Madoff wasn’t a hedge fund

Bernie Madoff is back in the news lately as it’s now been 5 years since he was arrested for the largest Ponzi Scheme. For some reason, the name is commonly linked to “hedge funds”. Yet, the Bernie Madoff scam wasn’t a hedge fund, his company was a registered and regulated brokerage firm called Bernard L. Madoff Investment Securities. Madoff founded the Wall Street brokerage firm Bernard L. Madoff Investment Securities LLC in 1960. Some large hedge funds lost money because they had invested in Madoff’s managed account. They had Madoff managing some of their funds money. But Madoff Investment Securities LLC wasn’t a hedge fund.

If you had an account managed by Bernie Madoff at Madoff Investment Securities LLC  you would have had an account owned and titled in your own name. You would have gotten trade confirmations from Madoff Investment Securities LLC when he bought or sold. You don’t get that in a fund. You don’t know when a fund buys or sells. His investment program, then, offered the appearance of transparency – you could see what he was doing at any time.

As it turned out, the appearance of transparency enabled the thief to defrauded customers of approximately $20 billion over several decades. You see, Madoff’s investment program was a fraud, and the reason he was able to do it is that:

1. He was the portfolio manager: he made the trading decisions.
2. He owned the broker that executed the trades (as it turned out, they were fake; he didn’t do trades).
3. He owned the custodian: the custodian and broker was the same company.

Since Madoff Investment Securities LLC was the portfolio manager, broker, and the custodian, that allowed him to pretend to do trades and print trade confirmations and statements with fake information on them. Madoff Investment Securities LLC was regulated and registered as a brokerage firm, just like Wells Fargo Advisors, Edward Jones, Schwab, Morgan Stanley, and other brokers. You can probably see how the real issue was that his program was a fraud and he was able to do it because he controlled the trading decisions, trade confirms, account statements, and custody, because his company did it all. What if he had been required to custody an another company independent of his? he would have had to convince the other company to participate in his scheme which would likely have gotten him busted sooner. Most investment companies aren’t a fraud, so they would likely report him. Madoff was large and respected – but don’t think that made it any safer.

Whether you invest in a separately managed account or a private investment partnership, require that they use multiple service providers that are independent of each other instead of all one company. For example, your portfolio manager is an asset management firm, the broker is a different company that executes the trades and the custodian is a separate company that holds the securities and handles the cash in and out. Then, require it be audited by even another independent company. For example, if you enter into an investment management agreement with ABC Capital Management, LLC that firm is the portfolio manager and the agreement gives it authority to buy and sell in your account. Your account should then be held at a financial institution registered as a broker or bank like Folio Institutional, Trust Company of America, or JP Morgan. You deposit money to that financial institution that holds your money and they send you statements. ABC Capital Management, LLC is just trading the account independently and shouldn’t have custody of the money. If the investment program is a “hedge fund” instead of a separately managed account then it’s typically structured as a private investment partnership, say: ABC Fund, LP. A private fund is operated like a business – the business is trading for profit. You review a Private Placement Memorandum that explains every detail of ABC Fund, LP. When you invest, you sign a “Subscription Agreement” instead of an investment management agreement. You wire the deposit to the bank account of ABC Fund, LP and that money is then wired to the funds brokerage account. It’s best to require the fund to have a “third party administrator” who acts as the funds controller and accountant. That third party administrator is who accounts for your investment and sends you statements showing the value of your investment. You can probably see why you want the administrator to be a third party – independent from the fund manager. Then, the fund is audited annually to verify the administrators accounting is accurate. When ABC Fund, LP is a private investment partnership, it should be operated like any other major business with multiple investors. It has a bank account that sends/receives wires, a custodian that holds securities, a broker that executes trades, a third party administrator that does the accounting and creates profit and loss statements, and an independent accountant that audits all of it. Those should be separate companies independent of each other, not one.

Unfortunately, most of the smaller scams we hear about are even worse than the Madoff scheme. The investors write a check to “John A. Doe” which isn’t even a company at all. I don’t think any legitimate investment program has you writing a check to the individual portfolio manager. Deposits should be made to an independent bank or custodian and statements should come from that custodian. In fact, it’s even better to wire the funds rather than write a check. But “You can’t fix stupid”. There will always be Madoff-like scams and people stupid enough to write them a check. If you simply require that all the service providers be separate companies you won’t be one of them.

Playing with Words: Education, Knowledge, Skill, Experience, and Expert


The first step to understand something and to draw distinctions between them is to define the words we use. This isn’t always and easy task since many words don’t have a clear definition that everyone agrees on. In fact, I write my own definitions for many of the specialized topics I speak of and list them in the “definitions” pages of this website. I find that thinking deeply about the meaning of a word is useful. That is especially true for me, since I develop and operate quantitative decision making systems and program them to automatically generate the answer. Once I’ve done that, I can operate it across global markets and an unlimited number of securities and do it with a level of precision and consistency not found in humans. When I say “quantitative systematic decisions” that are processed by a computer algorithm, I think many people envision a computer doing everything on its own. That’s because most people don’t develop a program, they use one someone else developed. I’m writing this using Microsoft Word, but I am an operator of Word, but not a developer. It was just there. I don’t think about or understand what went on behind the scenes to create it. What you may not consider is that a human has to tell the computer program what it will do. I create the algorithm, which is a series of processes: if this input, then that output. You can probably see how that series can be a mile long if we’ve thought about possibilities everyday for a decade. To do that requires me to think very deeply about every single detail because software doesn’t know what to do until I tell it. The only way it will fail is if we leave something out and it has no way to move forward – no answer for the input. This gives me a unique advantage from the start: I have probably thought far more deeply about everything I do than those who spend every day trying to figure out what to do next because I am putting my thinking into more than just a trading plan, I’m putting it into a trading system. A computer needs very precise instructions to operate. A human with a “rules-based” plan has a lot of room for error because it doesn’t have to be so precise – they can make it up as they go and do one thing today and another tomorrow.

You can probably see where I am coming from when I do the “play with words”. In this case, we don’t need perfect definitions everyone agrees with to get the point.

What is education? Wikipedia defines education as:

Education in its general sense is a form of learning in which the knowledge, skills, and habits of a group of people are transferred from one generation to the next through teaching, training, or research. Education frequently takes place under the guidance of others, but may also be autodidactic. Any experience that has a formative effect on the way one thinks, feels, or acts may be considered educational.

What is knowledge? Wikipedia defines knowledge as:

Knowledge is a familiarity with someone or something, which can include facts, information, descriptions, or skills acquired through experience or education. It can refer to the theoretical or practical understanding of a subject. It can be implicit (as with practical skill or expertise) or explicit (as with the theoretical understanding of a subject); it can be more or less formal or systematic.[1] In philosophy, the study of knowledge is called epistemology; the philosopher Plato famously defined knowledge as “justified true belief.” However, no single agreed upon definition of knowledge exists, though there are numerous theories to explain it. Knowledge acquisition involves complex cognitive processes: perception, communication, association and reasoning; while knowledge is also said to be related to the capacity of acknowledgment in human beings.

What is skill? Wikipedia defines skill as:

A skill is the learned ability to carry out a task with pre-determined results often within a given amount of time, energy, or both. In other words the abilities that one possesses. Skills can often be divided into domain-general and domain-specific skills. For example, in the domain of work, some general skills would include time management, teamwork and leadership, self motivation and others, whereas domain-specific skills would be useful only for a certain job. Skill usually requires certain environmental stimuli and situations to assess the level of skill being shown and used.

Since we are speaking of skill, let’s also define luck: Luck or chance is an event which occurs beyond one’s control, without regard to one’s will, intention, or desired result. Luck can be good or bad. If skill is what we intentionally do and some degree of control in the outcome from our actions, luck is the part beyond our control. A good rule of thumb is: if you can’t lose on purpose, it’s luck. For example, a roulette table is luck. You can’t win or lose on purpose. Poker is skill-based games were we can apply probability and money management toward a better outcome. If you want to lose, you can.

What is experience? Wikipedia defines experience:

Experience comprises knowledge of or skill of some thing or some event gained through involvement in or exposure to that thing or event. The history of the word experience aligns it closely with the concept of experiment. For example, the word experience could be used in a statement like: “I have experience in fishing”.

The concept of experience generally refers to know-how or procedural knowledge, rather than propositional knowledge: on-the-job training rather than book-learning. Philosophers dub knowledge based on experience “empirical knowledge” or “a posteriori knowledge”.

A person with considerable experience in a specific field can gain a reputation as an expert.

What is an expert? Wikipedia defines an expert:

An expert is someone widely recognized as a reliable source of technique or skill whose faculty for judging or deciding rightly, justly, or wisely is accorded authority and status by their peers or the public in a specific well-distinguished domain. An expert, more generally, is a person with extensive knowledge or ability based on research, experience, or occupation and in a particular area of study. Experts are called in for advice on their respective subject, but they do not always agree on the particulars of a field of study. An expert can be, by virtue of credential, training, education, profession, publication or experience, believed to have special knowledge of a subject beyond that of the average person, sufficient that others may officially (and legally) rely upon the individual’s opinion. Historically, an expert was referred to as a sage (Sophos). The individual was usually a profound thinker distinguished for wisdom and sound judgment.

Experts have a prolonged or intense experience through practice and education in a particular field. In specific fields, the definition of expert is well established by consensus and therefore it is not necessary for an individual to have a professional or academic qualification for them to be accepted as an expert. In this respect, a shepherd with 50 years of experience tending flocks would be widely recognized as having complete expertise in the use and training of sheep dogs and the care of sheep. Another example from computer science is that an expert system may be taught by a human and thereafter considered an expert, often outperforming human beings at particular tasks. In law, an expert witness must be recognized by argument and authority.

Research in this area attempts to understand the relation between expert knowledge and exceptional performance in terms of cognitive structures and processes. The fundamental research endeavor is to describe what it is that experts know and how they use their knowledge to achieve performance that most people assume requires extreme or extraordinary ability. Studies have investigated the factors that enable experts to be fast and accurate

We can now draw a few distinctions here. A person with education is one who has been taught by others or learned from others. Any experience that changes the way one thinks, feels, or acts may be considered educational. You can have an education in investment, trading, and finance, but that may indicate you have gained some knowledge, but not necessarily skill or experience. Knowledge is when we actually understand something and are familiar with it. It seems one way to gain new knowledge is through education – learning from others, researching, etc. Experience comes from the word experiment, so it is knowledge of or skill of some thing gained through involvement in and exposure to that thing. We have experienced it before, or not. Experience can have a wide range of magnitude. Many investors and traders may believe looking at charts for a few hours over a few years makes them experienced. But imagine the difference if they’ve been doing it for several hours a day for two decades. The more experience we have, the more we get in the zone. Experience creates the flow zone: when we have done something so many times we don’t have to think about doing it, we just do. Like driving a car. We don’t think of putting on the brake, but a new driver does. Someone who has an excellent driving record for many years is an expert. Experts have a prolonged or intense experience through practice and education in a particular field. There are different degrees of expert. A professional race car driver is a different level of expert than a person who has just been driving to work every day for years. In racing, you have to be very good to become a professional. In the asset management industry, that isn’t necessarily the case. Investment advisers who work with individual investors often don’t show their potential clients their actual past performance history since they’ve been a professional. They can instead show potential clients performance of something that they didn’t actually invest in when it had good results or even make up past performance with hypothetical and back-tests. A race car driver can’t do that.

I point out these words and draw some distinctions because I am amazed on the magnitude of overconfidence people have when it comes to portfolio management decision-making. For example, I say that I consider an “expert” portfolio manager one who has spent all of his or her time making tactical trading decisions daily for more than a decade and has an excellent actual performance history doing it. This expert has examined well over 10,000 charts with knowledge of how markets interact and how price trends begin and end. An expert portfolio manager developed computer programs designed to define global market trends, separate them out, and enter and exit them while controlling risk systematically.  The expert has been operating those systems with discipline for more than a decade and the outcome from that is his or her good track record.

If we define it that way, then we can get an idea where we fit in regard to education, knowledge, skill, expertise, and experience.

What is “News”?


News is Information not previously known to someone. New information, newly received information, or noteworthy information, especially about recent or important events.

For example:

“I’ve got some good news for you”

“This was hardly news to her”

Do you choose the blue pill or the red pill?


I have been talking to a financial planner recently who is struggling between the red pill and the blue bill.

On the one hand, the poor performance of stock and bond indexes over the past decade or so, particularly the losses in bear markets, led him to study long-term market cycles. An understanding that markets don’t always go up over long periods is the reality of the red pill.

On the other hand, much of the investment industry still believes in getting “market returns” and that a simple plan of “asset allocation” and occasional re-balancing is prudent enough, so a financial planner can choose to keep his practice simple by continuing that plan. Some investment advisers even consider re-balancing and an occasional change “tactical”. It isn’t.

The blue pill and the red pill are opposites, representing the choice between blissful ignorance of illusion (blue) and embracing the painful truth of reality (red).

On the one hand, after understanding the trends of global markets based on simply looking at their history, he realizes the probable outcome of stocks and bonds based on trends I discuss in The S&P 500 Stock Index at Inflection Points and 133 Years of Long Term Interest Rates. Though price trends can continue far more than you expect, the stock and bond markets are at a point that their trends could reverse. The financial planner realizes if he takes the red pill of reality, he’ll have to embrace these facts and do something rather than sit there. He’ll have to change his long-held beliefs that markets are efficient and the best you can do is allocate to them. He’ll have to do extra assignments and homework to find alternative investment managers whose track record suggests they may have the experience and expertise to operate through challenging market conditions.

On the other hand, changing ones beliefs and taking a different approach can be extra work and have risks. If he continues the static asset allocation to stocks and bonds he’s always done, he says he won’t be doing something so different from the majority of advisers. He knows his career and his life will be easier. When the markets go up, his clients make market returns (minus his fees). When the markets go down, other people are losing money too, and he certainly can’t control what the market does, so: it’s the market. I can see how this is an enticing business model, especially for a busy person who has a life outside the office. That’s probably why it’s so popular.

A similar theme of duality happens in the movie The Matrix. Morpheus offers Neo either a blue pill (to forget about The Matrix and continue to live in the world of illusion) or a red pill (to enter the sometimes painful world of reality). Duality is something consisting of two parts: a thing that has two states that may be complementary or opposed to each other. We all get to choose what we believe and our choices shape the world we individually live in.

I can’t say that I can totally relate to the financial adviser because it is my nature to be more tactical and active in decision-making. I believe we should actively pursue what we want. And, I believe what we want from the markets is in there, I just have to extract it from the parts we don’t want. I once explained my investment strategy to a life-long friend and he replied “you have always been tactical” and reminded me of my background. Though it’s different from me, I can truly appreciate the struggle advisers and investors face choosing between the red or blue pill. Investors and advisers like “market returns” when they are positive, which is what we experience most of the time. It’s when those markets decline that they don’t want what the market dishes out. The markets don’t spend as much time in declines. I pointed out in The Real Length of the Average Bull Market the average upward trend for stocks (bull market) lasts 39 months while the average decline ( bear market) is about 17 months. Investors eventually forget and become complacent about the time they need a reminder. Though the stock markets trend up about 3 times longer than they trend down, it’s the magnitude of the losses that cause long-term investors a problem. For example, the bull market from 2003 through October 2007 gained over 105% but the -56% decline afterwards wiped out those gains. You can see that picture in The S&P 500 Stock Index at Inflection Points.

The risk for the financial adviser who has historically focused on “market returns” is that a new strategy for them that applies some type of active risk management is likely to be uncorrelated and maybe even disconnected at times from “market returns”. For example, I discussed that in Understanding Hedge Fund Index Performance. Investors who are used to “market returns” but need a more absolute return strategy with risk management may require behavior modification. If they want an investment program that compounds capital positively by avoiding large losses and capturing some gains along the way they have to be able to stick with it. That requires the adviser to spend more time educating his or her investors about the reality of the red pill. Kind of like I am doing now. Some people have more difficulty doing something different, so they need more help. Others are better able to see the big picture. Some financial advisers would rather deal with explaining the losses when markets decline. For them, it can be as simple as forwarding his or her clients some articles about the market going down with a message something like “We’re all in this together – let’s just hunker down”. That doesn’t require a great deal of independent thinking or doing. While most individual investors probably do lose money when the stock and bond markets do, that isn’t the case for those who direct and control downside risk.

It isn’t enough to have a good investment program with a strong performance history. Just as important is the ability to help investors modify their beliefs and behavior. That is the reality of the red pill. By definition, active is more work that passive. Investors and advisers alike get to choose which pill they take: the blissful ignorance of illusion (blue) and embracing the painful truth of reality (red). I believe in individual liberty and personal responsibility, so the choice is your own. But my thoughts on the subject are directional – I am the red pill.

Morpheus: “You have to understand, most of these people are not ready to be unplugged. And many of them are so inured, so hopelessly dependent on the system, that they will fight to protect it.”

Like The Matrix, this is going to be a sequel.

To be continued… stay tuned.

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The Dow Jones Industrial Average is a Black Box

The black box:

In science and engineering, a black box is a device, system or object which can be viewed in terms of its input and output but without any knowledge of its internal workings. Its implementation is “opaque” (black). Almost anything might be referred to as a black box: a transistor, an algorithm, or the human brain.


The opposite of a black box is a system where the inner components or logic are available for inspection, which is sometimes known as a clear box, a glass box, or a white box.

Almost all investment programs are actually a black box. That is, the investment manager may allow the investor to see the holdings, but most investment strategies have many parts and parameters that are undisclosed to the public or even its investors. There is strong logic behind not disclosing ones intellectual property beyond the obvious. And, it isn’t just about intellectual property, it may be a fiduciary issue, too. When the public knows what a portfolio manager is going to do in advance, other portfolio managers can front-run the trade. Just ask Russell whose indexes are more transparent and we believe they’ve had issues because of it. I think a portfolio manager has an obligation to avoid that. And,  it just makes sense.

We can say the same for stock indexes like the Dow Jones Industrial Average or other Standard & Poors indexes. By now, it is public knowledge that the committee that oversees the Dow Jones Industrial Average has made 6 significant changes to the 30 stocks that make up the index. The Index Committee dropped Alcoa, Hewlett-Packard, and Bank of America, and added Goldman Sachs, Nike and Visa. Did you know in advance they would do that? We didn’t know until after they announced it. Why? because it’s something a committee decided. As we defined above, what is going on in the human brain is a black box. When people are going to make decisions, we can’t determine for sure in advance what the output will be.

Though we can’t actually invest in an index directly, index investors and traders gain exposure to indexes through index funds like exchange traded funds (ETFs). We say that ETFs allow us to gain exposure to a market, sector, country, etc. in a low-cost, transparent, and efficient format. But, the transparency is in regard to the index holdings and maybe the universe they select from, but not necessarily how they decide to add and delete holdings (causing the index ETF we may own to buy and sell the underlying stocks, bonds, etc.).

Is that process a black box? Yes, it is.

We know only parts of the input, we know the output, but we don’t actually know in advance the inner workings of the decision. An index like the Dow Jones Industrial Average is a system that can be understood in terms of its input and output, but not necessarily any knowledge of its internal workings. In the recent case of the Dow Jones Industrial Average, the changes will take effect with the close of trading on Sept. 20th. According to the Wall Street Journal, it was explained in a statement:

“we were prompted by the low stock price of the three companies slated for removal and the Index Committee’s desire to diversify the sector and industry group representation of the index,” S&P Dow Jones Indices LLC, the company that oversees the Dow”

Only the “low price” part of that is rules-based. The Index Committee made the decisions to reflect their desire. That doesn’t seem different from an “Investment” Committee that makes such decisions for a fund or other investment program. It isn’t.

What do you really know about indexes? We know the Dow is a price-weighted index, meaning the bigger the stock price, the larger the position for the stock, and vice versa. That is different from indexes such as the Standard & Poor’s 500, which are weighted by components’ market capitalization. But, we don’t know enough about how the Index Committee makes its decisions to have known in advance what stocks they will change. If we did know that, we could buy the new stocks and sell the outgoing stocks in advance of their announcement. That’s one reason they don’t publish it. However, the black box index goes beyond that. They couldn’t publish it before they decide the changes – they didn’t know either what the output would be until the committee members gave their input. Though many indexes may appear more quantitative (systematic decisions based on predefined rules) they are just as qualitative based on judgement and opinion (an Index Committee makes the decisions, so you don’t actually know what they’ll decide – it isn’t so “rules-based”). My point is: we couldn’t have known the outcome in advance because there was an internal meeting involved to decide.

But an index fund investor doesn’t really need to know this information in advance. Neither does an investor in any investment program. That’s why they are an “investor”. If they are a “portfolio manager” or “trader” they can do it themselves and make their own decisions deciding every little detail. When we choose to invest in any fund, index or not, we necessarily leave part of the process to the deemed expert. In the case of the index, the expert is the index provider like S&P Dow Jones Indices.

The Dow Jones Industrial Average index is totally transparent in regard to its holdings, but a black box in regard to how the additions and deletions are decided.

Stay tuned: I’ll get into this more next week…

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To learn more about the Dow Jones Industrial Average, visit its learning center which shows the Ins & Outs of the Dow since 1896 and read Dow Jones Industrial Average Historical Components.

The REAL Length of the Average Bull Market

How long is the average bull market and bear market?

With the current bull market in stocks at its 54th month, I’ve been hearing several different statistics thrown around lately about the “average” length of historical bear markets. To calculate how long the average uptrend lasts, we have to decide what index represents that stock market and use its most relevant data.

I was telling someone recently what I believe is the correct method to calculate the average bull market cycle. The average bull market lasts about 39 months.

Someone had used the S&P 500 data from Shiller’s database which goes back to 1871 to conclude the average bull market is 50 months. I note two issues with the way they calculated their average.

While that data can be useful for some purposes, we have to understand how the data was compiled and its details. For example, the S&P 500 has been widely regarded as the best gauge of the large cap U.S. equities market, but it was first published in 1957. You may wonder how the Shiller data goes back another 86 years before the index was first published. Other indexes were used and the short story is those indexes used far fewer than 500 stocks, were focused on a few industries, and monthly data wasn’t always available. For example, in Standard Statistics Co. is the predecessor of today’s Standard & Poor’s Corp. In 1926 they developed a 90-stock index that by the 1950s had evolved into the S&P 500. Many people speak of these indexes, but it seems few actually know much about them. You may consider if that index prior to 1957 data is actually relevant enough to understand modern bull and bear markets. If you want, you can visit the data website to fully understand how it was created.

Second, like many others do, they defined bear markets as a 20% decline from a prior peak lasting at least 3 months. They defined bull markets as an advance of 50% or more from the low of a bear market over 6 months or longer. From those definitions and parameters, they conclude the average bull market is 50 months.

I develop and operate quantitative portfolio management systems that I apply to price data to identify potentially profitable price trends and manage risk. In other words, I prefer to have exposure to rising trends and avoid (or short) falling trends. I can tell you from my expertise that one great thing about my process is that it required me to precisely define every single detail. The data, definitions, and parameters that create the decision-making algorithm – which is the process that tells me what to do next. That may give you some idea of how I observe things like this.

I found a similar study by JP Morgan that states the average bull market is a whopping 68 months long going back to 1946. The fine print at the bottom of the chart states they defined a bear market as “a peak-to-trough decline in the S&P 500 Index (price only) of 20% or more. The bull run data reflect the market expansion from the bear market low to the subsequent market peak.” That explains why their bull markets appear so long.

JPM average bull

Source: JP Morgan

While defining bull and bear markets with percentages is popular, it seems to leave out the reality of bull and bear market cycles: a full market cycle. A full market cycle includes both a bull and a bear market period, together. These cycles last about 56 months and some believe it is tied to the business cycle and others believe it may be more connected to politics. A data-driven researcher doesn’t need theory to explain what causes it – it is what it is.

I believe the table below from Ron Griess more accurately represents the average bull market by considering the full market cycle rather than defining them by percentages. The time frame is in weeks, so it shows the average bull market cycle is 155 weeks or about 39 months. The average bear market is about 17 months, which actually matches the most recent bear market from October 2007 to March 2009 (17 months). A full market cycle is 56 months.

Average Length of Bull and Bear Markets


Whatever we believe is always true for us. Whether you believe the average bull market lasts 39 months, 50 months, or 68 months, it seems the current one is likely late in its stage at 54 months as of September 2013.

As the bull market is aging learn about a strategy designed for it visit

Using September to Understand Probability and Expectation.

probabilty coin flip

From 1928-2012 the S&P 500 was up 39 months and down 46 months. It’s down 55% of the time in September…

Dow Jones Industrial Average 1886-2004 (116 years) 49 years the Dow was down, in 67 years the Dow was up. It’s down 58% of the time in September…

Those are probability statements. First, let’s define probability.

Probability is likelihood. It is a measure or estimation of how likely it is that something will happen or that a statement is true. Probabilities are given a value between 0 (0% chance or will not happen) and 1 (100% chance or will happen). The higher the degree of probability, the more likely the event is to happen, or, in a longer series of samples, the greater the number of times such event is expected to happen.

But that says nothing about how to calculate probability and apply it. One thing to realize about probability it that is the math for dealing with uncertainty. When we don’t know an outcome, it is uncertain. It is probabilistic, not a sure thing.

As I see it, there are two ways to calculate probability: subjective and objective.

Subjective Probability: assigns a likelihood based on opinions and confidence (degree of belief) in those opinions. It may include “expert” knowledge as well as experimental data. For example, the majority of the research and news is based on “expert opinion”. They may state their belief and then assign a probability: “I believe the stock market has a X% chance of going down.” They may go on to add a good sounding story to support their hypothesis. You can probably see how that is subjective.

Objective Probability: assigns a likelihood based on numbers. Objective probability is data-driven. The popular method is frequentist probability: the probability of a random event means the relative frequency of occurrence of an experiment’s outcome when the experiment is repeated. This method believes probability is the relative frequency of outcomes over the long run. We can think of it as the tendency of the outcome. For example, if you flip a fair coin, its probability of landing on head is 50% and tail is 50%. If you flip it 10 times, it could land on head 7 and tail 3. That outcome implies 70%/30%. To prove the coin is “fair” (balanced on both sides), we would need to flip it more times. If we flip it 30 times or more it is likely to get closer and closer to 50%/50%. The more frequency, the closer it gets to its probability. You can probably see why I say this is more objective: it’s based on historical data.

If you are a math person and logical thinker, you probably get this. I have a hunch many people don’t like math, so they’d rather hear a good story. Rather than checking the stats on a game, they’d rather hear some guru opinion about who will win.

Which has more predictive power? An expert opinion or the fact that historically the month of September has been down more often than it’s up? Predictive ability needs to be quantified by math to determine if it exists and opinions are often far too subjective to do that. We can do the math based on historical data and determine if it is probable, or not.

As I said in September is statistically the worst month for the stock market the data shows it is indeed statistically significant and does indeed have predictive ability, but not necessarily enough to act on it. Instead, I suggest it be used to set expectations: the month of September has historically been the worst performance month for the stock indexes. So, we shouldn’t be surprised if it ends in the red. It’s that simple.

Theory-driven researchers want a cause and effect story to go with their beliefs. If they can’t figure out a good reason behind the phenomenon, they may reject it even though the data is what it is. One person commented to me that he didn’t believe the September data has predictive value. But, it does.

I previously stated a few different probabilities about September: what percentage of time the month is down. In September is statistically the worst month for the stock market I didn’t mention the percent of time the month is negative, only that on average it’s down X% since Y. It occurred to me that most people don’t seem to understand probably and more importantly, the more complete equation of expectation.


There are many different ways to define expectation. We probably think of it as “what we expect to happen”. In many ways, it’s best not to have expectations about the future. Our expectations may not play out as we’d hoped. If you base your investment decisions on opinion and expectations don’t pan out, you may stick with your opinion anyway and eventually lose money. The expectation I’m talking about is the kind I apply: mathematical expectation.

We have determined above the probability of September based on how many months it’s down or up. However, probability alone isn’t enough information to make a logical decision. First of all, going back to 1950 using the S&P 500 stock index, the month of September is down about 53% of the time and ends the month positive about 47% of the time. That alone isn’t a huge difference, but what makes it more significant is the expectation. When it’s down 53% of the time, it’s down -3.8% and when it’s up 47% of the time it’s up an average of 3.3%. That results in an expected value of -0.50% for the month of September. If we go back further to 1928, which includes the Great Depression, it’s about  -1.12%.

The bottom line is the data says “based on historical data, September has been the worst month for the stock market”. We could then say “it can be expected to be”. But as I said before, it may not be! And, another point I have made is the use of multiple time frames for looking at the data, which is a reminder that by intention: probability is not exact. It can’t be, isn’t supposed to be, and doesn’t need to be. Probability and expectation are the maths of uncertainty. We don’t know in advance many outcomes in life, but we can estimate them mathematically and that provides a sound logic for believing.

We’ve made a whole lot of the month of September, but I think it made for a good opportunity to explain probability and expectation that are the essence of portfolio management. It doesn’t matter so much how often you are right or wrong, but instead the magnitude. Asymmetric returns are created by more profit, less loss. And that provides us a mathematical basis for believing a method works, or not. Not knowing the future; it’s the best we have.

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Here be dragons!

“Here be dragons” means dangerous or unexplored territories, in imitation of the medieval practice of putting dragons, sea serpents and other mythological creatures in uncharted areas of maps.

Most people fully accept paranormal and pseudoscientific claims without critique as they are promoted by the mass media. Here Be Dragons offers a toolbox for recognizing and understanding the dangers of pseudoscience, and appreciation for the reality-based benefits offered by real science. Real science is a process for proving something to have predictive ability through a process of testing.

The video below titled “Here Be Dragons” is an outstanding 40-minute video introduction to critical thinking. Watch it and see how you start to think more critically about what you believe.