(Image: Zen Buddha Silence by Marilyn Barbone.)
February 12, 2017
I’ve always deeply admired both great scientists and great artists. Science and art – each in its own way – attempt to grasp the nature of ultimate reality, or at least the nature of reality as far as we currently can see it. As Einstein wrote in his essay, “The World As I See It”:
The ideals which have lighted me on my way and time after time have given me new courage to face life cheerfully, have been Truth, Goodness, and Beauty. Without the sense of fellowship with people of like mind, of preoccupation with the objective, the eternally unattainable in the field of art and science, life would have seemed to me empty.
The pursuit of truth, goodness, and beauty is really everything that makes life worthwhile. (This includes, by definition, friendship and love.)
As a business person, I hasten to add that having the freedom to pursue one’s passion is obviously essential. As science moves forward and as the world economy evolves, ever more people are gaining a measure of freedom (including better access to healthcare and education). But there is still a long way to go.
What does this have to do with investing? Only that the scientific study of human nature – including biology, genetics, psychology, neuroscience, economics, and sociology – is as fascinating as other areas in science, such as physics and astronomy.
DECISION MAKING UNDER UNCERTAINTY
When people make investment decisions, they are making decisions under uncertainty – decisions where there are unknown future states of the world. Many economists have assumed that people make rational decisions under uncertainty. Most of these economists have held that people always maximize their expected utility. Maximizing expected utility means that people assign a probability and a reward to each possible future state, and then make a decision (e.g., an investment) that will maximize the expected utility. Expected utility is just the sum of each probability times each reward.
Expected Utility Example: Atwood Oceanics
The Boole Microcap Fund bought stock in Atwood Oceanics, Inc. (NYSE: ATW) at $6.46 in late January. Currently, ATW is at roughly $11.70, but it is still probably quite cheap, at least from a 3- to 5-year point of view.
Here is how to apply the expected utility framework. First note that under “normal” economic conditions, the market clearing price of oil is about $60-70. A market clearing price just means a price where the daily supply of oil meets the daily demand for oil. Let’s consider three scenarios, any of which could occur over the next 3 to 5 years, however long it takes for the oil markets to return to “normal”:
- Oil at $55 and ATW earns $3.00 per share. Under this scenario, ATW may be worth $30 per share (a P/E of 10).
- Oil at $65 and ATW earns $4.50 per share. Under this scenario, ATW may be worth $45 per share (a P/E of 10).
- Oil at $75 and ATW earns $6.00 per share. Under this scenario, ATW may be worth $60 per share (a P/E of 10).
Assume that each scenario is equally likely, so there is a 33.3% chance for each scenario to occur. To get the expected value of an investment in ATW today at $11.70, for each scenario we take the probability times the outcome (stock price). Then we add those numbers together. So we have $30 x .333 = $10, plus $45 x .333 = $15, plus $60 x .333 = $20. So we expect ATW to hit $45 = $10 + $15 + $20, and currently we can buy the stock for $11.70. That would be an expected return of almost 300% (or nearly double that if we were lucky enough to buy the stock at $6).
We could adjust the probabilities, oil prices, earnings, and P/E ratio’s for each scenario (as long as the probabilities add up to 100%). We could also decide to use more (or less) than three scenarios.
A Few More Expected Utility Examples
An obvious business example of expected utility is whether a company should invest in Product A. One tries to guess different scenarios (and their associated probabilities), perhaps including one that is highly profitable and another involving large losses. One also must compare an investment in Product A with the next best investment opportunity.
In theory, we can apply the expected utility framework to nearly any situation where the future states are unknown, even life and death.
I don’t think George Washington explicitly did an expected utility calculation. But like many young men of his day, Washington was eager to serve in the military. He had a couple of horses shot from under him. And there were several occasions when bullets went whizzing right past his head (which he thought sounded “charming”). In short, Washington was lucky to survive, and the luck of Washington has arguably reverberated for centuries.
Had Washington been able to do an expected utility calculation about his future war experience, it might have been something like this (crudely):
- 25% chance of death (even when he was a general, Washington often charged to the front)
- 75% chance of honor and wealth
A more realistic expected utility calculation – but not what Washington could have guessed – might have been the following:
- 50% chance of death
- 50% chance of great honor (due to great service to his future country) and wealth
(I’m oversimplifying in order to illustrate the generality of the expected utility framework.)
Von Neumann and Morgenstern
What’s fascinating is that the expected utility framework does a very good job describing how any rational agent should make decisions. The genius polymath John von Neumann and the economist Oskar Morgenstern invented this framework. (For some details on the most general form of the framework, see: https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Morgenstern_utility_theorem)
But ever since, many economists have assumed that people actually do make decisions with full rationality. Economists have argued that rationalist economics is the best approximation for how humans behave.
Others scientists and observers have long suspected (or, indeed, realized) that people are NOT fully rational. But it’s one thing to hold the view that much human behavior is irrational. It’s another thing to prove human irrationality scientifically.
The psychologists Daniel Kahneman and Amos Tversky did hundreds of experiments over the course of decades of people making decisions under uncertainty. What Kahneman and Tversky demonstrated conclusively is that most human beings are NOT fully rational when they make decisions under uncertainty.
Behavioral economics – based on the research of Kahneman, Tversky, and many others – is a fascinating field (and the reason I went to graduate school). But it has not yet developed to the point where its models can predict a wide range of human behavior better than the rationalist economic models. The rationalist economic models are still the best approximation for much human behavior.
THE MAKING OF BEHAVIORAL ECONOMICS
In his great book Misbehaving: The Making of Behavioral Economics (W. W. Norton, 2015), Richard Thaler discusses the development of behavioral economics. According to Kahneman, Richard Thaler is “the creative genius who invented the field of behavioral economics.”
Thaler defines “Econs” as the fully rational human beings that traditional economists have always assumed for their models. “Humans,” on the other hand, are the actual people who make various decisions, including often less than fully rational decisions under uncertainty.
For this blog post, I will focus on Part VI (Finance, pages 203-253). But first, a quotation Thaler has at the beginning of his book:
The foundation of political economy and, in general, of every social science, is evidently psychology. A day may come when we shall be able to deduce the laws of social science from the principles of psychology. – Vilfredo Pareto, 1906
THE BEAUTY CONTEST
Chicago economist Eugene Fama coined the term efficient market hypothesis, or EMH for short. Thaler writes that the EMH has two (related) components:
- the price is right – the idea is that any asset will sell for its intrinsic value. If the rational valuation of a company – based on normalized earnings or net assets – is $100 million, then the company’s market cap (as reflected by its stock price) will be $100 million.
- no free lunch– EMH holds that all publically available information is already reflected in current stock prices, thus there is no reliable way to “beat the market” over time.
NOTE: If prices are always right, that means that assets can never be overvalued (there are no bubbles) or undervalued.
Thaler observes that finance did not become a mainstream topic in economics departments before the advent of cheap computer power and great data. The University of Chicago was the first to develop a comprehensive database of stock prices going back to 1926. After that, research took off, and by 1970 EMH was well-established.
Thaler also points out that the economist J. M . Keynes was “a true forerunner of behavioral finance.” Keynes, who was also an investor, thought that animal spirits – emotions – played an important role in financial markets.
Keynes also thought that professional investors were playing an intricate guessing game, similar to picking out the prettiest faces from a set of photographs:
… It is not a case of choosing those which, to the best of one’s judgment, are really the prettiest, nor even those which average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects average opinion to be. And there are some, I believe, who practice the fourth, fifth, and higher degrees.
DOES THE STOCK MARKET OVERREACT?
On average, investors overreact to recent poor performance for low P/E stocks, which is why the P/E’s are low. And, on average, investors overreact to recent good performance for high P/E stocks, which is why the P/E’s are high.
Having said that, Thaler is quick to quote a warning by Ben Graham (the father of value investing) about timing: ‘Undervaluations caused by neglect or prejudice may persist for an inconveniently long time, and the same applies to inflated prices caused by overenthusiasm or artificial stimulus.’ Thaler gives the example of the late 1990s: for years, Internet stocks just kept going up, while value stocks just kept massively underperforming.
According to Thaler, most academic financial economists overlooked Graham’s work:
It was not so much that anyone had refuted Graham’s claim that value investing worked; it was more that the efficient market theory of the 1970s said that value investing couldn’t work. But it did. Late that decade, accounting professor Sanjoy Basu published a thoroughly competent study of value investing that fully supported Graham’s strategy. However, in order to get such papers published at the time, one had to offer abject apologies for the results. (page 221)
Thaler and his research partner Werner De Bondt came up with the following. Suppose that investors are overreacting. Suppose that investors are overly optimistic about the future growth of high P/E stocks, thus driving the P/E’s “too high.” And suppose that investors are excessively pessimistic about low P/E stocks, thus driving the P/E’s “too low.” Then subsequent high returns from value stocks and low returns from growth stocks represent simple reversion to the mean. But EMH says that:
- The price is right: Stock prices cannot diverge from intrinsic value
- No free lunch: Because all information is already in the stock price, it is not possible to beat the market. Past stock prices and the P/E cannot predict future price changes
Thaler and De Bondt took all the stocks listed on the New York Stock Exchange, and ranked their performance over three to five years. They isolated the worst performing stocks, which they called “Losers.” And they isolated the best performing stocks, which they called “Winners.” Writes Thaler:
If markets were efficient, we should expect the two portfolios to do equally well. After all, according to the EMH, the past cannot predict the future. But if our overreaction hypothesis were correct, Losers would outperform Winners. (page 223)
What did they find?
The results strongly supported our hypothesis. We tested for overreaction in various ways, but as long as the period we looked back at to create the portfolios was long enough, say three years, then the Loser portfolio did better than the Winner portfolio. Much better. For example, in one test we used five years of performance to form the Winner and Loser portfolios and then calculated the returns of each portfolio over the following five years, compared to the overall market. Over the five-year period after we formed our portfolios, the Losers outperformed the market by about 30% while the Winners did worse than the market by about 10%.
THE REACTION TO OVERREACTION
In response to widespread evidence that ‘Loser’ stocks (low P/E) – as a group – outperform ‘Winner’ stocks, defenders of EMH were forced to argue that ‘Loser’ stocks are riskier as a group.
NOTE: On an individual stock basis, a low P/E stock may be riskier. But a basket of low P/E stocks generally far outperforms a basket of high P/E stocks. The question is whether a basket of low P/E stocks is riskier than a basket of high P/E stocks. Furthermore, one can use other metrics such as low P/B (low price to book) and get the same results as the low P/E studies.
According to the CAPM (Capital Asset Pricing Model), the measure of the riskiness of a stock is its correlation with the rest of the market, or beta. If a stock has a beta of 1.0, then its volatility is similar to the volatility of the whole market. If a stock has a beta of 2.0, then its volatility is double the volatility of the whole market (e.g., if the whole market goes up or down by 10%, then this individual stock will go up or down by 20%).
According to CAPM, if the basket of Loser stocks subsequently outperforms the market while the basket of Winner stocks underperforms, then the Loser stocks must have high betas and the Winner stocks must have low betas. But Thaler and De Bondt found the opposite. Loser stocks (value stocks) were much less risky as measured by beta.
Eventually Eugene Fama himself, along with research partner Kenneth French, published a series of papers documenting that, indeed, both value stocks and small stocks earn higher returns than predicted by CAPM. In short, “the high priest of efficient markets” (as Thaler calls Fama) had declared that CAPM was dead.
But Fama and French were not ready to abandon the EMH (Efficient Market Hypothesis). They came up with the Fama-French Three Factor Model. They showed that value stocks are correlated – a value stock will tend to do well when other value stocks are doing well. And they showed that small-cap stocks are similarly correlated.
The problem, again, is that there is no evidence that a basket of value stocks is riskier than a basket of growth stocks. And there is no theoretical reason to believe that value stocks, as a group, are riskier.
According to Thaler, the debate was settled by the paper ‘Contrarian Investment, Extrapolation, and Risk’ published in 1994 by Josef Lakonishok, Andrei Shleifer, and Robert Vishny. This paper shows clearly that value stocks outperform, and value stocks are, if anything, less risky than growth stocks. Lakonishok, Shleifer, and Vishny launched the highly successful LSV Asset Management based on their research. Here is a link to the paper: http://scholar.harvard.edu/files/shleifer/files/contrarianinvestment.pdf
(Recently Fama and French have introduced a five-factor model, which includes profitability. Profitability was one of Ben Graham’s criteria.)
THE PRICE IS NOT RIGHT
If you held a stock forever, it would be worth all future dividends discounted back to the present. Even if you sold the stock, as long as you held it for a very long time, the distant future sales price (discounted back to the present) would be a negligible part of the intrinsic value of the stock. The stock price is really the present value of all expected future dividend payments.
Bob Shiller collected data on stock prices and dividends starting in 1871:
… for each year he computed what he called the ‘ex post rational’ forecast of the stream of future dividends that would accrue to someone who bought a portfolio of the stocks that existed at that time. He did this by observing the actual dividends that got paid out and discounting them back to the year in question. After adjusting for the well-established trend that stock prices go up over long periods of time, Shiller found that the present value of dividends was… highly stable. But stock prices, which we should interpret as attempts to forecast the present value of dividends, are highly variable…. (231-232)
October 1987 provides yet another example of stock prices moving much more than fundamental values. The U.S. stock market dropped more than 25% from Thursday, October 15, 1987 to Monday, October 19, 1987. This happened in the absence of any important news, financial or otherwise. Writes Thaler:
If prices are too variable, then they are in some sense ‘wrong.’ It is hard to argue that the price at the close of trading on Thursday, October 15, and the price at the close of trading the following Monday – which was more than 25% lower – can both be rational measures of intrinsic value, given the absence of news.
IS HUMAN BEHAVIOR INHERENTLY UNPREDICTABLE?
It’s very important to note (again) that although the assumption of rationality and the EMH have been demonstrated not to be true, behavioral economists have not invented a model of human behavior that can supplant rationalist economics. Therefore, rationalist economics, and not behaviorist economics, is still the chief basis by which economists attempt to predict human behavior.
In other words, scientists must learn much more – genetics, neuroscience, psychology, etc. – in order to better predict human behavior. But even then, individual human behavior (to say nothing of group behavior) may remain partly unpredictable for a long period of time.
At the sub-atomic level, most top physicists believe that a part of reality is inherently unpredictable. However, it’s always possible that this “inherent unpredictability” is a result of current limitations in theoretical physics. Once physicists make further advances, it’s at least possible that what is currently “inherently unpredictable” may turn out to be predictable after all. Einstein may be right when it comes to sub-atomic physics: “God does not play dice.”
Similarly with human behavior. What will be the state of genetics, neuroscience, psychology, physics, artificial intelligence, etc. one thousand years from today? Human behavior may be largely predictable. But it then seems to get paradoxical. How could one accurately predict one’s own behavior all the time, given that one could choose to act differently from one’s own predictions? Or, if only a super-advanced artificial intelligence could aggregate enough data to predict all the behavior of a human being, when would it be legal to do so? And who would own the super-advanced artificial intelligence, or would it be a benevolent entity guarding the universe?
In any case, rationalist economic models may continue to be useful for a long time. In fact, rationalist models, including game theory, may also be central to predicting how various artificially intelligent agents will compete against one another.
THE BATTLE OF CLOSED-END FUNDS
In an efficient market, the same asset cannot sell simultaneously for two different prices. Thaler gives the standard example of gold selling for $1,000 an ounce in New York and $1,010 an ounce in London. If transaction costs were small enough, a smart trader could buy gold in New York and sell it in London. This would eventually cause the two prices to converge.
But there is one obvious example that violates this law of one price: closed-end funds, which had already been written about by Ben Graham.
For an open-end fund, all trades take place at NAV (net asset value). Investors can purchase a stake in an open-end fund on the open market, without there having to be a seller. So the total amount invested in an open-end fund can vary depending upon what investors do.
But for a closed-end fund, there is an initial amount invested in the fund, say $100 million, and then there can be no further investments and no withdrawals. A closed-end fund is traded on an exchange. So an investor can buy partial ownership of a closed-end fund, but this means that a previous owner must sell that stake to the buyer.
According to EMH, closed-end funds should trade at NAV. But in the real world, many closed-end funds trade at prices different from NAV (sometimes a premium and sometimes a discount). This is an obvious violation of the law of one price.
Charles Lee, Andrei Shleifer, and Richard Thaler wrote a paper on closed-end funds in which they identified four puzzles:
- Closed-end funds are often sold by brokers with a sales commission of 7%. But within six months, the funds typically sell at a discount of more than 10%. Why do people repeatedly pay $107 for an asset that in six months is worth $90?
- More generally, why do closed-end funds so often trade at prices that differ from the NAV of its holdings?
- The discounts and premia vary noticeably across time and across funds. This rules out many simple explanations.
- When a closed-end fund, often under pressure from shareholders, changes its structure to an open-end fund, its price often converges to NAV.
The various premia and discounts on closed-end funds simply make no sense. These mispricings would not exist if investors were rational because the only rational price for a closed-end fund is NAV.
Lee, Shleifer, and Thaler discovered that individual investors are the primary owners of closed-end funds. So Thaler et al. hypothesized that individual investors have more noticeably shifting moods of optimism and pessimism. Says Thaler:
We conjectured that when individual investors are feeling perky, discounts on closed-end funds shrink, but when they get depressed or scared, the discounts get bigger. This approach was very much in the spirit of Shiller’s take on social dynamics, and investor sentiment was clearly one example of ‘animal spirits.’ (pages 241-242)
In order to measure investor sentiment, Thaler et al. used the fact that individual investors are more likely than institutional investors to own shares of small companies. Thaler et al. reasoned that if the investor sentiment of individual investors changes, it would be apparent both in the discounts of closed-end funds and in the relative performance of small companies (vs. big companies). And this is exactly what they found upon doing the research. The greater the discounts to NAV for closed-end funds, the more the returns for small stocks lagged (on average) the returns for large stocks.
NEGATIVE STOCK PRICES
Years later, Thaler revisited the law of one price with a Chicago colleague, Owen Lamont. Owen had spotted a blatant violation of the law of one price involving the company 3Com. 3Com’s main business was in networking computers using Ethernet technology, but through a merger they had acquired Palm, which made a very popular (at the time) handheld computer the Palm Pilot.
In the summer of 1999, as most tech stocks seemed to double almost monthly, 3Com stock seemed to be neglected. So management came up with the plan to divest itself of Palm. 3Com sold about 4% of its stake in Palm to the general public and 1% to a consortium of firms. As for the remaining 95% of Palm, each 3Com shareholder would receive 1.5 shares of Palm for each share of 3Com they owned.
Once this information was public, one could infer the following: As soon as the initial shares of Palm were sold and started trading, 3Com shareholders would in a sense have two separate investments. A single share of 3Com included 1.5 shares of Palm plus an interest in the remaining parts of 3Com – what’s called the “stub value” of 3Com. Note that the remaining parts of 3Com formed a profitable business in its own right. So the bottom line is that one share of 3Com should equal the “stub value” of 3Com plus 1.5 times the price of Palm.
When Palm started trading, it ended the day at $95 per share. So what should one share of 3Com be worth? It should be worth the “stub value” of 3Com – the remaining profitable businesses of 3Com (Ethernet tech, etc.) – PLUS 1.5 times the price of Palm, or 1.5 x $95, which is $143.
Again, because the “stub value” of 3Com involves a profitable business in its own right, this means that 3Com should trade at X (the stub value) plus $143, so some price over $143.
But what actually happened? The same day Palm started trading, ending the day at $95, 3Com stock fell to $82 per share. Thaler writes:
That means that the market was valuing the stub value of 3Com at minus $61 per share, which adds up to minus $23 billion! You read that correctly. The stock market was saying that the remaining 3Com business, a profitable business, was worth minus $23 billion. (page 246)
Think of it another way. Suppose an Econ is interested in investing in Palm. He could pay $95 and get one share of Palm, or he could pay $82 and get one share of 3Com that includes 1.5 shares of Palm plus an interest in 3Com.
Thaler observes that two things are needed for such a blatant violation of the law of one price to emerge and persist:
- You need some traders who want to own shares of the now publicly traded Palm, traders who appear not to realize the basic math of the situation. These traders are called noise traders, because they are trading not based on real information (or real news), but based purely on “noise.” (The term noise traders was invented by Fischer Black. See: http://www.e-m-h.org/Blac86.pdf)
- There also must be something preventing smart traders from driving prices back to where they are supposed to be. After all, the sensible investor can buy a share of 3Com for $82, and get 1.5 shares of Palm (worth $143) PLUS an interest in remaining profitable businesses of 3Com. Actually, the rational investor would go one step further: buy 3Com shares (at $82) and then short an appropriate number of Palm shares (at $95). When the deal is completed and the rational investor gets 1.5 shares of Palm for each share of 3Com owned, he can then use those shares of Palm to repay the shares he borrowed earlier when shorting the publicly traded Palm stock. This was a CAN’T LOSE investment. Then why wasn’t everyone trying to do it?
The problem was that there were very few shares of Palm being publicly traded. Some smart traders made tens of thousands. But there wasn’t enough publicly traded Palm stock available for any rational investor to make a huge amount of money. So the irrational prices of 3Com and Palm were not corrected.
Thaler also tells a story about a young Benjamin Graham. In 1923, DuPont owned a large number of shares of General Motors. But the market value of DuPont was about the same as its stake in GM. DuPont was a highly profitable firm. So this meant that the stock market was putting the “stub value” of DuPont’s highly profitable business at zero. Graham bought DuPont and sold GM short. He made a lot of money when the price of DuPont went up to more rational levels.
In mid-2014, says Thaler, there was a point when Yahoo’s holdings of Alibaba were calculated to be worth more than the whole of Yahoo.
Sometimes, as with the closed-end funds, obvious mispricings can last for a long time, even decades. Andrei Shleifer and Robert Vishny refer to this as the limits of arbitrage.
THALER’S CONCLUSIONS ABOUT BEHAVIORAL FINANCE
What are the implications of these examples? If the law of one price can be violated in such transparently obvious cases such as these, then it is abundantly clear that even greater disparities can occur at the level of the overall market. Recall the debate about whether there was a bubble going on in Internet stocks in the late 1990s….
Despite many market inefficiencies, the EMH – a part of rationalist economics – is still very useful:
So where do I come down on the EMH? It should be stressed that as a normative benchmark of how the world should be, the EMH has been extraordinarily useful. In a world of Econs, I believe that the EMH would be true. And it would not have been possible to do research in behavioral finance without the rational model as a starting point. Without the rational framework, there are no anomalies from which we can detect misbehavior. Furthermore, there is not as yet a benchmark behavioral theory of asset prices that could be used as a theoretical underpinning of empirical research. We need some starting point to organize our thoughts on any topic, and the EMH remains the best one we have. (pages 250-251)
When it comes to the EMH as a descriptive model of asset markets, my report card is mixed. Of the two components, using the scale sometimes used to judge claims made by political candidates, I would judge the no-free-lunch component to be ‘mostly true.’ There are definitely anomalies: sometimes the market overreacts, and sometimes it underreacts. But it remains the case that most active money managers fail to beat the market…
Most investors agree with Thaler on the no-free-lunch component of the EMH. In practice, it is very difficult for any investor to beat the market over time.
But do prices always accurately reflect intrinsic value?
I have a much lower opinion about the price-is-right component of the EMH, and for many important questions, this is the more important component…
My conclusion: the price is often wrong, and sometimes very wrong. Furthermore, when prices diverge from fundamental value by such wide margins, the misallocation of resources can be quite big. For example, in the United States, where home prices were rising at a national level, some regions experienced especially rapid price increases and historically high price-to-rental ratios. Had both homeowners and lenders been Econs, they would have noticed these warning signals and realized that a fall in home prices was becoming increasingly likely. Instead, surveys by Shiller showed that these were the regions in which expectations about the future appreciation of home prices were the most optimistic. Instead of expecting mean reversion, people were acting as if what goes up must go up even more.
Thaler adds that policy-makers should realize that asset prices are often wrong, and sometimes very wrong, instead of assuming that prices are always right.
BOOLE MICROCAP FUND
An equal weighted group of micro caps generally far outperforms an equal weighted (or cap-weighted) group of larger stocks over time. See the historical chart here: http://boolefund.com/best-performers-microcap-stocks/
This outperformance increases significantly by focusing on cheap micro caps. Performance can be further boosted by isolating cheap microcap companies that show improving fundamentals. We rank microcap stocks based on these and similar criteria.
There are roughly 10-20 positions in the portfolio. The size of each position is determined by its rank. Typically the largest position is 15-20% (at cost), while the average position is 8-10% (at cost). Positions are held for 3 to 5 years unless a stock approaches intrinsic value sooner or an error has been discovered.
The goal of the Boole Microcap Fund is to outperform the Russell Microcap Index over time, net of fees. The Boole Fund has low fees.
If you are interested in finding out more, please e-mail me or leave a comment.
My e-mail: firstname.lastname@example.org
Disclosures: Past performance is not a guarantee or a reliable indicator of future results. All investments contain risk and may lose value. This material is distributed for informational purposes only. Forecasts, estimates, and certain information contained herein should not be considered as investment advice or a recommendation of any particular security, strategy or investment product. Information contained herein has been obtained from sources believed to be reliable, but not guaranteed. No part of this article may be reproduced in any form, or referred to in any other publication, without express written permission of Boole Capital, LLC.