Stock Warrants | Edward Thorp’s 20% Annual Return For 30 Years



Edward Thorp is the bestselling author of Beat the Dealer. He revolutionized gambling as he proved how to beat blackjack with card-counting and invented the first wearable computer. As Thorp transitioned out of gambling, he then achieved the unthinkable with 20% annual returns over 30 years trading options. Below is an edited summary of his interview with The Investor’s Podcast where Thorp discusses probabilities and his storied investing career.

Preston Pysh: [6:09] I am curious to know how you came up with the idea to beat the odds of blackjack when everyone else believed that it could never be done.

Edward Thorp: By solving equations, it is possible to calculate the precise probabilities of losing, given any collection of cards for any number of decks. To calculate these probabilities, I first had a computer take out four aces from a full deck, and I discovered that the deck shifted in favor of the casino by quite a lot. This was good news because if I put back in four aces, I knew the exact opposite would happen and the cards would now be in my favor. I repeated this process with all ranks of the deck. When the deck is filled with big cards, it becomes in favor of the player. On the contrary, when the deck is filled with small cards, it shifts the edge in favor of the casino. Therefore, players want small cards to come out of the deck. I developed many card counting systems and spent the next year executing these systems. I started with hand calculations, which did not get me very far, and then I went to teach at MIT. There I had access to a high-speed computer. I spent almost a year teaching myself how to program and running subroutines that I would later piece together into a program that would evaluate how the missing cards affected the game of blackjack.

Pysh: [8:23] Do you think you could have solved the mathematics without the computer?

Thorp: At the time, I thought I had to make exact calculations. However, as I learned more about the game, I realized that you could make approximations that would still result in decent solutions. I probably could have reached those approximate solutions by hand.

Pysh: [8:57] With respect to probabilities, there are similarities between gambling and investing. How can you use the Kelly criterion in the stock market given a large array of potential outcomes and holding periods?

Thorp: The root idea of the Kelly criterion is that there is a tradeoff between risk and return. The big question is, what is the tradeoff? Let us look at a very simple scenario: tossing a biased coin with probabilities of 60% chance of landing on heads and 40% landing on tails. Clearly, you are betting on heads, but how much should you bet on heads? The Kelly criterion is the solution. In the coin tossing case — suppose the payoff is even — the criterion would suggest betting 20% of your bankroll on heads. This can be scary because of the large variability. If you only bet half as much as the suggestion, you end up growing it only three-quarters but your risk is reduced by half. So I generally recommend people to bet half of Kelly so they are less scared.

Pysh: [11:30] Is there a rule of thumb you use when conducting this math?

Thorp: The math of the Kelly criterion is fairly involved in real-world situations with many possible uncertainties. Mathematicians have solved a lot of these problems explicitly. The best compendium of information is The Kelly Capital Growth Investment Criterion. I would recommend this to those who want to learn more about this mathematically. Another thing I want to say about the Kelly criterion is that it has a world-scale applicability. If we observe various bubbles and disasters we have faced over the last century, most of them have occurred because there was too much leverage. From the frame of the Kelly criterion, this means that you are betting too much. The theory of the criterion suggests that if you bet too much consistently, you will be ruined. People were buying stocks at the 10% margin during the crash of 1929. Using portfolio insurance levered portfolios in very curious ways during the crash of 1987. During the long-term capital management disaster of 1998, they were levering at 30 to 1, sometimes even 100 to 1. The recent disaster of 2008 shows banks were levered up by 33 to 1; as for the banks that received this privilege, two of them are gone and one had to be bailed out by taxpayers. The Kelly criterion applies not only to individual investors but it also applies to nations.

Pysh: [11:50] How do you see the market today? Considering that we may be at the top of the credit cycle, how do you think through position sizes and what are your expectations?

Thorp: I think it might have been J. P. Morgan that asked me if he should sell because how high the market is. The advice I gave was this: sell down to the sleeping point. As far as asset classes go, it is hard to know when you are in a bubble, and if you are in one, when it will pop. You never know when it is exactly going to pop but you know it will at some point. Right now, we have an attack on regulations that are reining in the banks from levering up and the derivatives industry from taking too much risk. The more the regulations are removed, the more chance we have at a rerun of 2008. Last time, the taxpayers bailed almost everyone, and we will probably have to depend on that again. Heads, the risk takers win, and tails, the public loses.

Pysh: [17:45] One of the narratives we hear a lot of very intelligent people talk about is the idea that the next financial event will be induced by central bankers and the distrust of central banking. Do you personally see the next cycle being induced by central banks?

Thorp: I do not know the answer to that.

Pysh: [18:55] I love that response, that is something I can learn a lot from. I immediately thought about how Warren Buffett often says to have a strong understanding of what you know versus what you do not know.

Thorp: Well, I read a good book recently, Superforecasting by Dan Gardner and Philip Tetlock. They wanted to see whether people can forecast better than chance. What they found is that experts often do not have much to tell us things of value. Experts receive a lot of media attention because they make strong, definite claims. But definitive claims are usually not accurate predictions; we can only see the future fuzzily. People that tend to weigh different possibilities can make somewhat better predictions than chance. On most things, we can speculate about a lot of possibilities. But it is difficult to get enough of an edge to actually make a bet and expect to make a profit. Regardless, it is still worth speculating because you can be ready psychologically.

Stig Brodersen: [21:48] You were successful in the blackjack scene, but you also have had an annual return of 20% for 30 years. Could you talk about your career transition?

Thorp: I became interested in investing because I had made some money through gambling and royalties. This meant that for the first time in my life, I had enough money in savings. After doing poorly in my early investments, I was determined to take it more seriously. By chance, I got a book called Common Stock Purchase Warrants As soon as I read about them, I realized that I could get rid of almost all risk in investing and still get some return if those loans were priced incorrectly. In a telephone market, there was every reason to believe that they were not priced correctly quite often. That summer, I met a professor at UC Irvine who wrote a thesis about common stock purchase warrants. We hit it off on our ideas, and we decided to meet every week to improve the theory as well as his investment returns. We made about 20 to 25% a year. The dean of the graduate admission had become one of the investors, and he introduced me to Warren Buffett. I saw that Buffett was very intelligent and dedicated. He really understands long-term compounding. I learned from Buffett that a more official way to operate was to have a limited partnership, so I set up the first quantitative market neutral hedge fund.

Brodersen: [26:03] Why do you think that the majority should invest in exchange traded funds instead of buying individual securities?

Thorp: I found that situations can give you extra returns, but they require work and timing. Simply reduced, there are three groups of investors. The first group of investors are those who do not want to do a lot of work who should invest in indexes. Index investors do better than maybe 90% of all other investors who are busy paying fees to advisors. The second group are those who would like to learn more about securities. They are entertained by following and analyzing securities. I think they can learn about special, unusual things although there is a price for that education. The last group are those who make the money in the market. They tend to have large staffs and capital resources. They charge fees to other people and by doing so make the most profits. With that in mind, do not expect as a small investor to make a lot of money in the market.

Pysh: [28:09] What is a book that has influenced your life the most?

Thorp: The first book that really influenced me in a quantitative way was The Random Character of Stock Market Prices by Paul Cootner. It was one of the first collections of quantitative papers about the market. An early warrant model in the book enabled me to figure out the option formula.

Pysh: [29:48] When I saw a picture of you at the back of your book, I thought you looked about 55, which was odd because I knew you were very active during the 60s. I could not believe it when I read that you are 84 years old in your bio. What is your secret for longevity?

Thorp: I held a poll of strangers where I asked them what they thought my age was. I offered to pay them $1 if they came close and $5 if they came within 5 years of my actual age. The average guess was about 55 to 60, and the highest guess has been 72. Exercise is really important to me. I ran marathons for about 20 years. Now I do a lot of walking and working out with a trainer at the gym. I watch my diet as I try to eat healthily and in moderation. I never smoked and I never played football to avoid concussions. Another tip is to get medical testing regularly to prevent and treat problems earlier.

Preston Pysh is the host of the business podcast, We Study Billionaires.  The show studies the books billionaires read and attribute to their success.

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