One of my favorite investing books is 100 Baggers: Stocks That Return 100-1 And How To Find Them, written by Christopher Mayer. It’s also one of the top two books on the bookshelf of Mohnish Pabrai. The other book is 1,000 Dollars and an Idea: Entrepreneur to Billionaire, by Sam Wyly.
The book is about 100-baggers – stocks that return $100 for every $1 invested. The inspiration for the book came by way of another book he’d read called, 100 to 1 in the Stock Market by Thomas Phelps.
One of my favorite parts of the book is in Chapter 10: Kelly’s Heroes: Big Bet, in which Mayer writes about the idea of making big bets on your best investment ideas. He provides some great examples from some of our best known Superinvestors – Klarman, Watsa, Ackman and Berkowitz. Here’s an excerpt from the book:
I can’t be involved in 50 or 75 things. That’s a Noah’s Ark way of investing—you end up with a zoo that way. I like to put meaningful amounts of money in a few things. — Warren Buffett
Thomas Phelps wrote, “Be not tempted to shoot at anything small,” the idea being you want to focus your capital on stocks with the potential to return 100x. You don’t want to own a zoo of stocks and ensure a mediocre result.
In this chapter, we explore the idea of concentration in your portfolio. In Zurich, at the ValueX conference, Matt Peterson of Peterson Capital Management presented the idea of the Kelly criterion. This can get mathematical and wonky, but the basic idea is simple: bet big on your best ideas.
It all began with a man named John L. Kelly Jr. (1923–1965).
Kelly was a Texan, a pilot for the navy in WWII and a PhD in physics. He worked at the storied Bell Labs, where he whipped up what became known as the Kelly criterion in 1956. The story is wonderfully told in William Poundstone’s Fortune’s Formula.
Kelly sought an answer to a question. Let us say a gambler has a tipoff as to how a race will likely go. It is not 100 percent reliable, but it does give him an edge. Assuming he can bet at the same odds as everyone else, how much of his bankroll should he bet? Kelly’s answer reduces to this, the risk taker’s version of E = mc2:
f = edge/odds
F is the percentage of your bankroll you bet. Say you can bet on Big Brown at 5–1 odds at the Kentucky Derby, meaning, if you bet $1, you would stand to win $5 if Big Brown wins. (Plus, you’d get your $1 back.) Odds = 5.
What about your edge? Your inside tip says Big Brown has a one-in-three chance of winning. That means a $1 bet gives you a one-third chance of ending up with $6 ($5 plus your initial $1 bet). On average, such $1 bets are worth $2—for a net profit of $1. Your edge is your profit divided by the size of your wager, in this case, $1. Edge = 1.
Plug it all into the formula, and Kelly says you should bet 20 percent of your bankroll on Big Brown. If you don’t get the math, don’t worry about it. The aim of the formula is to find the optimal amount to bet. And the rough answer is this: when you have a good thing, you bet big.
As you might imagine, this is useful for investors because they too face a question: how much do I put in any one stock? Kelly’s formula gives you an objective way to think about it. But it has quirks. For one thing, the formula is greedy. “It perpetually takes risks in order to achieve ever-higher peaks of wealth,” as Poundstone writes. It is for making the most the fastest, but that goal is not for everyone.
Yet it is also conservative in that it prevents ruin. It has, as one professor put it, an “automatically built-in . . . airtight survival motive.” Even so, it produces large swings in your bankroll. The same can be said for those venturing into биткоин казино, where the allure of big wins comes with the risk of significant losses. As you can see from our Big Brown example, if you lost—and you would have—you lost 20 percent of your bankroll. This has led some to try to smooth the ride a bit by taking a “half-Kelly.” In other words, if the formula says you put 20 percent of your account in one stock, you put half that amount, or 10 percent. Just as investors moderate their stakes in volatile markets, online gamblers must also calculate their risks and rewards, maintaining the balance between potential gains and the safety of their digital assets.
I favor the half-Kelly because it cuts the volatility drastically without sacrificing much return. Poundstone says a 10 percent return using full Kellys turns into 7.5 percent with half-Kellys. But note this: “The full-Kelly bettor stands a one-third chance of halving her bankroll before she doubles it. The half-Kelly better [sic] has only a one-ninth chance of losing half her money before doubling it.”
The formula has more ins and outs than I care to tackle here. It set off lots of catfights among academics that raged for decades. (See Poundstone’s book for a good look at the debates. Also, Michael Mauboussin has a summary discussion in a 2006 paper titled “Size Matters.” You can find it free online.)
For me, the big obstacle is that in the stock market, you can’t know your odds or your edge with any certainty. You must guess. Nonetheless, the idea is alluring. Ed Thorp used it in his hedge fund, Princeton/Newport. Started in 1974, it averaged 19 percent returns for nearly 30 years without a down year. How much of that is due to Kelly’s formula and how much to Thorp’s own genius is hard to say.
Thorp’s example is not a lonely one. Many great investors seem to intuitively use Kelly’s formula. Which brings us back to Matt’s presentation. He had a fascinating slide, which I reproduce here. (This data was current as of the end of 2014 and relies on public filings. This is not an accurate way to get a read on a portfolio because of certain limitations. For example, investors don’t have to disclose foreign-listed stocks and other positions. But it gives you a rough idea of a manager’s concentration in disclosed stocks.)
You’ll see a number of standout investors and how they bet big on their best ideas. These portfolios look a lot like what Kelly’s formula would demand.
Now, I doubt any of them is actually going through the trouble of plugging numbers in the edge/odds formula I showed you before. But it is like an analogy I heard once about Minnesota Fats and physics. Fats didn’t use math formulas from physics when he lined up a pool shot. But the principles of physics were at work nonetheless. It’s just that Minnesota Fats had internalized them through experience.
We might say the same thing for these super investors. The principles of using edge and odds are part of what they do. Matt’s slide showed this in a striking way. To maximize your returns, you’re better off following these examples.
To flip it around, look at what unsuccessful investors do. The typical mutual fund holds about 100 stocks. None matters very much (or for very long). And most funds are poor mimics of the market.
As Buffett says up top, reject the Noah’s Ark way of investing. It seems many great investors do. And it is what I try to do in my own portfolio: Keep the list of names relatively short. And focus on the best ideas. When you hit that 100-bagger, you want it to matter.
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