Market Hypothesis: Can I Get Rich by Chance
- Spencer
- Jun 21, 2024
- 7 min read
How to Read This Article
All research projects at GVR are meant to be digestible by both beginners and advanced readers. In order to achieve this, no definition is given in the text body itself. Instead, all concepts and words that I believe need explaining are bolded, italicized, and subscripted[1]. At the bottom, there is a definition and concepts page. I recommend having this open on two tabs. One will be for the reading portion, and the other with the definitions open so you can quickly pan back and forth without having to scroll annoyingly.
This is a "hypothesis" article. My goal is to structure it like an experiment. The article will be organized in the following way, with the following possible sections:
Article Structure
Hypothesis:
All of my testing starts with a question. Some come from observation, and others from reading white papers (if there were black/brown papers I would read those too, calm down) and academic publications. I'll start the email with the question I hope to answer
Testing Methodology:
How are we going to define the question and test it?
Results:
What have we found? Did we confirm or deny others research?
Discussion:
Explain the results and any interesting insights
Economic Concepts:
What are some economic concepts that would be important to understand when testing this theory? What explanations do economists give?
Math / Stats Concepts:
In testing this idea, what concepts from math and stats can we incorporate to ensure the integrity and validity of the test?
Coding Concept:
What interesting techniques can we employ to test it faster, better, more efficiently, etc.
Financial Markets Concept:
There are some ideas that have more to do with financial markets nuance than overarching economic principles. If they apply to our situation, what are they and how are we taking advantage of them?
Trading Concept:
Just like the Financial Markets and Economics Concepts, there are some ideas that are purely short term in nature, and have more to do with market microstructure and timing than sound economic and financial concepts. Although largely a big bag of lies, there are things that can be gleaned from those concepts. If any apply, they will be here.
Further Testing:
Did this hypothesis spark more ideas? How can we change our current test or definitions to test slightly different phenomena? Can we break down the idea further to better understand the game we are playing?
Reference Papers:
Links to the publications and media you can go to to learn more about any of the mentioned concepts.
Definitions:
Part of my hope is that anyone can read these no matter your familiarity with stupid financial lingo. Half the battle of being able to effectively read market publications is understanding the absurd language they speak. I'm hoping to write these emails as 'financy' as possible, but put definitions in the bottom so that anyone can begin to get comfortable with terminology that they will see outside of these
Question / Hypothesis
What are the chances that someone performs extremely well in the stock market by simply being lucky? If someone claims to be outperforming the market, how can I know if that is truly the case?
Testing Methodology
I chose to simulate two different random portfolios. One where the returns over a randomized number of stocks were averaged together to give the idea of a portfolio[1]. The other was just a randomized investment into individual stocks. The portfolio simulation was done assuming a random number of stocks from the S&P500 were chosen, with random number of trades being taken for each chosen company in the portfolio. The timing of the trades were also randomized. This process was repeated 50,000 times, with a total of 10M simulated stock investments, and somewhere around 500M simulated trades. In order to randomize returns, a few design decisions were made. 1. Should the portfolio be allowed to take short positions, or only long? In order to maintain simplicity, I chose to have a long only bias. 2. What stocks are you going to test on? I chose the S&P500. I didn't use delisted[2] stocks in this test, because investing in an index means that there is active management only allowing the best companies to trade in it. By investing in the S&P500, the issue of survivorship bias is less of an issue. (I will admit, I was also concerned with computation time, so this decision is up for judgement as to whether or not it was a good call). 3. Should there be a maximum number of trades allowed? A concern of mine was if there were too many trades taking place, and if I should cap it at x number of trades per week. I decided to not cap it, but run the simulation enough times that it would get a good mix of active and passive trading strategies. 4. Should I include trading costs? I've selected not to include any trading costs, due to the variety in them depending on brokerage, as well as many brokers offering commission free trading. It also sets a higher bar, and therefore a more conservative estimate when benchmarking portfolio performance. I'm not entirely sold on this decision though. Similar design decisions were made for the single stock portfolio simulation. I ran 1.7M different trade configurations for that.
RESULTS:
After running 1.7 million simulations, the average single stock return was 25.6%, with a standard deviation[3] of 49.07%. This means that to beat randomness assuming the veracity of a single stock portfolio, you would need to return at least 123% over 10 years. (an important caveat to remember is that these returns are nominal[4].)
After running 50,000 portfolio simulations, there was an average return of 65%, with a standard deviation of 15%. This means that you would need to return 95% over ten years to beat a random portfolio.
DISCUSSION:
There was obviously much bigger variation in the returns of a single stock portfolio. (as measured by standard deviation). The maximum return simulated was a 25,000% return trading a single stock. While obviously an outlier, it does beg the question of how many years an outstanding performance must be repeated to be indicative of actually good performance. Obviously that return was due to dumb luck because it was randomly generated. According to all of our analysis however, that return should not be possible by chance. (Food for thought)
MATH & STATS CONCEPT:
To understand the significance of this question, we need to understand the concepts of a standard deviation, and normality.
Standard Deviation: A standard deviation is a measure of how far away something is from its average. For example, let's say the average weight of a newborn is 7.5 pounds, with a standard deviation of 2 pounds. If you birth an absolute monster at 11.6 pounds, then you would say that baby is '2 standard deviations away from the mean.' I know it sounds like a dumb thing to know, but the reason it's useful is that it also gives us a way that we can measure how rare something is. How rare is it to have a baby that is 11.6 pounds? Standard deviations give us a way to answer that question. (another question it can answer, is how rare is it to achieve a 250% return over 10 years as we saw in the last analysis?) However, in order to use the standard deviation, we need a condition called normality.
Normality: Everywhere you look. you can find recurring patterns in nature. One such pattern is called 'normality.' How can you tell if data is normal? Let's say you weigh 100,000 babies and track how often each weight occurs. If the data is normal, then you would have a more or less equal number of babies on each side of the average, with the majority of the weights being right around 7.5 pounds. This is where the idea of a standard deviation comes in. If the data follows this symetric shape of most of the data being around the mean, then we have a way of classifying how likely something is to occur. We measure that likelihood in 'standard deviations away from the mean.' The rule of thumb is that 95% of the data should fall within two standard deviations from the mean. In our baby weight example, this means that 95% of all babies born are going to be between 3.5 pounds and 11.5 pounds. So how likely is it to have a baby born at 11.6 pounds? If 95% of all baby weights are between 3.5-11.5, then there is less than a 5% chance of birthing a baby that heavy! (it's actually less than 2.5%, but I'll let you figure out why) We can use these principles to simulate a bunch of different portfolios, find out the average (mean) and then calculate the range of 2 standard deviations above the average. Once calculated, we now have a meaningful number to say "I want to know, with 95% confidence, that the person I am giving my money to is better than dumb luck."
TRADING CONCEPTS:
We are always hearing that we should diversify our portfolio. Why is that? Well putting any theories aside, this experiment shows us the benefits beyond just "not putting all your f*king eggs in one basket." Even though these stocks aren't necessarily "diversified" (Mind you these were all stocks in the S&P500, which have a some correlation[5] by nature) but even spreading out between random stocks in the same index, we increased our average return, and lowered our volatility[6]. The trade off was that we didn't get that huge score of 25,000%, but over the long run, trading a basket[7] of securities was much more lucrative than just trading single stocks.
FURTHER TESTING:
Something not explored is how much variation these random portfolios exhibit on a year to year basis. What would happen if we averaged yearly returns instead of over 10 years. Would our outcomes be wildly different? This is something you might try at at home.
Definitions and Concepts
Portfolio
Another fancy way of saying a collection of stocks you own. If you buy Amazon and Apple stock, you have created a two stock portfolio.
Delisted
A delisted stock is one that has been taken off the public markets for one reason or another. The reasons can vary, anywhere from the company buying back all of the shares, to a company going out of business
Standard Deviation
See the section on math concepts
Nominal
Unadjusted for inflation.
Let's say you earn 1 dollar a month, and all you ever need to buy is butter. Right now in this fiction world, butter is priced at 1 dollar. Next year, you are expecting a raise of 2%, which means you earn a whopping $1.02 per month! Now let's say that butter also went up in price by 2%. Since all you buy is butter, your ability to purchase more butter with your raise is off set by the fact that butter has become more expensive. Last year you could buy one stick per month, and this year you can still only buy one stick per month. Your 2% raise is a "nominal" value. If you adjust it for inflation, you received a raise of 0%, because your purchasing power didn't change.
Correlation
A measure of how closely two variables follow each other. For example, if you were tracking someone's height and weight overtime, you would expect them both to grow and change together, or in other words, you would expect them to be highly correlated. When analyzing stocks and creating a portfolio, you generally want to invest in companies that are NOT correlated. The reason is that if you were to invest in company A and B, and they were both perfectly moving together, then you would have essentially just bought one stock with two different names.
Volatility
A measure of how much a stock bounces up and down. Generally seen as bad, because one day you can be up a lot, and another you can be down a lot on your investments. What happens if you need to sell your stock on a down day? Then you are out of luck. For this reason people tend to prefer less volatile and more smooth stocks. It's easier on the nervous system.
Basket
Just another way to say group or portfolio.
Mean: average
DISCLAIMER:
The information provided is for informational purposes only and does not constitute financial, investment, or other advice. The content is based on our analysis and opinions, which are subject to change without notice. We make no representations or warranties regarding the accuracy, completeness, or timeliness of the information provided. Past performance is not indicative of future results. Always conduct your own research and consult with a qualified financial advisor or investment professional before making any investment decisions. We disclaim any liability for any loss or damage incurred as a result of the use of the information contained in this email.
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