Tag: Behavioral Finance

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Demystifying Position Sizing: A Dive into Probabilities, Payoffs, and Risk Management

Statistician and Black Swan author Nassim Taleb said “if you gave an investor the next day’s news 24 hours in advance, he would go bust in less than a year.” Taleb is implying that even with an informational advantage, investors must properly manage their risk. The feeling of having an edge, be it real or perceived, tends to lead investors to overconcentrate their bets. This type of behavior has been shown in behavioral experiments with simple mathematical solutions. In one study,[1]  participants were given a biased coin with a 60% chance of a flip landing on heads. They were given $25 and were able to bet any size and configuration for thirty minutes. They would also be able to pocket any winnings, subject to a cap of $250. Given the large probabilistic advantage, the researchers expected the participants to do reasonably well. As Nassim Taleb probably would have expected, the results were shockingly underwhelming with 28% of participants going bust and 67% betting on tails at least once. With no upper limit on the amount one could win, 300 flips with the optimal bet size could have yielded an astonishing value of over $3 million in this game. Why did so many participants fail to earn anything and what could they have done differently to convert their advantage into wealth?

The aforementioned study is ultimately a challenge related to bet sizing. Mathematically, the optimal bet size for this problem is 20% of each participant’s “wealth.” This can be derived from the Kelly Criterion. The Kelly Criterion is a well-known formula for determining optimal bet size developed in 1956 by John L. Kelly, a scientist at AT&T Bell Laboratories. For a bet like a coin flip, where a negative outcome amounts to a total loss on the bet, the Kelly position size can be given by:

 

Kelly Bet Size = Probability of a Win – Probability of a Loss/ Fraction of Bet Gained with a Win

 

The expected value in this biased coin flip example is 0.6-0.4/1 = 0.2 on every dollar bet, or 20% of available wealth. The researchers point out that repeatedly betting a fixed 20% size gives a 95% chance of reaching the maximum payout of $250. Yet they found that participants frequently gambled everything on one bet and one third of participants ended with less money than they started with. This experiment shows that decisions around the allocation of funds are often sub-optimal. Heuristics like the Kelly Criterion can help investors to make rational decisions around position sizing and capital allocation.

The coin flip example is fairly straightforward: you have an advantage in knowing that heads is weighted to occur 60% of the time, and the payout will always match your bet, no matter which side you take. Thus, a rational player would always bet on heads, and with the correct position sizing, would have a fairly good chance to make substantial sums of money. Unfortunately, the real world is not so advantageous. Consider a pastime that has recently exploded in popularity due to regulatory changes: sports betting. Here, individual gamblers have no particular edge. In fact, they actually have a slight disadvantage since the sportsbook has to have their cut of the profits. To illustrate, we can examine the recent big football game between the Kansas City Chiefs and the San Francisco 49ers. Avid football fans already know the Chiefs won this game, but prior to the game, the odds had the 49ers favored at -128 and the Chiefs as underdogs at +108 according to CBS Sports. This strange notation simply relates to the profit received from a winning bet. To bet on the Niners and receive a $100 profit, bettors would need to wager $128. A $100 bet on the Chiefs would yield a profit of $108 in a Chiefs win. These payouts are based on probabilities which can be calculated as:

 

Implied Probability of a Win = Capital Risked/(Capital Risked + Potential Profit)

 

In this case, the implied probability of a 49ers win was 128/(128 + 100) = 56.14%. The probability of a Chiefs win was 100/(100 + 108) = 48.08%.[2] Using the Kelly Criterion with the market implied odds, the optimal bet size on the 49ers would be… 0%. Would a rational person bet on the 49ers then? The answer is: maybe. Suppose a person with superior football expertise who has performed deep analysis on the teams comes up with a 59% probability of the 49ers winning. With this increased win probability, our hypothetical gambler has an edge over the odds that the betting market is giving him. The Kelly Criterion now says that this gambler should bet 6.5% of his total capital on the 49ers. Of course, this presents two problems. First, our gambler could very well be wrong on his probability assumptions. That is, is he really smarter than the overall betting market? Second, as we now know, the Chiefs won. Despite a bet on the Niners being entirely rational, assuming our gambler’s probability estimates are correct, we are still dealing with probabilities. There is still a 41% chance that the bet will lose. This is why position sizing is so important. By only risking 6.5% percent of capital, our gambler can survive to keep making more bets and have a chance to gradually compound his winnings.

With this backdrop, there are several takeaways from these examples that can be applied to investing in financial markets. The first is that investing is a zero-sum game, much more closely represented by the sports betting scenario than the coin flip example. When an investor purchases an asset, there is always another party across the table selling the asset, similar to betting on the other team. Like sports betting, the asset will be priced according to market expectations. A rapidly growing company with solid underlying fundamentals will very likely trade at a higher valuation compared to a distressed company on the verge of bankruptcy. In financial theory, a higher valuation implies a lower expected return in the future. Conversely, a lower valuation would portend a higher expected future return. Of course, those return expectations come with extreme differences in risk. Investors are compensated, or given a premium, for taking on risk. What sort of payoff would you require to bet on the local high school junior varsity football team versus the 1985 Chicago Bears?[3]

A second takeaway is that the ability of investors to consistently outperform the markets ultimately depends on their ability to examine outcomes not in terms of certainties but in terms of probabilities, and investors must be able to convert those probabilities into rational position sizes given that financial markets contain high levels of uncertainty. Even the sports betting example above is ultimately too simplistic as it focuses on a single estimate of probability. Investors must instead recognize that outcomes are not binary; there are numerous scenarios which could play out, each with their own likelihood of being realized. When you add this uncertainty, the optimal bet size likely becomes smaller and begins to level off for larger bet sizes.

A hypothetical example with non-linear bet sizing. As the bet size becomes larger, the increase in bet size becomes smaller. In this case, the individual does not wish to bet more than 15% of capital on one bet, no matter the advantage they have (or think they have).

 

The final key takeaway is that investors must be aware of potential biases which could affect their decision-making. For example, in the example of the hypothetical gambler who believes his estimates are more accurate than the odds given by sportsbooks, one must ask if the gambler actually has an edge or if he is overconfident in his abilities. There is a reason the famed psychologist and Nobel Prize winner Daniel Kahneman called overconfidence “the most significant of the cognitive biases.” Similarly, it is challenging to beat the stock market consistently. Having a rigorous investment process in place can help to instill discipline and avoid overconcentrating in  too few positions.

An additional bias that could impact position sizing is loss aversion. The Kelly Criterion, for example, will give a rational position size for risk-neutral investors, but in reality, most investors are risk averse. This means losses have a larger psychological impact than gains. Suppose the Kelly Criterion indicates optimal position sizing of 20% of wealth. Someone starting with $100 may be very willing to risk $20, but an investor with $500,000 may not be willing to risk a daunting $100,000 on a single trade.  For this reason, it is common to see traders use a fraction of the optimal Kelly bet size to make the volatility more tolerable.

Ultimately, investors must consider expectations of both risk and return before translating investment opportunities into potential positions. Furthermore, systematically applying a heuristic such as the Kelly Criterion can help to determine appropriate position sizes, but the overall portfolio must also be a consideration. By just applying the Kelly Criterion to individual positions, the portfolio may be taking on much more risk than intended if the positions are highly correlated. Position sizing is a key driver of portfolio returns, and it is essential to ensure positions are sized not only to take full advantage of solid opportunities when they arise but also to ensure portfolio survival in the long run.

 

 

[1] Haghani, Victor and Dewey, Richard, Rational Decision-Making under Uncertainty: Observed Betting Patterns on a Biased Coin (October 19, 2016).

[2] Note that the sum of the alternative win probabilities exceeds 100% since the bets are priced to make money for the sportsbook, no matter who wins.

[3] The ’85 Bears are widely regarded as one of the best NFL teams of all time, scoring 456 points while only allowing 198 according to ESPN.

 

 

 

 

The views expressed represent the opinion of Passage Global Capital Management, LLC. The views are subject to change and are not intended as a forecast or guarantee of future results. This material is for informational purposes only. It does not constitute investment advice and is not intended as an endorsement of any specific investment. Stated information is derived from proprietary and nonproprietary sources that have not been independently verified for accuracy or completeness. While Passage Global Capital Management, LLC believes the information to be accurate and reliable, we do not claim or have responsibility for its completeness, accuracy, or reliability. Statements of future expectations, estimates, projections, and other forward-looking statements are based on available information and Passage Global Capital Management, LLC’s views as of the time of these statements. Accordingly, such statements are inherently speculative as they are based on assumptions that may involve known and unknown risks and uncertainties. Actual results, performance or events may differ materially from those expressed or implied in such statements.

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Market Corrections are Inevitable; Panic Selling Shouldn’t Be

Investors can quickly become panicked when they see the stock market experiencing a market correction, or even more daunting, entering bear market territory. The market recently experienced a correction, but these events are more common than one may think. Although the past is no guarantee of the future, over the last century, the market has recovered from drawdowns and provided higher gains for long-term investors. Market corrections are inevitable, and they are bound to happen multiple times during every investor’s life. It is easy to become negatively influenced and anxious during times of market turmoil, but rather than acting out of fear, learning the facts about similar events will provide you with a more encouraging mindset. Experienced investors are more likely to be well-informed on volatility and past market behaviors, so they are able to stay committed to their investment strategy. Having this beneficial knowledge will allow you to look past the discomfort more easily to avoid the urge to respond in a costly manner that you may later regret.

A major stock index, such as the S&P 500 or the DJIA, experiences a market correction when it falls more than 10%, but less than 20%, from a recent peak. When the decline exceeds 20%, the index enters bear market territory, which involves a higher degree of detrimental impact compared to a market correction. Market corrections are generally caused by current factors that disrupt the markets; these factors are typically temporary and quickly fade. On the contrary, bear markets are more likely to be the result of substantial imbalances that have built up over the years. These may coincide with recessions, defined as at least two consecutive quarters of decline in Gross Domestic Product (GDP), which is a measure of general economic health. Fortunately, bull markets generally last longer than bear markets and corrections. The average bull market lasts 8.9 years, whereas the average bear market lasts 1.4 years. Market corrections can be viewed as short-lived market setbacks that occur over a few months, and they are called “corrections” because the markets historically “correct” themselves where prices return to their longer-term trend. Market corrections are undeniably going to continue and affect most investors’ lives at some point. Many may find this frightening, but actually in a lot of cases, market corrections have acted as a healthy reset for investor expectations and stock valuations.

Overall, predicting stock market behavior is beyond difficult, and if incorrect, an investor may experience tremendous opportunity cost. Educated investors know that time in the market beats trying to time the market. To corroborate this point, a research study1 from J.P. Morgan found that “investors who missed the top 10 trading days during a recent 20-year stretch would have seen their returns fall by almost half, compared to those who stayed invested the whole time.” It is accurate to conclude that market corrections may damage short-term investors, but for long-term investors, they often provide buying opportunities. Times as this cause discomfort, but it is normal. Investors have to “pay to play”, and sometimes that means going through short-term discomfort to experience long-term success.

Financial markets kicked off 2022 with turmoil, where the economy is encountering a rise in geopolitical tensions, a four-decade high inflation rate, COVID-19 impacts, and interest rate hikes from the Fed – to name a few headwinds. The last factor is critical. The majority of market corrections happen during rate hiking cycles. Of course, the dynamic between the Fed Funds rate, economy, and stock market is complicated and may be different across cycles. So far this year, all three major stock market indexes, the S&P 500, the Dow Jones Industrial Average, and the tech-heavy NASDAQ, suffered corrections with the latter entering bear-market territory. However, the discomfort of market underperformance today may be softened for the average investor due to a tight labor market and strong consumer balance sheets. Additionally, market performance is ultimately driven by fundamentals such as corporate revenue and earnings. For 2022, investors will continue to stay up to date on a variety of risk factors including the Fed monetary policy, consumer spending, COVID-19, and the Russia-Ukraine crisis, but the most alarming of all is the persistently high inflation rate. Although markets do move faster than they have in the past, we can analyze past market corrections to get a better understanding of how the market may behave in the future.

Since 1950, there have been approximately 39 market corrections.2 The stock market does not follow the pattern of averages, but to put it in perspective, that is equivalent to a double-digit decline occurring in the S&P about every 1.85 years. On average, a stock market correction will take 6 months to reach its trough. 7 of those corrections took more than a year to reach its bottom, and 24 of them took approximately 3.5 months. Additionally, 6 of these 39 corrections occurred in the 2010’s. However, over the 2010 decade, the S&P 500 received a total return of about 256%; this alone proves how the market rebounded and rewarded investors who stuck it out with outstanding gains. Another example is 2018, when the S&P 500 plummeted more than 10% in the first and fourth quarter. This was abruptly followed by a rebound of over 13% in the first quarter of 2019. In the bear market between 2007 and 2009, the S&P 500 declined over 48%. On a brighter note, the S&P 500 was up 68.6% from the low point one year later and up a total of 95.4% 2 years later. Market corrections are actually extremely common. When looking at 2002 through 2021, there has been a decline of more than 10% in 10 of those 20 years – or 50% of the time. In 2 other years in that timeline, the decline was very close to 10%. Even though the markets experienced these deep falls from 2002 to 2021, they rose and provided positive returns in all but 3 years. A report from Crestmont Research3 looked into the years of 1919 to 2021 to analyze the rolling 20-year average annual total returns. The results are optimistic, as it was found that the “S&P 500 always made money for investors on a total-return basis if they held for at least 20 years”. Out of all these years, only 2 of them ended with an average annual total return of less than 5%, and more than 40 of those years ended between 10.8% and 17.1%. Furthermore, we can examine how the market tends to perform after exiting the market correction. Using data beginning in 1928, the S&P 500 had an average gain of nearly 14% one year after a market correction. One of the quickest and deepest corrections was during COVID-19, but this was also one of the speediest recoveries. In the span of a few weeks, the S&P 500 lost 30%, but it then regained all of that loss within 5 months. Within one year following the bottom of this correction, the value of the S&P 500 doubled. This example, as well as all the others, prove that market corrections are common, and that investors should avoid attempting to “fix” the correction. As mentioned, panic moves will lock in your losses and you will lose out on the future gains from recovery. Investors can benefit from understanding these historical tendencies. The market has volatility and times such as this are normal, so it is important for long-term investors to remain confident in their investment strategy.

 

 

 

 

1 Azzarello, Samantha and Roy, Katherine. “Impact of being out of the market.” J.P. Morgan Asset Management, 5 June 2020.

2 Williams, Sean. “How Long Do Stock Market Corrections Last?” The Motley Fool, 20 March 2022.

3 “Returns Over 20-Year Periods Vary Significantly; Affected by the Starting P/E Ratio.” Crestmont Research. 2022.

 

The views expressed represent the opinion of Passage Global Capital Management, LLC. The views are subject to change and are not intended as a forecast or guarantee of future results. This material is for informational purposes only. It does not constitute as investment advice and is not intended as an endorsement of any specific investment. Stated information is derived from proprietary and nonproprietary sources that have not been independently verified for accuracy or completeness. While Passage Global Capital Management, LLC believes the information to be accurate and reliable, we do not claim or have responsibility for its completeness, accuracy, or reliability. Statements of future expectations, estimates, projections, and other forward-looking statements are based on available information and Passage Global Capital Management, LLC’s views as of the time of these statements. Accordingly, such statements are inherently speculative as they are based on assumption that may involve known and unknown risks and uncertainties. Actual results, performance or events may differ materially from those expressed or implied in such statements.

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Compounding the Issue

Compounding Coins

“Compound interest is the eighth wonder of the world. He who understands it, earns it. He who doesn’t, pays it.”

– Albert Einstein

The most important concept pertinent to investing is the arithmetic of compounding. The math is not immediately intuitive, but the effects, both positive and negative, have momentous impacts on portfolio returns. Investors who understand the drivers of compounding are best positioned for long-term success. Alternately, nearsighted investors who ignore the significance of compounding may struggle to reach their desired objectives.

Much has already been written about the importance of long-term investing, but the specific reason why it is essential to retain a long-term mindset often goes overlooked. It is easy to believe that stock market riches lie in huge overnight gains, especially after the GameStop incident earlier this year. The firestorm of media coverage surrounding these events can easily induce investors to subconsciously overestimate the frequency of such occurrences. However, in reality, patient investors have a much better chance of reaching “riches” in the stock market due to the exponential growth of compounding over time. Suppose an investment returns 10% per year. After ten years, each dollar invested would be worth $2.59. After twenty years, each dollar would be $6.72. After 30 years, each dollar would be $17.45. It is evident that the growth is not linear; it is exponential. Each incremental  increase in portfolio value leads to larger changes in the future.


Exhibit I: Exponential growth of portfolio for differing return assumptions.

Despite the benefits, compounding can also have tremendously adverse consequences for investors. The effects of positive and negative returns are asymmetrical, meaning negative returns actually have a larger impact on the portfolio in dollar terms than positive returns of the same percentage. To illustrate, consider an investment of $1 million. After undergoing a rough period in the market, the value of the investment is now $500,000, for a 50% loss. However, we cannot simply rely on a 50% gain to bring the investment back to $1 million. Now that the value is only $500,000, we must double our money for a 100% gain in order to get back to where we started.

Exhibit II: If an investment returns an initial amount shown on the x-axis, what subsequent return needs to be achieved in order to match the starting dollar amount?

The question then becomes how investors can use compounding to their advantage rather than fall prey to unfavorable outcomes. Risk management and investor temperament are crucial. Risk is unavoidable. However, the amount of risk that is being taken must be carefully measured and monitored to ensure that it is not out of line with what the investor can tolerate. Investment professionals typically measure risk by volatility, or standard deviation. High volatility implies a magnitude of returns higher than historical tendencies would estimate. Note that magnitude says nothing about direction. It is not necessary that volatility will ultimately result in harm to an investors’ portfolio since volatility does not imply permanent loss; it only implies wide swings in value. However, when investor behavior is involved, volatility can easily result in permanent loss. This is especially true if it turns out that the portfolio risk was not properly managed or was more than the investor’s risk tolerance could allow for. The investor may panic and sell, foregoing potential high volatility gains in the recovery. Over the long-term the impact of these mistakes can be devastating even though the true impact might not be clear on the surface. The reason: compounding. The investor is missing out on the largest gains of the recovery, and when they do eventually get back in, their portfolio is starting from a lower value. Investors would be wise to follow Charlie Munger’s first rule of compounding: “Never interrupt it unnecessarily.”

Of course, the caveat to Munger’s quote is the word, “unnecessarily.” Just as investors can fall into the trap of panic selling, they may be influenced by the disposition effect. The disposition effect is a behavioral anomaly referring to investors’ natural tendencies to sell assets that have risen in price (thus locking in gains) and hold onto assets that have fallen (thus avoiding the aforementioned permanent loss). Each situation is different, and there is no clear answer on how to act. To maximize the probability of success over the long-term, it is vital for investors to have an investment process that they follow with discipline. This can help minimize the influence of emotions and allow their investments to compound over time.

Compounding, as it relates to investing, occurs at multiple levels. At the highest level is the compounding of the portfolio value. This is not only related to the individual performance of the underlying securities but also how the portfolio is constructed and how drawdowns are managed (drawdowns are the losses of the portfolio from peak to valley). Diversification is imperative for reducing portfolio risk. The bellwether for diversification is the balanced portfolio consisting of stocks and bonds. Historically, the correlation between stocks and bonds has been low. This has allowed the two asset classes to perform particularly well together and lessen the volatility as compared to an all-stock portfolio. There are also more complex strategies that can be used. Hedge funds are well known for their focus on risk mitigation. Many hedge funds employ long-short strategies where they bet on certain stocks and against others. The offsetting positions, they hope, will minimize the systematic (market) risk and allow the fund to grow steadily despite market conditions (depending on the specific strategy; there are many variations of the long-short portfolio). These are only a few examples, but there are numerous types of strategies with the same aim: achieving steady returns and avoiding significant drawdowns to maximize portfolio growth over time.

The second level of compounding occurs at the individual stock price level. Famed mutual fund manager Peter Lynch popularized the term “tenbagger” to describe stocks that increase ten-fold over the initial buy price. Many investors focus specifically on seeking out these kinds of stocks. Needless to say, tenbaggers are rarities, but not every stock needs to be a tenbagger for an investment to be considered a success. Some investors may even find success through trading stocks over short time horizons (e.g., weeks, days, seconds, etc.). Renaissance Technologies’ Medallion Fund is the quintessential example. The quantitative hedge fund (which is now closed to the public) is believed to have achieved an astonishing average annual return of 66% gross of fees from 1988 to 2018 according to author Gregory Zuckerman. This was done by consistently generating small gains and using a fair amount of leverage in a large portfolio of securities. Due to the mathematics of compounding, these small gains do not simply add up over time; they multiply, which can result in staggering numbers.

Exhibit III: Compounding should  not be treated as some abstract mathematical mirage. Investors should understand how compounding occurs at multiple levels and directly affects value over time.

 

 

Disclaimer

The views expressed represent the opinion of Passage Global Capital Management, LLC. The views are subject to change and are not intended as a forecast or guarantee of future results. This material is for informational purposes only. It does not constitute investment advice and is not intended as an endorsement of any specific investment. Stated information is derived from proprietary and nonproprietary sources that have not been independently verified for accuracy or completeness. While Passage Global Capital Management, LLC believes the information to be accurate and reliable, we do not claim or have responsibility for its completeness, accuracy, or reliability. Statements of future expectations, estimates, projections, and other forward-looking statements are based on available information and Passage Global Capital Management, LLC’s views as of the time of these statements. Accordingly, such statements are inherently speculative as they are based on assumptions that may involve known and unknown risks and uncertainties. Actual results, performance, or events may differ materially from those expressed or implied in such statements.

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Fallacies and Financial Markets

Hand Flips Coin Image

When predicting uncertain, random events, we often take mental shortcuts or go with our gut feelings, which can lead to statistical illusions and suboptimal actions. Our cognitive biases are not consistent with the law of probability because most of us find it frustratingly unintuitive and challenging.

The gambler’s fallacy, also known as the Monte Carlo fallacy (first coined by famous researchers Amos Tversky and Daniel Kahneman in 1971), is a cognitive error that describes our tendency to believe a previous event or series of events can influence the outcome of a future, random event. This can be simply illustrated with a coin toss. If a person flips a fair coin five times and each time it lands on heads, the observer may erroneously conclude the next flip is more likely to be tails. This line of thinking involves an inaccurate understanding of probability. Each coin flip is randomly generated and statistically independent, which means previous flips have no bearing on future flips. If we keep flipping the coin indefinitely, the fraction of heads in the total number of outcomes converges to 50 percent, the long-run average. Ultimately, the gambler’s fallacy is the mistaken belief that random sequences should exhibit systematic reversals.

Another statistical illusion is related to the hot hand in basketball, in which people predict that random sequences will exhibit excessive persistence rather than reversals. Nearly every basketball player, coach, or fan believes that players can have “hot hands,” meaning that they are on a hot streak and are more likely than average to make their next shot. However, in the landmark 1985 paper, The hot hand in basketball: On the misperception of random sequences, psychologists Thomas Gilovich, Robert Vallone, and Amos Tversky (GVT) concluded that the hot hand is a cognitive illusion representing the tendency to detect patterns in randomness. The expectation that a trend will continue in the future is known as the hot hand fallacy.


Hot Hands and Gamblers Fallacy
The hot hand and gambler’s fallacies are two important cognitive biases that affect investment decisions in financial markets. The hot hand belief is at play when investors chase hot stocks or funds believing that the past strong performance will be indicative of future results. The gambler’s fallacy manifests as the disposition effect when investors sell winners too soon and hold losers too long. Unfortunately, such biased decisions often lead to unfavorable consequences for investors. As the famous British economist and mathematician, John Maynard Keynes once said, “The market can stay irrational longer than you can stay solvent.”

 

Disclaimer

The views expressed represent the opinion of Passage Global Capital Management, LLC. The views are subject to change and are not intended as a forecast or guarantee of future results. This material is for informational purposes only. It does not constitute investment advice and is not intended as an endorsement of any specific investment. Stated information is derived from proprietary and nonproprietary sources that have not been independently verified for accuracy or completeness. While Passage Global Capital Management, LLC believes the information to be accurate and reliable, we do not claim or have responsibility for its completeness, accuracy, or reliability. Statements of future expectations, estimates, projections, and other forward-looking statements are based on available information and Passage Global Capital Management, LLC’s views as of the time of these statements. Accordingly, such statements are inherently speculative as they are based on assumptions that may involve known and unknown risks and uncertainties. Actual results, performance, or events may differ materially from those expressed or implied in such statements.

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The Wisdom of Crowds

“In the short run, the market is a voting machine but in the long run, it is a weighing machine.” – Benjamin Graham

One of the founders of modern quantitative investment management is Jack Lawrence Treynor, a doctor’s son born in Council Bluffs, Iowa on Feb. 21, 1930. His pioneering work on how discount rates should depend on risk contributed to the development of the Capital Asset Pricing Model, which quantifies the trade-off between risk and return. That relationship is what gave rise to the notion of a stock’s beta, or its sensitivity to market movements. Jack Treynor also wrote extensively on quantitative analysis, anticipating seismic shifts in the financial world by decades as the chief editor of the Financial Analysts Journal.

He is also known for his jelly bean Experiment in 1987, when as a finance professor, he brought a jar into his class that held 850 jelly beans and asked the students to guess the number of beans inside. The group estimate was 871, which was about 2.5% off; only one of the 56 people in the class made a better guess.

Michael Mauboussin, a global financial strategist and an adjunct professor of finance at the Columbia Business School also did a similar experiment in January 2007. He asked his 73 students to independently guess the number of jelly beans in a jar. There was a $20 reward offered for the best guess, and a $5 penalty for the guess farthest from the correct answer. The average guess of the class was 1,151 while the actual number of beans was 1,116. The consensus was off by 35 beans, or 3.1 percent.  Of the 73 estimates, only two were better than the average.

These are some classic examples of group intelligence commonly known as the Wisdom of Crowds, which is also the name of a thought-provoking book authored by the New Yorker business columnist James Surowiecki. He examined the proposition that, under the right circumstances where topics are complex, problems are large, and outcomes are uncertain, the crowd can make a smarter decision by leveraging the collective intelligence and insight of a group of people rather than an elite few, no matter how brilliant. However, for Wisdom of Crowds to work, it requires that the group needs diversity (cognitive and social) and independence (without too much influence from others).

When there is a lack of diversity and independence, the collective wisdom stops working efficiently. Jack Treynor tested this new idea with a second experiment.  He provided two bits of misinformation to the class after students recorded their first guess. He warned the students that there was air space at the top of the jar and the jar walls were thinner than normal.

Such misinformation prompted most students to change their original answers, causing the modified average results to be worse than the original by a factor of four. When making the first guess, students could see with their own eyes that there was air space at the top of the jar, and they could see exactly how thick the glass was. Yet, they were swayed by the influence of Treynor and the narrative he cleverly constructed. Just as there is wisdom in crowds, there is sometimes madness in crowds.

As the jelly bean experiments demonstrate, the wisdom of crowds concept tends to be more effective when there is a diverse group of opinions in the crowd and guesses are not influenced by others. The stock market is certainly one such place where group consensus and sentiment affect asset prices, especially in the short run (although it is highly efficient in the long-term). Discerning predictable information from random noise in the markets requires independent research, strict discipline, and a knack for analyzing the rationality of group behavior. Short-term madness may lead to longer-term opportunities as the wisdom of crowds ultimately prevails. This is key to the success of active investors.

 

Disclaimer

The views expressed represent the opinion of Passage Global Capital Management, LLC. The views are subject to change and are not intended as a forecast or guarantee of future results. This material is for informational purposes only. It does not constitute as investment advice and is not intended as an endorsement of any specific investment. Stated information is derived from proprietary and nonproprietary sources that have not been independently verified for accuracy or completeness. While Passage Global Capital Management, LLC believes the information to be accurate and reliable, we do not claim or have responsibility for its completeness, accuracy, or reliability. Statements of future expectations, estimates, projections and other forward-looking statements are based on available information and Passage Global Capital Management, LLC’s views as of the time of these statements. Accordingly, such statements are inherently speculative as they are based on assumption that may involve known and unknown risks and uncertainties. Actual results, performance or events may differ materially from those expressed or implied in such statements.

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The Greater Fool Theory

“Men, it has been well said, think in herds; it will be seen that they go mad in herds, while they only recover their senses slowly, and one by one.”

– Charles MacKay

Extraordinary Popular Delusions and The Madness of Crowds (1841)

 

In the early morning hours of Friday, December 15, 1989, an Italian-American artist, Arturo Di Modica, with the help of a few friends dropped his latest work, the world-famous Charging Bull sculpture, outside of the New York Stock Exchange. The 7,100-pound, 11-foot-tall bronze sculpture was later re-erected on Broadway just north of Bowling Green in the Financial District of Manhattan, New York City.  Arturo Di Modica first conceived of the Charging Bull in the wake of the 1987 Black Monday stock market crash. His Charging Bull statue has become a physical manifestation of a ubiquitous Wall Street term, the bull market, and it has inspired veneration from tourists and investors hoping for a cut of the stock market riches it represents.

The current bull market, fueled by record low interest rates and friendly fiscal policies, continues to attract more, especially younger, investors. Homebound, internet savvy folks jump on the speculative bandwagon to try to make fast money without much regard to the business fundamentals of company shares and valuations. The proliferation of online trading platforms like Robinhood and commission free stocks and options trades offered by brokerage houses are also helping propel the huge momentum rally. Shares of dying retail chain GameStop rose a meteoric 1,625% in January, epitomizing a speculative mania not seen since the dot-com bubble in the late 1990s. There is a distinct difference between investing and speculation. However, day traders’ temptations to make quick profits and a sense of FOMO, or fear of missing out, are pushing them into new asset classes such as silver, which is another example of market madness and the herding behavior.

The problem with such speculative moves and chasing momentum stocks like GameStop and AMC Entertainment is that investors are betting that someone will buy the investment from them at a higher price. This is called the Greater Fool Theory. They are hoping that a greater fool will come along and take the shares off their hands. However, as experienced and professional investors know well, momentum fueled by the madness of crowds is a double-edged sword. It amplifies gains but can also magnify losses when the sentiment changes with almost no notice.

As Isaac Newton eloquently stated in the spring of 1720, “I can calculate the motions of the heavenly bodies, but not the madness of people.” When you are riding atop the charging bull and the bubble is burst, take care not to get bucked. If you are thrown from the reigns, beware the stampede.

 

The views expressed represent the opinion of Passage Global Capital Management, LLC. The views are subject to change and are not intended as a forecast or guarantee of future results. This material is for informational purposes only. It does not constitute as investment advice and is not intended as an endorsement of any specific investment. Stated information is derived from proprietary and nonproprietary sources that have not been independently verified for accuracy or completeness. While Passage Global Capital Management, LLC believes the information to be accurate and reliable, we do not claim or have responsibility for its completeness, accuracy, or reliability. Statements of future expectations, estimates, projections, and other forward-looking statements are based on available information and Passage Global Capital Management, LLC’s views as of the time of these statements. Accordingly, such statements are inherently speculative as they are based on assumption that may involve known and unknown risks and uncertainties. Actual results, performance or events may differ materially from those expressed or implied in such statements.

 

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Why Magnitude of Payoff is So Important

Manager hits a ball creating rising business chart. Concept business vector illustration

“If I’d tried for them dinky singles, I could’ve batted around six hundred.” – Babe Ruth

Babe Ruth is considered one of the greatest baseball players of all time. He hit 714 home runs, a league record at the time. Over his career, he collected 2,873 base hits. He was a seven-time World Series champion, and he made baseball’s “All Century” team. However, for many years, Babe Ruth was also known as the “King of Strikeouts.” He led the American League in strikeouts five times and accumulated 1,330 of them in his career. However, despite his large number of strikeouts, he was one of baseball’s greatest hitters, establishing many MLB batting records, including career home runs. Babe Ruth accepted his failures because he knew his successes would more than make up for them. His approach and mindset illustrate one of the most important concepts in portfolio management and investing: expected value or mathematical expectancy. Celebrated hedge fund tycoon George Soros, the man who broke the Bank of England after making a profit of $1 billion by shorting the British pound, once summed up the same concept by stating: “It’s not whether you’re right or wrong that’s important, but how much money you make when you’re right and how much you lose when you’re wrong.” This is also called the Babe Ruth effect. In other words, it is not the frequency of winning that matters but the frequency times the magnitude of the payoff.

However, many people are wired to avoid losses when making risky choices when the probability of different outcomes is unknown. In fact, investors are known to perceive losses on their investments as greater than they actually are. This is outlined in prospect theory, which was formulated in 1979 by Daniel Kahneman and Amos Tversky. Investors naturally prefer to be right more frequently than they are wrong. However, this mindset causes investors to overlook the key concept that the frequency of correctness does not matter as much as the magnitude of correctness.

The understanding of frequency versus magnitude, or in other words, the understanding of winning a few big payoffs while taking small, frequent losses, goes against investors’ intuitions. This investor bias of prioritizing correctness over payoff magnitude goes to show the importance of focusing on expected value when making investment decisions.

For example, take a look at this hypothetical portfolio below:

As you can see, even though the probability of the portfolio going up is less than the probability of the portfolio going down, the magnitude of portfolio return when the portfolio goes up offsets the higher probability of loss when the portfolio goes down. Therefore, the expected value, how much your portfolio is expected to gain or lose on average, is positive.

To sum it all up, investors do not necessarily need to be exactly like Babe Ruth or George Soros to have long-term success in these types of probabilistic exercises. However, it is essential that investors understand expected values, risk management, and perhaps, most importantly, themselves and their own emotional tendencies if they wish to achieve success with their investments. Keep in mind, just because something has a lower probability, it doesn’t mean that it’s not worth betting on.

 

The views expressed represent the opinion of Passage Global Capital Management, LLC. The views are subject to change and are not intended as a forecast or guarantee of future results. This material is for informational purposes only. It does not constitute as investment advice and is not intended as an endorsement of any specific investment. Stated information is derived from proprietary and nonproprietary sources that have not been independently verified for accuracy or completeness. While Passage Global Capital Management, LLC believes the information to be accurate and reliable, we do not claim or have responsibility for its completeness, accuracy, or reliability. Statements of future expectations, estimates, projections, and other forward-looking statements are based on available information and Passage Global Capital Management, LLC’s views as of the time of these statements. Accordingly, such statements are inherently speculative as they are based on assumption that may involve known and unknown risks and uncertainties. Actual results, performance or events may differ materially from those expressed or implied in such statements.

 

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Skill Versus Luck

Paul DePodesta, a former baseball executive and one of the protagonists in Michael Lewis’s Moneyball, shares a story about playing blackjack in Las Vegas when a guy to his right, sitting on 17, ask for a hit. Everyone at the table is surprised and even the dealer asks if he is sure. The player nods yes, and the dealer produces a four and says, “Nice hit.” But was it really a smart play? Of course not (unless you work for the casino). The probability of going bust with a 17 is 69%. The player was simply lucky. If he continued to hit on every 17 he had been dealt, he would lose most of the time.

On the other side of the coin, sometimes decisions that may have seemed sound at the time they were made result in unfavorable outcomes. Consider an example highlighted by poker champion Annie Duke in her book Thinking in Bets: Making Smarter Decisions When You Don’t Have All the Facts. It involves one of the most infamous play calls in the history of football: the decision by Seattle Seahawks coach Pete Carroll to throw the ball at the one-yard line rather than hand the ball off to star running back Marshawn Lynch to end Super Bowl XLIX. The pass was intercepted in the end-zone and the decision cost the Seahawks not only the game, but the NFL championship. Carroll was widely ridiculed for the decision but perhaps the hate is undeserved considering that an incomplete pass would have stopped the clock giving the Seahawks some much needed time to score. Additionally, according to Duke, only 2% of passes from the 1-yard line within the previous 15 years had been intercepted. In all likelihood, the play should have either resulted in a touchdown or a clock stoppage giving the Seahawks more chances to run the ball. Because of the outcome, football fans perceive the play call as an atrocious one.

These anecdotes highlight a cognitive bias known as outcome bias. This has to do with one of the most fundamental and underappreciated concepts in sporting events, gambling and investing: process versus outcome (or skill versus luck). Just like the gambler in the hit-on-17 story, investors tend to make similar errors by placing too much weight on the outcome of a decision rather than the process by which the decision was made. The focus on the outcome is to some degree understandable because the outcome is what ultimately matters. However, it could be due to pure luck or some other random factors. People are not good at understanding the interplay between luck and skill. Luck is the force that brings good fortune by chance and not as a result of effort or ability. Skill, on the other hand, is the ability to do something competently due to learned power or acquired knowledge.

Some activities involve more luck than skill (e.g. playing roulette versus investing). There is, in fact, a simple way of determining whether an activity is based on skill proposed by Wall Street investment strategist, author, and professor Michael Mauboussin – just ask if the player can lose on purpose. If they can, it is a skill-based game (to a degree). If they cannot, luck plays a major role (again, to a degree).

A process is simply a methodology utilized to achieve a goal. It could be a simple checklist, or it could be a more sophisticated approach. Processes concentrate on the specific actions that must be followed in a discipled and systematic way, regardless of results. In investing, a traditional process might involve analyzing the last five years of financial statements for a company before buying their stock. Alternatively, more quantitatively oriented investors might develop intricate models with pre-defined rules to decide which stocks to buy and sell.

But investors often are mistaken by associating good outcomes with skill. Often, outsized gains are the result of a lucky stretch for a particular style of investing with the eventuality of that luck running out. Over time, abnormal returns are bound to revert to the mean, or average, as dictated by the law of large numbers. On the other hand, the best long-term money managers all emphasize a systematic and informed process. They are not concerned with failure in the short run due to factors outside of their control (e.g. global pandemic; shifting market sentiment; sudden outbreak of geopolitical events; etc.)

Jay Russo and Paul Schoemaker emphasize the importance of this process-versus-outcome decision making in their book Winning Decisions: Getting It Right the First Time (see Graph below). Their main point is that an individual who relies on process-based decision making deserves praise regardless of the outcome. Likewise, a person who uses a poor process but is met with a good outcome deserves neither praise nor promotion. This fortunate individual is simply the recipient of dumb luck. This is why it is so essential that investors shun activities such as chasing hot stocks or mutual funds that would make them vulnerable to the influence of psychological biases such as herding behavior or short-term oriented speculative trading. Instead, they should follow a more process-driven system to make informed decisions with a long-term perspective. As the co-founder and CEO of Twitter Jack Dorsey has opined, success is never accidental.


With or Without Skill Image
The views expressed represent the opinion of Passage Global Capital Management, LLC. The views are subject to change and are not intended as a forecast or guarantee of future results. This material is for informational purposes only. It does not constitute as investment advice and is not intended as an endorsement of any specific investment. Stated information is derived from proprietary and nonproprietary sources that have not been independently verified for accuracy or completeness. While Passage Global Capital Management, LLC believes the information to be accurate and reliable, we do not claim or have responsibility for its completeness, accuracy, or reliability. Statements of future expectations, estimates, projections and other forward-looking statements are based on available information and Passage Global Capital Management, LLC’s views as of the time of these statements. Accordingly, such statements are inherently speculative as they are based on assumption that may involve known and unknown risks and uncertainties. Actual results, performance or events may differ materially from those expressed or implied in such statements.

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Prospect Theory & Investments

In 1738 the Swiss mathematician Daniel Bernoulli wrote a famous essay in which he introduced utility theory about the psychological value of money. Bernoulli’s model assumed that the utility that was assigned to a given state of wealth did not vary with the decision maker’s initial state of wealth.

Later in the 20th century, two psychologists, Amos Tversky and Daniel Kahneman (the 2002 Nobel Memorial Prize winner in Economic Sciences), concluded in their 1979 seminal paper, “Prospect Theory: An Analysis of Decision under Risk,” that people make decisions based on changes of wealth as opposed to states of wealth. In an investing context, when looking at brokerage account statements, people psychologically place greater emphasis on the gains and losses for the period than the ending balance of their portfolio.

As an example, consider two investors: John and Mary. John’s wealth has gone up from $1 million to $1.5 million, and Mary’s wealth has gone down from $4 million to $3.5 million. Who is happier? Obviously, John is happier than Mary. Who is better off financially? Mary is better off given her larger amount of wealth.

Bernoulli’s model focuses on the utility of wealth, which essentially measures who is better off financially, but ignores the all-important role of the reference point, the earlier state relative to which gains and losses are evaluated. While Bernoulli’s utility theory requires one to know only the state of wealth to determine its utility, prospect theory also requires knowing the reference state.

Prospect theory has three cognitive principles that govern the value of outcomes: Adaptation level: this is the evaluation relative to a neutral reference point. Financial outcomes that are above the reference points are gains. Below the reference points are losses.

Diminishing sensitivity: the subjective difference between $900 and $1000 is much smaller than the difference between $100 and $200.

Loss aversion: when people think in terms of the final state of wealth, they tend to be much less risk-averse. However, when people think in terms of gains and losses, they tend to be more risk-averse, because losses loom much larger than gains.

To demonstrate a loss aversion example, consider a flip of a coin. If it lands heads, you gain $150, but if it is tails, you lose $100. Is this gamble attractive enough for you to play? This will require you to evaluate the psychological benefit of gain versus the psychological cost of loss. Most people tend to avoid this gamble for fear of potentially losing $100 versus the hope of gaining $150 despite the fact that the expected value of the gamble is positive. This helps explain risk aversion in the sense that the disutility of losing $1 is higher than the utility of winning $1.


In conclusion, prospect theory highlights the short-term asymmetrical emotional impact of gains and losses on people as opposed to long-term prospects of wealth. It attempts to model real-life choices, rather than optimal and rational decisions, thus creating a psychologically more accurate description of the decision-making process under uncertainty.

The views expressed represent the opinion of Passage Global Capital Management, LLC. The views are subject to change and are not intended as a forecast or guarantee of future results. This material is for informational purposes only. It does not constitute as investment advice and is not intended as an endorsement of any specific investment. Stated information is derived from proprietary and nonproprietary sources that have not been independently verified for accuracy or completeness. While Passage Global Capital Management, LLC believes the information to be accurate and reliable, we do not claim or have responsibility for its completeness, accuracy, or reliability. Statements of future expectations, estimates, projections, and other forward-looking statements are based on available information and Passage Global Capital Management, LLC’s views as of the time of these statements. Accordingly, such statements are inherently speculative as they are based on assumption that may involve known and unknown risks and uncertainties. Actual results, performance or events may differ materially from those expressed or implied in such statements.

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Expected Utility Theory & Investments

Decision making plays a key role virtually in every aspect of human life such as buying a house or choosing a career. It is the process of selecting a course of action from available options so that the desired result or predetermined objective may be accomplished. However, when decision making is about the future, uncertainty and risk become involved. For instance, how much should one save for retirement given the uncertainty involving such variables as future income and longevity? What is the expected return on different investment choices given the risks? In economics, utility is a measure of how much benefit consumers derive from certain goods or services. From a finance standpoint, it refers to how much benefit investors obtain from portfolio performance considering risk.

It is assumed that an individual, when making a decision in the face of incomplete knowledge, will choose to act in a manner that will result in the highest expected utility with respect to the individual’s subjective probability. This is the expected utility theory that was first introduced by Swiss mathematician Daniel Bernoulli and was later expanded upon in the 20th century by the mathematician John von Neumann and the economist Oskar Morgenstern.

There are three types of individual behaviors that the von Neumann–Morgenstern expected utility function can be used to explain: risk-averse, risk-neutral, and risk-seeking. For example, consider an individual deciding to invest in one of two portfolio strategies, Strategy A or Strategy B. Suppose that Strategy A has a 5% chance of producing $80, a 90% chance of producing $100, and a 5% chance of producing $120. Thus, the expected payoff from Strategy A would be calculated as follows:

Expected Payout for Strategy A: 5% x $80 + 90% x $100 + 5% x $120 = $100
Now suppose Strategy B has the same payoffs but the respective probabilities for the payoffs change to 40%, 20%, and 40%. It is easy to verify that the expected payoff is still $100:

Expected Payout for Strategy B: 40% x $80 + 20% x $100 + 40% x $120 = $100

In other words, mathematically speaking, nothing has changed. The only difference is that the probabilities of the lowest and highest payoffs rose at the expense of the middle one. This means there is more variance (or risk) associated with the possible payoffs. Despite the strategies being mathematically equivalent, the investor may not see them as equal. If she values both investment options equally, she is considered risk neutral. The implication is that she equally values a payoff of $100 with any set of probabilistic payoffs whose expected value is also $100. If she prefers Strategy A over Strategy B, she places higher value on less variability in payoffs. In that regard, by preferring more certainty, she is considered risk averse. Finally, if she actually prefers the increase in variability, she is considered risk-seeking. In a gambling context, a risk averter puts higher utility on the expected value of the gamble than on taking the gamble itself. Conversely, a risk-seeker prefers to take the gamble rather than settle for a payoff equal to the expected value of that gamble.

The implication of the expected utility theory is that individuals seek to maximize the expectation of utility rather than monetary values alone. Since utility functions are subjective, different people can approach any given risky event with quite different valuations. Having a solid understanding of one’s utility of money can help investors make investment decisions that are best suited to their risk attitudes and investment strategies.

The views expressed represent the opinion of Passage Global Capital Management, LLC. The views are subject to change and are not intended as a forecast or guarantee of future results. This material is for informational purposes only. It does not constitute as investment advice and is not intended as an endorsement of any specific investment. Stated information is derived from proprietary and nonproprietary sources that have not been independently verified for accuracy or completeness. While Passage Global Capital Management, LLC believes the information to be accurate and reliable, we do not claim or have responsibility for its completeness, accuracy, or reliability. Statements of future expectations, estimates, projections, and other forward-looking statements are based on available information and Passage Global Capital Management, LLC’s views as of the time of these statements. Accordingly, such statements are inherently speculative as they are based on assumption that may involve known and unknown risks and uncertainties. Actual results, performance or events may differ materially from those expressed or implied in such statements.