of the portfolio. Arguably, it was one: both companies were in the same industry, in the same country, and had virtually the same competitive position and business model, and so they carried the same fundamental drivers and risks.

Clearly, both men shared the opinion there were stocks where at a certain price, a rational person should conclude that, given the facts, they had extreme conviction in their idea and the risk/reward was phenomenal. A “cinch”.

I almost — but not quite — feel this way about Brookfield.

We Bought More BN

On Friday, after I wrote about the fact-checking and thinking I did, I shifted ~4% of the portfolio into BN. I sourced cash selling some BAC, GM, KKR, and BRK. In my mother’s portfolio, I added 2-3% to BN selling some KKR and BRK (she owns less BAC and GM to begin with, and far more Berkshire). Except for GM, all the positions I was selling have inferior risk/reward. I’m either as convicted or more convicted in BN than what I sold. E.g., for GM, there are two potentially serious industry issues we’ll talk about.

This took Brookfield from ~23% to ~27% of the portfolio. It looks like this after market close Monday, June 10th:

(Funny note: you really can’t time the market. I hadn’t touched the portfolio for months until Friday. After the market close, it was announced KKR would be included in the S&P 500 index. The stock ripped 12% Monday once the market opened. Before Monday’s open, GM also announced it closed a labor agreement, and closed up 4%. Brookfield was flat. I literally did nothing for months, and on the day I did something, it would have been better to wait a single more day. The weights in KKR and GM decreased by less than the amounts I sold because of this relative performance against the other positions, and I may sell 1-2% more KKR and toss it into BN, or something, and take the weight to around 30% for now.)

Why, again, am I comfortable owning this much? Alternatively, perhaps he should own more? Is The Madman’s Portfolio really madness? Won’t he eventually lose digits juggling those chainsaws?

Meet Kelly

In the 1950s, John L. Kelly Jr derived a formula4 to answer the following.

You’re faced with a probabilistic financial decision. There’s a set of known outcomes with known probabilities. You can calculate the expected value and see if you have a numerical “edge” in this bet or not. You have an investment portfolio or a gambling bankroll to wager on this bet. The question is: if your objective is to maximize the bankroll’s growth rate (the compounded return), is there an optimal wager size?

There is. We won’t go into detail today, but visually, Kelly plots like this:

Don’t think about the inputs shown, just know that this bet has a positive expected value. Look at the plot’s shape.

On the x-axis, we have the percentage of the portfolio you bet. On the y-axis, we have the resulting portfolio growth rate you’d earn assuming you have no other bets on (you hold cash with the rest). If you bet 0% of the portfolio, obviously the portfolio will neither grow nor decline, so the curve starts at 0%. Increasing from a zero wager, the expected portfolio return goes up. Then it peaks, which is the optimal or “Kelly” wager. It then falls and even goes into negative territory. Keep that last bit in mind.

The curve is shaped differently for different kinds of bets, but it follows this general pattern.

For a bet with the values given, our gambler could grow their bankroll at an average rate of 2.5% per bet if they wagered 20% of the bankroll. With this available bet, they cannot grow their portfolio any faster. Again, notice that if they just try to bet harder in an effort to win more, the bankroll’s growth rate declines and even turns negative. That happens even though the bet itself is favorable! (That is, it has a positive expected value, like say a coin toss where you win $1 if you get heads, but lose $0.50 if it’s tails: 0.5 * $1 + 0.5 * (-$0.50) = +$0.25.

You can’t win by over-betting.

You can actually lose money by repeatedly betting too heavily, even if the bet has a positive expected value like this one. Loads of overly ambitious investors get this wrong. Reddit is full of meme stock buyers who have blown their life savings. Even professionals have blown up this way.

(By now, maybe you’re starting to see why I’m allowed to juggle the chainsaws and the fire sticks, and you aren’t.)

The easiest way to explain how you can get killed even when you’re making good bets is this:

You have some bankroll, say $1,000,000. You can take a bet that has two outcomes: 90% of the time, you’ll gain 100%, and 10% of the time, you’ll lose 100%. That bet has a very positive expected value, yet if you wager 100% of the bankroll, eventually you’ll get hit with that 10% outcome and lose everything you accumulated, no matter how much you have.

In gambling and financial academia, this is called ruin. The way Kelly is derived, one of the constraints is that the bettor cannot be subject to ruin — under no circ*mstances can the bankroll go to zero.

The bet size can go to extremes both ways, by the way. For example, Kelly might tell you the optimal wager is -15%. That means that if you can find a sucker, you should sell this bet to them (or short the stock, say). It might also spit out 235%, meaning you should take on leverage — borrow someone’s money — to buy even more. (There are loads of reasons not to do that. That is beyond chainsaw and fire stick territory.)

That’s the gist. I hope to write a fulsome article on the Criterion soon.

Out-of-the-box, vanilla Kelly doesn’t apply to portfolio management exactly. The assumptions aren’t true: you don’t know all the outcomes of an investment, and you don’t know the probabilities. But it is a useful tool.

So I used it.

I took this formula’s ideas and ran with them. I’m not special: many, many other investors have. I used to maintain a more rigorous spreadsheet that ran a simplified distribution of 2-5 outcomes of each of my investments through Kelly. When I analyze each investment, I flex the assumptions in my valuation. If X happened, how much is the business worth and how much would I gain or lose? Roughly what are the chances of X? Those outputs then become the portfolio “optimizer’s” inputs. I’d then normalize the numbers since a portfolio is a bunch of parallel bets, whereas Kelly is based on a single bet made sequentially. That’d spit out “optimal” portfolio weights, which were useful for me to then weigh against what I thought made sense qualitatively, and to challenge my beliefs. I’d run sensitivity analyses around the estimates that I put in.

When I plug Brookfield into Kelly, it usually spits out answers like 300% and wants me to borrow then invest all your money on my behalf.

But there are tons of qualitative factors to consider when deciding how much to actually own. There’s no single correct answer here.

For example, I’m personally quite comfortable with a highly concentrated portfolio of stocks. Other people might not sleep well at night investing their family’s money this way, and that might lead them to make irrational decisions in the future (e.g., because they panic-sell something big). The “Kelly” weight will in most cases be far too much for them.

For me, there’s a ton I consider.

For example, Brookfield is different from many other investments because the stock itself is a conglomerate of businesses, which each generate their own free cash flows and in many cases are uncorrelated to each other. If you have a 20% portfolio weight in BN, say, and 50% of the intrinsic value is BAM and 20% of the intrinsic value is BNRE, then what you’ve really got is a 10% weight in BAM, a 4% weight in BNRE, and so on across the other businesses.5 This makes it appropriate to take on a larger weight than you might otherwise think, since Brookfield’s management is taking on a number of different bets internally. Kelly misses this when I am just inputting upsides and downsides for BN.

I also run through a risk assessment checklist, and think Brookfield is qualitatively one of my lower risk bets. For example, I think that the management will allocate capital very smartly, in ways that will on average create a lot of shareholder value. I don’t think this is as likely at certain other investments and believe there is a higher risk of value destruction, such as at GM. The checklist goes on.

There’s no exact numerical probability that comes out of this thought process — what is the chance that Bruce Flatt has made a bad bet on BNRE and we will lose $10 billion, or 20% of Brookfield’s intrinsic value? Well, tell me, what’s the number? It’s unknowable, right? That’s where things like the sensitivity analysis above come in.

Real quick, meet Lindy.

The Lindy Effect, named after a New York City delicatessen and popularized by trader and author Nassim Taleb, is the idea that the longer a non-perishable thing has existed, the longer it will exist in the future. For example, trains have been around longer than cars and planes, and so — more likely than not — they will still be a mode of transportation long after cars and planes are gone. Boats are likely to outlast them all. And so on.

In a simplified way, you could say part of the reason for this is that older things have “stood the test of time” and been subject to more of the world’s ebbs and flows, and have survived a greater variety of changes and problems. By definition, young things have not, and so it remains to be seen how durable they are.

In Brookfield’s case, people have been running other people’s money for a very long time, and people have owned businesses since before merchants first led trade caravans between nascent cities and settlements. There are very strong fundamental reasons for that, which are hard to supplant. I think Brookfield’s products have no real chance of being made obsolete in the near future, and that it will be selling products with more or less the same customer value proposition in 20 years. There’s more to it than this, but you get the idea.

If for example, you owned Apple instead, you have a little small problem to think about that involves both Lindy and Kelly. You basically own iPhone-based free cash flows. One product is nearly all the value. You really, really, really need to be convinced that device is heavily integrated into people’s lives, habits, and behaviors, and that you’ve got strong reasons to believe that’ll stay true for a long time.

Lindy, Kelly, my checklist, and other ideas feed into how much to bet. In Brookfield’s case, I’m comfortable betting a heckuva lot at the right price, but I have a hard time getting to the level Charlie Munger got to, just knowing that in practice that kind of stuff is often mathematically unfavorable.

Takeaways

• It’s possible to take a huge bet on a business like Brookfield for a number of reasons. There’s the sheer number of things I understand well about the business, the customer, and the industry, which aren’t going away anytime soon. It’s also possible because the business’ cash flow profile is very durable and the conglomerate is highly diversified across a number of business lines that aren’t totally (but somewhat) correlated to each other. A 20% position in Brookfield is only a 10% position in Brookfield Asset Management, and so on across the other businesses.

• Capital allocation is hard and involves many, many considerations. You were introduced to some like the qualitative risk and business/management quality checklists I run through.

• There are arguably “forever” or “inevitable” businesses which are very durable and at the right price, can be bet very heavily on. On the flip side though, it’s clearly a bad idea to be over-betting. In fact, it’s worse to over-bet than it is to under-bet, according to the Kelly Criterion. That often gives me some pause. Bet sizing is both a quantitative and qualitative exercise.

• Frameworks like Kelly are helpful, but it’s important to know their shortcomings. For example, in the real world of investing, both the outcomes and the probabilities of those outcomes can’t be known with precision (they’re both uncertain and unknowable). This fact limits the use of many quantitative tools. Investing isn’t like playing blackjack, where all the potential outcomes are known in advance (the deck only has 52 cards). They’re still useful, especially if you’re doing a lot of sensitivity analysis to test your assumptions, but they require a lot of context and qualitative thinking.

Until next time!

Chris

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