Card Counting the Market: The Importance of Cash

When Ed Thorpe played blackjack to beat the casinos at their own game, he did it by strategically betting into “good decks” and staying away from bad decks. Can you apply this same idea to investing by investing into good markets, and staying away from bad ones? I believe you can, which is why Geometric Balancing has held more cash than usual this year. Let’s explore.

Blackjack is a Losing Game

On average, blackjack is a losing game. The casino has a small edge, and by edge I mean the gambler has both a negative expected arithmetic and geometric return. But because the remaining cards in the deck change through time, the edge isn’t constant. It changes. And if it changes, could it sometimes be in the player’s favor and not the casinos?

If the edge moves, a gambler could theoretically transform blackjack from a losing game to a winning game simply by betting big when the odds are in your favor, and betting small when they are not.

It’s a similar concept I described in Investing Games, where a gambler can take a game with poor long term returns, shrink their bet size, and convert it to a winning game. The rules outlined in Investing Games still apply, but now the properties of the bet are no longer stable, they change.

Therefore by monitoring the properties of the current game–knowing if you have an edge and how big– you can size your bet properly for the next hand. Then repeat many properly sized games over and over again, and let the law of large numbers converge upon the maximum compound growth rate as time progresses.

This is how Ed Thorpe beat the casinos.

Card Counting

Ed Thorpe understood that your chances of winning a blackjack hand are not static. The odds of winning depend on the cards remaining in the deck. When a deck is full of face cards, and light on lower numbers, the odds improve for the gambler, to the point that they can be favored to win the hand. In the opposite occurrence, when the deck is full of low numbered cards and light on face cards, the odds move strongly in the casino’s favor.

Since the properties of the beginning deck are known (52 cards, one of each number and suit), a gambler can count the number of face cards and low number cards when they are delt, and in doing so, deduce what cards remain in the deck. If early in the game the gambler sees more low number cards than face cards, the gambler knows the odds have moved to their advantage and can therefore confidently bet more.

If instead the gambler sees many face cards and few low number cards, they know that the odds have moved against them and gotten worse. They can confidently reduce their bet size and wait for the deck to be reshuffled.

Applying to Markets

Just as a blackjack deck’s odds change and evolve over time, investing environments change and evolve over time. They aren’t static. Sometimes they are more favorable than others. Therefore, the ideas Thorpe used to size blackjack bets apply to investing markets.

The key is to count the “market’s cards”. You have to monitor the market’s volatility, the market’s, correlation, and the market’s return premium to know when the deck is in your favor and when it isn’t.

Kelly is About Slope

Let’s go back to a post from a couple years ago. “Kelly is all about Slope“. This was one of my most important posts, but before I get into the guts of why, I want to ask a couple questions.

Question One:

The P/E ratio of stocks is 15, equating to an earnings yield of 6.6%. Volatility seems pretty standard around 17% per year. The risk free rate is 2%. Do you invest in stocks?

Question Two:

The P/E ratio of stocks is 20, equating to an earnings yield of 5%. Volatility is a bit elevated around 25% per year. The risk free rate is 4%. Do you invest in stocks?

The first one feels like a good idea. You’re theoretically getting a decent return (4.6%) above the risk free rate. The second one isn’t as comfortable. The earnings yield is only 1% above the risk free rate. And the market is more volatile than normal. If you had to pick, all things being equal, you would take the first every time.

You always prefer a high return/risk slope over a flat one. Get flat enough, and you may start wondering if the risk is worth the modest return.

Efficient Market

There is a version of the efficient market theory which believes all assets should have the same return/risk slope. I’m not fully onboard with the idea, but there is logic to the idea that everything should tend to have a similar risk/return profile.¹ In a perfect world it makes sense.

But does this slope need to be static? Can it move up and down? Just like the count of cards in blackjack changes, can the market’s return/risk change? If it can, then a wise investor should adjust their bet size as it changes: invest more aggressively when the slope is steep and move conservatively or even get out when it flattens out.

Back to Kelly Slope

Ok, so in the post from 2 years ago, I stated that Kelly betting is really about understanding the slope of the geometric frontier.

“So please remember, when you read about partial Kelly investing, its foundation comes from monitoring the risk/return slope of the geometric frontier.

Full Kelly moves along the curve until the slope is flat.

Partially Kelly pushes up the curve until the slope provides the desired risk/return.”

Let’s look at our two questions with this mindset. To keep this simple, I’m going to take the earnings yield (1/PE ratio) as the Geometric Return. I don’t belive it’s the best estimator of the geometric return of the stock market as I discuss here. So I don’t recommend you do this exact method in practice.² But we can still show conceptual relationship using the earnings yield to create our frontier.

Applying the Kelly slope concepts, he proper bet size is determined from the way the geometric frontier slope degrades and flattens out as the bet size increases. Let’s look at our two examples, and then put a geometric frontier on them to see how they bend. Following the concepts from the post on Kelly and slope, we will focus on a half Kelly point as our theoretical target return/risk investing point.

Steep Slope

The return/risk in the first example is pretty good. Reaching the peak of the curve in this example requires leverage, and plenty of it. Even half Kelly calls for a bit of leverage. If you were running a strategy that doesn’t use leverage, you would still invest fully.

The slope of this chart is steep. The market is paying you well to take the risk. Our goal of half Kelly tells us to go ahead and invest fully.

Flat Slope

But look at the second one. The peak of the curve is much further to the left. It’s so far left, it tells us to hold some cash to simply maximize growth! Not a good sign.

However, we are targeting half Kelly not the peak. And that point sits at only 33% stocks and 67% cash. This portfolio is much more conservative.

The second example has a flat return/risk slope, causing for a low and left Kelly peak, and therefore a very low and very left half Kelly investment point.

Card Counting the Market

You can see one market is much more favorable than the other. In the first market, our half Kelly rule says to invest fully. This deck is full of face cards.

But in the second, our half Kelly rule says to put 2/3rds of our portfolio in cash and wait. This deck is full of low numbers.

This is how you “count cards” in the market.

Focus on the slope of the geometric frontier, and let it tell you when to use cash to “sit out” a bad market and when to invest fully in a good market.

Correlation with Today

So what does this mean for today’s investing environment? Well, the Fed has been jacking up rates aggressively. It’s crazy to think that we are over 4% today and we started the year at 0%. The PE ratio is about 20. The second example matches today’s environment for stocks.³

Now when stocks get in this position, diversification from bonds and gold often means the total portfolio volatility is lower, making the return/risk slope higher. However, right now all three are quite correlated. There isn’t much diversification benefit going on. And volatility in all assets is a bit elevated.

Even our portfolio return/risk ratio right now isn’t great. It’s not a good deck.

This is why Geometric Balancing is Holding Cash

This is essentially the reason the portfolio has held at least some cash for much of the year. Rates have come well off of zero. Yet the PE ratio and earnings yields have stayed fairly stable. Gold and bonds are correlated with stocks. Once the Fed started raising rates, the slope of our geometric frontier started flattening. The return/risk ratio got worse.

Therefore, Geometric Balancing moved to hold a bit of cash. It’s averaged 28% cash this year. Not as much as I wished it had in hindsight, but more cash than typical.

And today with the Fed having raised rates over 4% and the market rallying in October and November–reducing the earnings yield–the return premium on stocks is so small, and the slope of the geometric frontier so flat, that cash becomes a meaningful part of a balanced portfolio. ⁴

How Does the Market Correct This Imbalance?

I don’t think this investing environment is sustainable. The market isn’t providing enough return for the level of risk. So how does this environment “correct” itself?

Well, if volatility goes down, that will help steepen the slope. If correlations release and stocks/bonds/gold start to act uncorrelated–or better yet negatively correlated–it will help even more.

But absent those moves, only a widening of the spread between the risk free rate and the earnings yield will cause Geometric Balancing to move out of cash. The return premium has to grow. Either interest rates have to fall, or stock’s earning yield needs to go up.

I don’t see the Fed dropping rates in the near term since they are still fighting inflation. Which means stock’s earnings yield needs to rise. How does that happen?

Earnings could go up. But many think we are entering a recession. This doesn’t seem likely.

So that only leaves one thing: prices have to go down.

Will prices fall? I don’t know. As I just said, there are other ways to fix the imbalance. But falling prices are definitely one way the market can bring the return/risk relationship back to typical levels.

You Can Wait Until The Deck Gets Reshuffled

If you work into a bad deck in blackjack, you should bet the table minimum and wait it out (or even walk away from the table). The deck is going to get reshuffled soon. The odds will come back into your favor. When they do you can bet big again. But you don’t have to bet big with a bad deck.

You don’t have to play every round. You’re allowed to play only when the odds are in your favor.

Investing markets are no different. If the return/risk ratio is poor–if the slope of the geometric frontier is flat–you can bet less and wait for the environment to improve and hold more cash. The market will get reshuffled soon enough. When it does, you can invest aggressively again.⁵

Footnote:

1-This is where the concept of building a risk parity portfolio using inverse variance construction comes from.

2-In other posts I’ve talk about the PE ratio being the average PE ratio of an individual stock. Therefore, the total return of the market should be the earnings yield + half the variance of an individual stock, which is about an additional 4%. Therefore, my analysis above is overly conservative. But I’m not trying to teach the method here I’m trying to teach the concept of why and when you would introduce cash into the portfolio. This post and others on the blog describe the math of actually implementing these ideas.

3-I keep referencing stocks because they are typically the largest part of the portfolio. Bonds can drive the same kind of behavior. Today, since the bond yield curve is flat, the premium in long term bonds over short term bonds isn’t very high. This creates a similar effect, where you question the logic of owning long term bonds if they aren’t providing negative correlation and they aren’t providing any meaningful premium over short term rates.

4-This is a reference to this blog’s portfolio specifically and it’s own goals specifically. Other portfolios may have better diversification properties and not need cash in this market.

5-It is very difficult to predict future returns. This post isn’t trying to get you do that. What I’m hoping you do is think about the relationships between investment return, volatility, and the risk free rate, how they relate to each other, and how changes in each should affect your portfolio. When the risk free rate changes notably, as it did this year by rising 4%, ask yourself if the returns of your assets also increased by an equivalent amount. If the answer is no then you should think about scaling back. The inverse is also true. If the risk free rate falls, ask yourself if your investment’s expected returns have fallen as well. If the answer is no, then maybe the environment is good and you should think about being more aggressive.