Sponsor (20:25)

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Kyle Grieve (22:25)

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That's V A N T A dot com billionaires for $1,000 off. All right, back to the show. The next person I want to chat about in this book is Thomas Base. Now, you may have heard us speaking of Bayes Theorem on the podcast before, as it's just a central tenet in using probability in investing terms. Now, in Bayes Essays in Philosophical Transactions, he mentioned a problem that he was trying to solve. Determine the probability that an unknown event's likelihood of occurring in a single trial falls between any two specified probability values given the number of times it has happened and failed. Bernstein points out that the primary application of the Bayesian system is the ability to utilize new information to revise probabilities based on old information. Let's circle this back to investing. So I mentioned earlier in this Episode that I like to look at a bear base and bull probabilities on my investments to try and incorporate risk into my evaluation and my decision making. Bayes Theorem takes it one step further and allows us to revise our numbers when the information changes. John Maynard Keynes once said, when the facts change, I change my mind. And this is exactly what Bayes Theorem does, but in mathematical terms. Now let's say I apply a 33% probability to my bear case, my base case and my bull case. Lets just say something bad happens with the business that I applied these probabilities to. There's a business right now, for instance, where gross profit margins have been compressing down from 50% about a year ago to about 30% today. Management has noted that the normalized range is likely to be in the middle of these two numbers. Now when I update my numbers, knowing this new information, I might increase the probability of my bear case and decrease the probability of my bull case. Maybe I move the bear case to 40% probability, keep the base case at about 33% and reduce the bull case to 26%. Obviously this is inexact as it's hard to quantify precisely how likely a lousy outcome is. But I think this is more useful than just doing nothing. I know one of my personal problems in investing was holding onto ideas for too long. If I had focused more on using Bayes Theorem, I think I might have realized that the bear case was becoming more and more likely and I would have been able to let go of an idea faster and therefore lose less money. Now all investors should attempt to think probabilistically about their businesses during bull markets. It's just incredibly easy to forget the potential downside of businesses that you own. You'll often see investors giving the rosiest possible forecast on businesses, forgetting the base rates for businesses were much lower. Now it's important to remember that even the best businesses go through some degree of cyclicality. So modeling for the best possible numbers when you're at the top of a cycle is only going to be a disservice to you once the cycle turns. This is why having conservative forward numbers is such an intelligent strategy. It builds in an extra safety net and any surprise to the upside is obviously going to be very welcome. It's easy when looking at a new business to assume only the best case scenario is the one that's going to play out. Nobel Laureate Kenneth Arrow said, our knowledge of the way things work in society or in nature comes trailing clouds of vagueness. Vast ills have followed a Belief in certainty and when investor certainty is at the highest is usually a period where vast ills is likely in the very near future. Now let's discuss Carl Friedrich Goss and Francis Galton. First, Gauss Gass's brilliance came in a pretty unlikely form. He was tasked with conducting a geodesic survey of Bavaria. Now the geodesic measurements were used to estimate distances between sample areas in the study. As Gauss analyzed the distribution of these estimates, he found that the results varied. But as he collected more and more data, got more and more data points, the numbers seemed to cluster around a central point. Bernstein writes that central point was the mean statistical language for the average of all observations. The observation also distributed themselves into a symmetrical array on either side of the mean. The more measurements Gauss took, the clearer the picture became and the more it resembled a bell curve that a gentleman named Demouavois had come up with 83 years earlier. Now the primary use case I've seen for Goss's distributions are in average returns. You may have come across the graph that shows the average returns over a variety of time periods. So that graph will display that during short time periods, if we use Goss's example, the numbers cluster a lot less. And as anyone in the stock market knows, the short term is a bit of a dart throw. And so because those clusters are a lot less, there's a lot more volatility and there's a lot more potential outcomes. So the chances of you being up 20% are about the same as you say being down 20%. But then when we look at shorter time periods, such as a ten year time period, the data begins clustering towards making more and more money. If we look at that chart that I just discussed, over a 10 year period, our range of outcomes is essentially always profitable and in the positive 8 to 9% range. Now another brilliant scientist, Francis Galton, who was also Charles Darwin's cousin, continued on with Goss's theories about distribution. Galton suggested two conditions are necessary for observations to be distributed around their average. First, there must be a large number of observations and second, the observations must be independent. Now the point here about independent observations is very important. Bernstein gives a great example of this magazine that sent out returnable ballots in the form of postcards to name selected from both telephone directories and automobile registrations in 1936. Now they essentially were asking who was going to win the election. So 59% of the ballot favored Landon, while only 41% favor Roosevelt. When the real ballots came in, Roosevelt won with 61% of the votes compared to only 39% for Landon. And the point here was that the recipients of the postcards were not independent enough to represent an independent observation, and therefore it was invalid. Now, Galton was interested in distribution, not just in the sense of furthering science, but also for practical purposes. He wanted to find out how many people in a sample size could achieve eminence, and this led to his findings on peapods. He analyzed thousands of peapods, specifically looking at the size of the parent seeds and the size of their offspring. What he found out was that small parents generally had larger offspring and the larger parents generally had smaller offspring. As a result, regression to the mean was born, Galton wrote. Regression to the mean or reversion is the tendency of the ideal mean filial type version to depart from the parental type, reverting to what may be roughly and perhaps fairly described as the average ancestral type. Bernstein added that if this narrowing process didn't exist, nature would become freakier, with each generation creating dwarfs and giants with nothing in between. My favorite example of regression is looking at a business's returns on invested capital. Michael Mauboussin has done tons of research in this area and really no matter the industry, as time goes by, the returns on invested capital decreases over time, in a business sense, it's pretty easy to see why, right? As more capital is added to the industry, competition then goes up. And since many businesses have fixed costs, as the industry becomes more competitive and products become more commoditized, the only way to differentiate yourself from competitors is to decrease pricing. And over time, if you decrease pricing while capital costs remain the same, your returns on invested capital will eventually decrease. This is also important to think about when looking at investors single year track records. A good year just doesn't say that much about an investor's level of talent. They may have one stock pick that produced outsized rewards during one specific year. It's only when you zoom out and look at a multi year time period that an asset manager's talents becomes more visible. This is why most managers with multi decade track records tend to hug the results of the index over time. There are some outliers, but most of them will be around average or even below average as well. In any one year they may be much better or worse than the index, but it's important not to get swept up by the short term. Bernstein gives another excellent example of regression in the mean. Economists Richard thaler and Werner DeBont did a study lasting between 1926 and 1982 where they studied three year returns of over 1000 stocks. Now each of these stocks was classified. Winners were classified as stocks that had gone up or had fallen less than the market average in each three year period. Losers went up less or fell more than the market average. Then they just calculated the performance of each class over the last half century. Loser portfolios outperformed the market by on average 19.6% 36 months after portfolio formation. Winter portfolios, on the other hand, produce returns about 5% less than the market. If an investor were inclined to hire a manager to manage their money, this means the logical step would be to look for a manager that currently has a short term losing track record. Now this is extremely counterintuitive. Believe me, I understand. But this is why so few investors do it. I could maybe see myself doing it if I had someone that I wanted to invest in, if they had a very, you know, long term track record of beating the market. But maybe over the short term we're going over some turmoil. Now A great example of this would be Scott Barbee, who I got the chance to interview back on tip 651. Scott's fund, the Ages Value Fund, had beaten the market for a good amount of time, well over a decade. But during the great financial crisis, his fund decreased by 72% over a two year period. In terms of understanding intrinsic value, Scott was unfazed. He knew his businesses simply had gotten very cheap, they had not decreased in value. Then in one of the best examples of regression to the mean that I've ever seen, he returned 91% in 2009 and made it onto the COVID of the Wall Street Journal. Scott told me that he didn't really do anything special to earn that 91%. He simply held onto his shares. And once the selling stopped and capital eventually came back into the market, they bought his highly undervalued stocks and they rerated them higher. Now I'll end this discussion on reversion to the mean with a very thought provoking statement that Bernstein wrote. Dependence on reversion to the mean for forecasting the future tends to be perilous when the market itself is in flux. Now the next area I want to touch on is luck, which plays a massive role in decision making and what I view as even more important than decision making, which is process and outcome. Bernstein makes some crucial notes in his books about luck and cause and effect. Many intelligent mathematicians and the characters that we've covered believe in cause and effect. But how do we face issues that arise that don't have one cause for the effect, October 1987 is a great example that Bernstein gives. In that month, the market fell more than 20%. Bernstein adds, There is no agreement on what caused it, though theories abound. It could have occurred without a cause, and yet that cause is obscure. Despite its extraordinary character, no one could come up with strong proofs of its origin. Now, my thoughts on luck have evolved over time, and I now settle on the fact that I will have lucky and unlucky decisions. There's no way to be lucky all the time. If that were possible, we could subscribe to the cause and effect theories in investing and decision making. But we do not have that luxury. And since investing is such a problematic puzzle full of information gaps that we will always have, the best we can do is just to play the odds. And this is why investing is so difficult. Let's say I make a decision to buy a stock. Let's use one I bought in the past but no longer own, which is bank ozk. I bought this in 2020 at around $23 and sold it about a year later at $47. When I first purchased the shares of the business, I believed they were undervalued. There was a short report out, and when you mix that with COVID and the fact that they financed real estate, there was a lot of uncertainty surrounding the business. But I decided to buy it, thinking the returns would be somewhere around my hurdle rates. Nowhere did I theorize that I would double my money in a year. The fact that happened was luck. But I think that luck was built upon decent decision making, that the business would get better over some period of time. Earnings per share EPS had been depressed in 2020, dropping from about $3.30 in 2019 to $2.30 in 2020. That would likely mean that there would be some regression to the mean as Covid fears went away and the business could release some of its provisions for credit losses back into the income statement. And that itself provided a massive boost in 2021 with EPS going all the way back up to $4.50. Now the point here is that luck will have an impact on all of our decisions. It's essential to accept that sometimes it will be in our favor, and unfortunately, sometimes it will not be. The best we can do is to look at our prior decision making and try to make adjustments for future decision making. This reminds me of what Charlie Munger said about good versus bad businesses. The difference between a good business and a bad business is that a good business throws up one easy decision after another. The bad business throws up painful decisions time after time. Now, this relates to luck because I think good businesses also have more exposure to being lucky than a lousy business does. I prefer to take part in those businesses who create potential tailwinds over businesses that expose themselves to headwinds. Now, let's transition to some of the more modern areas of risk that are still in use today. For that, we're going to start by covering two brilliant economists. They are Frank Knight and John Maynard Keynes. Now, Frank Knight began picking away at utility theory, stating that humans default to acting irrationally. He said there is much question as to how far the world is intelligible at all. It is only in the very special and crucial cases that anything like a mathematical study can be made. Frank Knight believed that the real world had too many surprises and impacted future decision making to a very large extent. In a business sense, you have to look at all the parties involved, such as buyers, sellers, workers and capitalists. These people will never have all the information they need to make perfect decisions. Frank Knight believed that classical economics didn't take this uncertainty into account and therefore made it less applicable to real life. Now, John Maynard Keynes also had issues with the classical methods to measure decision making. He said, most of our decisions to do something positive can only be taken as a result of animal spirits and not as the outcome of a weighted average of quantitative benefit multiplied by quantitative probabilities. Now, this concept of animal spirits is essential because it altered people, like Galton's peapod analogy. Now, while Keynes agreed with his theory on pea pods in nature, he disagreed with it being relevant to human beings. For instance, he rejected analysis based on events, choosing to make predictions based on propositions. Additionally, he was scornful of the rules of large numbers. Just because a large amount of prior events happened in the past didn't mean they would continue happening in the future. This was an incredibly powerful notion. Keynes points were that all mathematical concepts on decision making were less valuable because events changed all the time that would alter human decision making. Bernstein points out that Keynes preferred to think in degrees of belief. This also allowed Keynes to change his belief system based on events. If a new event happened, then his degrees of belief would change based on that event. Now, before World War II, Keynes said, the characteristics assumed by the classical theory happen not to be those of the economic society in which we actually live, with the result that its teaching is misleading and disastrous if we attempt to apply it to the facts of experience. Now, building on Knight and Kane's importance of uncertainty, came game theory. Game Theory states that the true source of uncertainty lies in the intentions of others. John von Neumann, a brilliant scientist who had his hands in multiple scientific discoveries, invented game theory. Now, he first discussed game theory in one of his papers, where he discusses a childhood game that he called Match Penny. So here's how it worked. It had two players. Each of these players would have a coin that was either heads or tails, and they would put it down on the table however they wanted. They weren't flipping it or anything. It wasn't by chance. Now, both the players would then turn their hands up and display their coin to the other at the exact same time. If both the coins were heads, or if both of them were tails, then player A wins. And if different sides showed up, then player B would win. Now, where game theory comes into play is what side of the coins each player decides to play. Von Neumann concluded that the trick in playing Match Penny lies not in trying to guess the intentions of the opponent, so much as in not revealing your own intentions. So if one player, let's say, decides to play heads every single time, then his opponent is eventually going to figure that out and adjust. Both players would eventually adjust to randomly playing heads and tails at random sequences, and each player is going to win approximately 50% of the time. Now, the mathematical contribution that von Neumann made was that the outcome was a product of rational decision making by the players and not probability. It is the player themselves who caused the 5050 payoff in this game. Now, one of the most fascinating developments of this theory was what became known as the Nash equilibrium. The Nash equilibrium is a situation in a game where no player wants to change their strategy because they are already making the best possible choice given what others are doing. If you've seen the graph of how capital efficiency reduces over time for a given industry, I think that is a great example of Nash equilibrium. In other words, it can adjust. As more capital enters an industry, more capital needs to be spent to capture small market share over time. This means the entire industry suffers. Eventually, it becomes uneconomic for new entrants into the market, and it reaches a Nash equilibrium where the whole sector barely makes a profit. Let's take a quick break and hear from today's sponsors.

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Kyle Grieve (44:10)

All right, back to the show. Now we're at a point in against the Gods where we're going to start talking about a lot of theories that are still very deeply embedded into the investing industry today. Let's start with Harry Markowitz, who's the grandfather of portfolio management theory. His most significant premise was that most investors desire returns that minimize variance. For him, risk and variance were the exact same thing. His aim was to construct portfolios that had low variance because that was what he assumed most investors wanted. Now, I haven't spent too much time studying portfolio management theory, which I'll call pmt, because people like Buffett and Munger always said you're probably better off ignoring it, and I think you'll do just fine. But over the course of my education as an investor, you can't help but pick up a few things. So first off, I think I'm going to give Markowitz some credit here because I think he was actually right that most investors would prefer returns that are less volatile. The problem is that the market is so volatile anyways that even if your portfolio were constructed to have minimal variance with the market, you'll still end up making all the classic investor blunders because the market itself has a lot of variance from year to year. Another one of Markowitz's theories was that he rejected John Burr Williams premise that investing is a process focused on identifying the best possible investment at the best price. Instead of that, Markowitz thought that investors should diversify in their investments because diversification was simply the best weapon against the variation of return. Again, he was onto something here. Most investors are best with widely diversified investments. It protects them from losing too much on one investment, and it allows them to reap the rewards of a few outsized winners. But you have to remember that the average person finds reading a 10k to be about as attractive as shoveling their walkway to take out the trash. It's just not something they want to do or derive enjoyment out of. But for the few people who do enjoy doing things like this, like myself and probably our listeners, diversification can be seen as a handicap to getting better results. Robert Hagstrom pointed out in the Warren Buffett Portfolio that random portfolios with fewer positions had a better chance to both outperform and underperform the market. So for investors who have an edge in picking great businesses or investing in great investing opportunities, there are advantages to making more considerable concentrated investments. Another problem with Markowitz's theories is in understanding what you own. The average person Let alone a professional money manager cannot possibly understand 100 plus businesses at a very deep level. This is why Buffett said portfolio concentration may well decrease risk if it raises, as it should, both the intensity with which an investor thinks about a business and the comfort level he must feel with its economic characteristics before buying into it. And as Tobias Carlisle pointed out in his book Concentrated Investing, some of the best investing legends have come to the same conclusion about concentration with Warren Buffett, Charlie Munger and Seth Klarman preferring, say, 10 to 15 positions. Tobias also points out that research from Patrick O'Shaughnessy found that about 25 positions offered the best volatility adjusted returns. Now, the last point I'd like to make on Markowitz was that his theories always feel so academic to me. You know, while much of investing definitely does rely on academic theories, I think a lot of successful investing also relies just simply on common sense. And that is the ingredient that seems to be missing in some of Markowitz's theories. And let's go over an example here. Let's say I'm offered two different portfolios. One has high variance, but on average earns 50% per year. The other has low variance but on average earns 10% per year. According to MPT, I should take the second portfolio, but personally I don't care about variance. And I'd instantly choose the high variance portfolio with a better long term return. Another theory in conjunction with Markowitz's theories on the market was created by Bill Sharp. And this was called the Capital Asset Pricing Model, or capm, which used the term beta to describe the average volatility of individual stocks or other assets relative to the market as a whole over some specific period of time. So that you know what beta means in reality. Let's say a portfolio has a beta of 1.5. It means that when the index goes up 1%, it goes up 1.5%. And let's say the market falls 10%, it would go down 15%. The goal was to have a low beta stock so that your results wouldn't defer much from the index. Now let's take the same example I just gave. But instead of a portfolio, I now look at a single stock. Let's say I'm offered stock A or stock B. A has a beta of 1.5 and B has a beta of 1. I think A will return 14% in the next five years, and I think B will return 9% over the next five years. Now, modern portfolio theory would have me choose a lower beta position to put into my portfolio, even though I prefer the higher returns with the accompanying roller coaster ride on the higher variance option. Now, for investors with specific risk appetites, MPT is simply nonsensical. I also think MPT plays into what Buffett and Munger used to call helpers who are paid by other companies to provide help, when in reality they're just collecting fees for providing very little help to zero or negative value. In some cases, when you can slap on numbers and terms like beta, you simply just look smarter and have more pages that you can write reports on to sell to potential customers. But it doesn't necessarily help anyone other than the helpers themselves. Now I'm super excited here to discuss the next topic of the book, which is based around prospect theory and many of the remarkable findings that Amos Tversky and Daniel Kahneman discovered Together, their work layered on Markowitz's work. So Peter Bernstein named the chapter the Failure of Invariance. Bernstein writes the classical models of rationality, the model on which game theory and most of Markowitz's concepts are based, specifies how people should make decisions in the face of risk and what the world would look like if people did in fact behave as specified. Extensive research and experimentation, however, reveal that departures from the model occur more frequently than most of us would admit. This is where Kahneman and Tversky came in. They wanted to understand how people manage risk and uncertainty in real life, and not just in terms of how utility theory stated, which assumed that people should act a certain way. Prospect theory discovered specific behavior patterns that hadn't been recognized by proponents of rational decision making. They noted two significant shortcomings in human behavior. 1 emotions destroy self control that is necessary for rational behavior, and 2 people tend to be unable to understand what they're dealing with, or in other words, they succumb to all sorts of cognitive biases. Now, one of the most significant discoveries of prospect theory is the asymmetry between decisions involving gains versus decisions involving losses. For instance, when discussing larger sums of money, people will reject a fair gamble in favor of a certain gain. For example, a certain gain of $100,000 is preferable to a 5050 possibility of winning 200k versus winning 0, but the expected value of each scenario is the same it's $100,000. If we look at another example, they gave people options again with smaller sums of money. Here. This time they were offered an 80% chance to win $4,000 or 20% chance to win zero. Or they could make a certain gain of $3,000. In this case they took the $3,000, even though the expected value of the former option is actually $3,200. And this means that a rational person would take the first option. But 80% of subjects chose the certain things. We are risk averse, but how do we act when our choice involves losses? In a follow up experiment, they offered a choice between taking the risk of an 80% chance of losing $4,000 and a 20% chance of breaking even versus a 100% chance of losing $3,000. Now, 92% of respondents chose the gamble even though its mathematical expectation of a loss of 3200 was once again larger than the certain loss of 3000. So this shows us that when the choice involves losses, we are actually risk seekers, not risk averse. Now let's loop this into investing and see how this plays out in real life. Risk aversion is rife in the stock market, especially with how investors treat gains. Remember, when we are dealing with larger sums of money, we become more risk averse. This means that when we have a position that goes up in price, we become more and more likely to sell our position and lock in a profit. The problem with doing that consistently is that you miss many of the large run ups in businesses that can continue growing for long periods of time, which are often much longer than investors believe they can grow for. So even if we lock in our gains, we are now ignoring the fact that there is a chance that we could make more in the future. Of course, we could also be wrong on the idea and we could risk it going below our purchase price or worst case scenario is going to zero. Now if we look at risk seeking with losses, you see this all the time as well. So I had these businesses that were all in the red, but I continued holding them hoping that someday they would rebound. Then I eventually just cut ties with the three of them. And since then the capital has been put to other use. But I can admit that I held them hoping to recoup some of my losses. And this is the same as the experiment above, where we become risk seeking when faced with the potential of a certain loss. I simply could have cut my losses sooner and have lost less money. Another problem that is rife in the value investing community regarding losses and risk seeking is adjacent to the example above, which is adding to our losers or, you know, averaging down. Now I did this on one of the businesses in the bucket that I mentioned, which was Alibaba. Now averaging down is a fantastic opportunity, if you're correct, that the business will once again pick up and that the market will once again assign it a reasonable multiple. Now, I'm just speaking from my own experiences here, as I'm sure there's tons of people who have opposite experiences to me, but I've rarely had a positive experience when I averaged down. Averaging up has actually been much more lucrative for me. Now, this goes a little bit outside the realm of prospect theory, so I won't go into any more detail, but needless to say, I much prefer averaging up. I mentioned earlier that there was a chapter in Bernstein's book titled the Failure of Invariance, but what exactly is the failure of Invariance? In this episode, we're exploring one of the most fascinating concepts in investing, which is risk. We'll unpack how humanity's understanding of risk has evolved over centuries, and why improving our knowledge of it is key to becoming a better investor. We'll rewind to the earliest forms of gambling, dice games played with bones in ancient Egypt. And we'll trace how humanity began quantifying uncertainty. We'll explore how thinkers like Fibonacci, Pascal and Fermat laid the groundwork for probability theory, helping us shift from relying purely on luck to calculating odds. You'll also learn how gamblers like Girolamo Cardano, who learned the hard way about the dangers of chance, helped shape ideas foundational to modern investing. But investing isn't just about the quantitative it's about psychology, too. We'll explore how risk is deeply intertwined with human behavior and psychology. You'll hear how thinkers like Daniel Bernoulli taught us that managing risk requires understanding not just the odds, but human motivation, like how our perception of gains and losses shift as our wealth changes. And of course, we're going to connect these ideas to investing. You'll hear why Charlie Munger believes most academic models fall short because they fail to capture the real world complexities of the markets. We'll learn about Munger's approach to risk and his appreciation of Pascal and Fermat's work. You'll also hear how probability theory applies directly to your investment decisions, from building bear base and bull cases to assessing the odds of different outcomes. Plus, we'll explore how risk management changes over your investing lifetime. I'll share how my approach to risk has evolved. Why, you know, in my 30s now I'm chasing specific hurdle rates, but how I expect that strategy to probably shift as I focus more on wealth preservation, as I get older and accumulate more wealth. We'll break down the powerful insights from prospect theory, which was a concept pioneered by Daniel Kahneman and Amos Tversky, which expanded heavily on utility theory. Prospect theory reveals things such as how investors often feel the pain of losses far more intensely than the joy of equivalent gains, what's known as loss aversion. We'll discuss how this impacts everything from selling our winners too early to holding on to losers for too long. Understanding this area of prospect theory is crucial for managing emotions during market swings and just making more rational decisions under uncertainty. Lastly, we'll circle all this around with practical lessons on why risk is just really about survival. Peter Bernstein argued that avoiding financial ruin is the most crucial investment rule. We'll talk about why investors who survive the longest, not just those who win the biggest bets, tend to end up ahead, and I'll provide some valuable tips to help you tilt the odds in your favor. Now, this episode isn't just about removing risk, as that's impossible to do anyways. It's about understanding it. It's about knowing when to bet big and when to fold, when to embrace uncertainty, and how to hedge against it. By the end, you'll have a clear understanding of how to use the tools of probability, Bayes theorem, and prospect theory to become a better investor. Now, without further ado, let's get right into this week's episode. The failure of invariance is pretty similar to mental accounting, where we change our decisions based on how the question is framed. Let's imagine that you're buying a jacket and let's say that this jacket usually costs 100 bucks. Now you find out that there's a store that's five minutes away from the one that you saw at $100 and that they're selling it for $75, a $25 discount. Most people are happily going to take the five minutes and enjoy the $25 discount. But now let's take another situation. So now let's say we're at some store and there's a laptop that we want. It's $2,000. You then hear that the same laptop is available for $1,975 in a store, once again, five minutes away. And again, that's a $25 discount. This time most people won't bother making the five minute journey to save $25. In both cases, you're saving $25. But in the first case of the jacket, it obviously feels like a significant percentage of the total price as it's 25% off. While the second case, a laptop, is small, it's just 1.25% off. Now if we're looking at utility theory and from a rational perspective, $25 is still $25 no matter what you're buying. But our brains don't see it that way. We are influenced by how the choice is framed rather than focusing purely on the actual dollars that are saved. Bernstein covers this feeling in investing exceptionally well writing. One of the most familiar manifestations of the failure invariance is in the old Wall street saying, you never got poor by taking a profit. It would follow that cutting your losses is also a good idea. But investors hate to take losses because, tax considerations aside, a loss taken is an acknowledgment of error. Loss aversion combined with ego leads investors to gamble by clinging to their mistakes in the fond hope that someday the market will vindicate their judgment and make them whole. Another point worth mentioning is in regard to how we use information. We often believe that more information will help us make better decisions and be more rational. Daniel Ellsberg published a paper which discussed a concept known as ambiguity aversion. That cognitive bias states that we prefer taking risks on the basis of known versus unknown probabilities. This is why I think investors can often make bad investment decisions after spending a large amount of time researching an investment. I know I've done this before. So, you know, put yourself in this position. Sometimes you find a stock, you start liking it more and more. You put more and more time researching. Let's say you spend, you know, 10, 20, 30, 40 hours learning about it, researching competitors, maybe speaking with other investors or maybe company insiders. And after this time, you know, you, you begin to develop an attachment to the business. You know, you learn more about it, you consume more information, and let's say maybe you eventually purchase shares in the business. Even though maybe when you try to look at the numbers of the returns that you're going to get, they're kind of unattractive. Now, I think there's some degree of ambiguity aversion at play here because we've now obviously increased the amount of information we know about this business. We're actually taking a larger risk based on buying that business because we know more about it. When it comes to a name that we barely understand or haven't spent any time researching on, we have no problem taking a pass. So let's look at some of the other behavioral finance points that Bernstein discusses. One of the most significant contributors to behavioral finance is a man named Richard Thaler. Behavioral finance studies how investors balance logic and emotions and decision making leading to market behavior that often defies theoretical models Many of which are the models we have discussed already in this episode. Now, Bernstein points out that Thaler was a member of what he called the theory police. And the theory police were people who constantly checked to see whether investors were obeying or disobeying the laws of rational behavior that we've covered from the Bernoulli's to Markowitz. Thaler ran an experiment where he asked two questions. One, how much would you be willing to pay to eliminate a one in a thousand chance of immediate death? And two, how much would you have to be paid to accept a one in a thousand chance of immediate death? The results were simply fascinating. So a typical answer was I wouldn't pay more than $200, but I wouldn't accept an extra risk for $50,000. Thaler concluded that the disparity between buying and selling prices was very interesting. He considered this to be called anomalous behavior, which was behavior that violated the predictions of standard rational theory. Some of his other anomalous behaviors included large differences in what people would be willing to buy an item and sell the exact same item, as well as the failure to recognize sunk costs. Thaler then connected with some of Tversky and Kahneman's converts and realized that his anomalous behavior was really normal behavior and that the rational behavior was the exception. Now remember back when I was talking about Bayes and Keynes, I said that investors can and should update their probabilities based on new information. Thaler and Debaunt found that investors don't actually update their beliefs the way they should. Instead of following Bayes rule, they put too much weight on new information and they ignore past trends. Basically, they make decisions based on gut reactions rather than historical probabilities. And the result is that stock prices swing too far in either direction, creating predictable reversals regardless of what's actually happening with earnings, dividends or other fundamentals in the business. Now this is a super powerful message and I think does this a really good job of explaining why markets just in generally swing so widely. But this also shows why individual stocks can be so volatile in any one year. One thing you can do is just look at some of your recent buys and sells and identify where maybe your gut prompted you to make a mistake. You may find there's some very particular errors in the fact that you're selling businesses maybe just because the price is going down. And obviously that error is going to be quite obvious if you're selling it even though the business's fundamentals are continuing to improve. In that case, you know you're succumbing to bias, and you can try to create some strategies to try and deal with them as best as you can. One strategy that I like to talk about pretty often is list limiting the frequency that you allow yourself to look at stock prices. Now, as we've explored in this episode, risk is a concept that has evolved over centuries, from the ancient Gammas of Egypt to the mathematicians who laid out the groundwork for probability theory, and ultimately to the modern frameworks that are used in investing today. The journey through Bernstein's against the Gods highlights one central theme, which is our understanding of risk is still evolving and it will likely never be a solved equation. For investors, the key takeaway here is that while models, theories, and probabilities provide some very valuable tools, they're never a substitute for things like judgment, adaptability, and experience. Risk isn't just about numbers. It's about uncertainty, human behavior, and decision making under pressure. Behavioral biases shape markets just as much as any mathematical model, and understanding those biases can be just as important, if not more, as understanding the underlying businesses that we invest in. So I want to finish this episode just talking about how we can tilt the odds in our favor. First, we need to think probabilistically. The best investors don't just assign a single outcome to an investment. They consider a range of possibilities and assign probabilities to each of them. Instead of thinking, you know this stock is going to double, a more helpful approach is this Stock has a 30% chance of doubling, a 50% chance compounding at, say, market average rates, and a 20% chance of underperforming or declining. This way, you build a more realistic framework for decision making. Secondly, here embrace Bayes Theorem. You can do this by updating your probabilities as new information emerges. Investors who just stubbornly cling to their original theses ignore negative signals and often get burned. Conversely, those who react impulsively to every piece of news are just as likely to make costly mistakes. The right balance is learning to weigh new data appropriately without overreacting. Third, structure your portfolio to take advantage of asymmetry. Buffett and Munger talk about betting big when the odds are overwhelmingly in your favor. This doesn't mean reckless concentration, but it does mean allocating more capital to opportunities where you have a high conviction and where the risk reward profile is disproportionately in your favor. The best investors aim for situations where the upside potential far outweighs the downside risk. This is how you compound capital effectively over multiple decades. Fourth, always consider the role of psychology Investors love certainty, but markets don't provide it. Unfortunately, understanding how fear and greed manifest in market cycles, I think allows you to act rationally when others are acting more emotionally. Having an investment checklist can help you remain disciplined and help you avoid making impulsive decisions that are based on short term noise. And finally, recognize reversion to the mean as one of the most powerful forces in investing. Periods of extreme optimism or extreme pessimism don't last forever. Overvalued markets eventually correct and beaten down stocks often rebound when sentiment shifts. Understanding these cycles and having the patience to wait for favorable opportunities gives you a significant edge over those who chase momentum or panic during the first signs of volatility. Investing is not about eliminating risk, but learning how to navigate it intelligently. Whether through Bayesian updating, strategic concentration, or understanding market psychology, the best investors consistently look for ways to stack the deck in their favor rather than just seeking certainty where none exists. That's all I have for you for today. If you want to interact with me on Twitter, please follow me at irrational mrkts or on LinkedIn under Kyle grief. If you enjoy my episodes, please feel free to let me know how I can make your listening experience even better. Thanks again for tuning in. Bye bye. Thank you for listening to tip. Make sure to follow we study billionaires on your favorite podcast app and never miss out on episodes. To access our show notes, transcripts or courses, go to theinvestorspodcast.com this show is for entertainment purposes only. Before making any decision, consult a professional. This show is copyrighted by the Investors Podcast Network. Written permission must be granted before syndication or rebroadcasting.