August 2020
Yes, Sam Dogen
No, Sam Dogen
“Leaving the party too early can cost you as much as leaving too late”
Cash is King. Until it’s not.
What card counting can teach us about beating benchmarks
I do not gamble. Ever. But I cannot resist the mathematics of card counting.
Photo credit: Mark Jordan, http://www.edwardothorp.com/
Was it risky for Edward Thorp to play Blackjack? Thorp of course was a “founding father” of card counting, author of Beat the Dealer and Beat the Market, and pioneered the application of probability theory to hedge fund management. Sure, there was a risk that he did not disguise himself sufficiently well - or act sufficiently inebriated - to deter scrupulous pit bosses. But what financial risk was Thorp taking through a card counting system that yielded a 0.42% edge over the house?
Given our discussion last month about risk, let’s presume my working definition of risk as “the Likelyhood of a permanent loss of capital”. In this sense, Thorp’s risk was determined by his bankroll relative to the variation in outcomes. So long as Thorp had a sufficient bankroll to ensure his solvency through the worst drawdown, his card counting system’s positive expected value and the law of large numbers assured Thorp would beat the casino in the long run. The concept of remaining solvent is known as “Risk of Ruin”, which is the probability that one loses so much capital that they are unable to continue employing that strategy. Yet again, this analysis highlights the difference between volatility and risk.
If you have noticed money managers flaunting their outperformance when they beat the market but move the goalposts to citing “risk-adjusted returns” when they lag the market, you are not alone. The Efficient Frontier is elusive and virtually impossible to identify, even in hindsight. Typical stock picking funds seek to outperform a benchmark index, say the S&P 500 index, through a concentrated portfolio of equities. Sacrificing diversification, managerial hubris, and other risk factors create the losing game that has been playing out for many years now, one whose underperformance is raising an existential crisis among long-short funds in particular.
“Most stock-picking stories, advice and recommendations are completely worthless.”
--Edward Thorp
But what is the alternative? First, managers should understand different forms of uncertainty. Two primary forms of uncertainty are Epistemic and Aleatory, and both markets and Blackjack clearly highlight their differences.
Blackjack is a well-defined game of chance involving primarily Aleatory uncertainty, which is derived from the natural randomness in a process. The game’s rules, payouts, numbers of decks, cards remaining in the shoe, and other parameters enable precise calculations of outcomes, subject to the uncertain randomness of which cards a player is actually dealt. On the other hand, markets primarily have Epistemic uncertainty, which is derived from limited, insufficient, and/or conflicting information. It is this complex web of Epistemic uncertainty, together with managerial hubris, that makes stock-picking a losing game. As Edward Thorp said, “Most stock-picking stories, advice and recommendations are completely worthless.”
Card counting in beating the casino has informed my investment management in beating the S&P 500 index. Card counting to beat casinos can teach investment managers loads about outperforming benchmarks, including that:
“Risk of Ruin” analyses are a viable and superior alternative to traditional long-short strategies for hedging risk.
Managers must know the difference between volatility and risk. Professional card counting has volatility, but with disciplined execution has low risk. Investment management should be the same.
Managers should be adept at parsing out Epistemic versus Aleatory uncertainties in markets. Managers can improve effectiveness by accurately identifying market dynamics in which managerial decision making cannot systematically overcome what are fundamentally unpredictable Aleatory uncertainties.
On the topic of uncertainty, Annie Duke’s book Thinking in Bets: Making Smarter Decisions When You Don’t Have All the Facts is fabulous. Of additional interest is James Owen Weatherall’s The Physics of Wall Street: A Brief History of Predicting the Unpredictable. For further reading on the Blackjack Wars, try A Professional Card Counter's Chronicle Of The Blackjack Wars
Double or Nothing
Now for some real fun. Assume that you are willing to gamble. No counting cards, just playing basic strategy and ceding its 0.5% house edge. What is the optimal strategy to double your money before you go broke?
Henry Tamburin has the answer:
“You stand the best chance of doubling your bankroll by making a minimum number of large-size bets in relation to the size of your bankroll. (Ideally, the best bet is to wager your entire bankroll on one hand, but few blackjack players would want to play that way.)”
With some simplifying assumptions, betting your entire bankroll on one hand essentially gives a 50% - 0.5% (house edge) = 49.5% chance of doubling your money and an attendant 50.5% chance of ruin. Betting less than your entire bankroll actually increases your chance of ruin before doubling. This makes sense because the longer you play a game with a negative expected value, the more Likely you are to attain that average expected loss in the long run. To be clear, the probability of doubling your money before going broke, regardless of your bankroll and unit, will always be less than 50% - the question is just how much less. “Making a minimum number of large-size bets” is your best chance at winning a losing game.
Well then! Last year, in the depths of Greenlight Capital’s underperformance and significant redemptions, David Einhorn announced his plan to turn things around. What was that plan? To make fewer, more concentrated bets - in other words, employing the less-than-50%-but-still-best-chance at winning a losing game. No thanks.
ONE MORE THING…
Yes, Sam Dogen: Always think in Likelyhoods. What missing out on $150,000 in Tesla gains taught him about good investing—‘I feel like an idiot’
No, Sam Dogen: Stock-picking is NOT the only way to beat the S&P 500 index. What missing out on $150,000 in Tesla gains taught him about good investing—‘I feel like an idiot’
“Leaving the party too early can cost you as much as leaving too late”: Always think about disciplined exit strategies. Investors should be wary of Warren Buffett’s crash warning
Cash is King… until it’s not: The flight to cash worked... for 2 months. Tough lesson. A small subset of Vanguard investors moved entirely into cash when the market tumbled. Here’s how they did
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