Three lessons in twelve pages

(see below to know the nice history of this unusual post hosted on my blog)

Luke Chung

Three Lessons in Twelve Pages from Financial Markets 1

The Power of Compounding

We began our venture into the world of financial markets by exploring compounding and its relationship with capitalization and the present value of an asset. Compounding is based on the mathematical formula (1+i)^n where n is the number of periods and i is the interest rate. In essence, compounding relies on the notion that interest is able to earn interest. This principle was once called by Einstein "the eighth wonder of the world." So why is it so important? 3

Suppose we lend money at a compounding rate. Then we will receive interest after the first period passes, which will then be added to the amount of money we will receive interest on in the next period. This contrasts with simple interest where we would receive the same amount of interest for each period. While compounding may not seem that powerful, a few statistics can dissuade this notion. Suppose we invest $1000 at an interest rate of 10%. If our investment is compounded annually, we will have $1610.51 after five years. If we invested at a simple interest rate we would have $1500. Therefore, we would have made an extra $110.51. This may not seem like much, but when looking at a long term investment over a 20 year period the benefits of compounding become more apparent. After 20 years, we would have $6727.50 with compounding as opposed to $3000 with simple interest. This equates to a difference of $3727.50, or 3.7 times the initial investment! The power of compounding lies in the fact that the difference between investing at a compounding versus simple rate increases exponentially with time. For younger people, such as my peers and myself, the importance of compounding is heightened, as we are looking to invest across longer time horizons. 4

If the empirical evidence for compounding wasn't convincing enough, the realization that compound capitalization formed the foundation for the course should suffice. The textbook highlights how one major benefit of compounding is that "compound capitalization allows decomposing financial operations by inserting intermediate moments without altering financial equivalence." We applied this principle in multiple ways, including creating amortization schedules, which are vital for calculating repayment of loans. In addition, the rule of 72, which states that the number of time periods to double an investment is roughly equal to dividing 72 by the interest rate across the period, is based on a compound capitalization. Take for instance an investment made at an interest rate of 10% - approximately the average annual return of the S&P 500 since 1957. Using the rule of 72, we find that the investment will double in a little over 7 years (7.2 years to be exact). The actual value is 7.273 (rounded to three decimal places), so the rule of 72 is generally a great estimate. Now if the investment was made at simple capitalization, this rule breaks down. This investment would take 10 years to double, which is almost three years or 37.5% longer than the time it would take for the investment at a compounding rate to double! Amortization schedules and the rule of 72 are two of many examples of important concepts in finance based on the principle of compounding. 

A final argument for the power of compounding lies in the historical context surrounding this concept. Interestingly, the textbook includes an excerpt from Jacques Le Goff's book, The Devil's Dung: Money in the Middle Ages, in which Le Goff writes: 6

The Church attacks the practice of lending for interest by defining it as a very grave sin, a true death of the soul. Money cannot beget money, and therefore profit that exceeds the initial loan is considered usury. (...) The usurer aims to earn without working, even while sleeping; this goes against the Lord's command.
Usury was a concept we touched on through visiting the Monte di Pieta exhibit and learning about the Medici family's methods to turn a profit even though lending at a non-zero interest rate was prohibited by the Catholic Church. Le Goff's excerpt highlights the core principle of why compound capitalization is powerful: money is able to "beget money." The Church saw compound capitalization as sinful, but they weren't the only institution to condemn usury. For example, Wayne A.M. Visser and Alastair McIntosh explain in A Short Review of the Historical Critique of Usury that usury was criticized in Islam and "by the time of Caliph Umar, the prohibition of interest was a well established working principle integrated into the Islamic economic system." The book Interest Rates and the Law: A History of Usury provides more examples of how "few practices have been so universally abhorred as usury" such as "the Roman senator Cato report[ing] that it was less disrespectful to have your father considered a thief than a usurer" and "Seneca considered it comparable to slow murder." Interest, especially interest on interest - compounding - was considered, in the words of the textbook, "diabolical." Hopefully the historical perspective of the power, albeit evil power in their view, of compound capitalization is persuasive.

Compounding isn't only a significant force in investments, but in most aspects of life in general. A prime example of this is the acquisition of knowledge, or "compound learning." Author and start-up analyzer Thomas Oppong explains that "knowledge begets knowledge." In other words, as one learns new skills, this enables them to learn more skills, creating a snowball effect. One of the most basic examples of this is learning math. As an individual progresses from learning addition and multiplication to algebra and calculus, they are stacking skills. Without understanding addition, calculus isn't possible. Calculus has broad applications across engineering, economics, and many other disciplines. Thus, learning concepts and skills opens doors to new opportunities, essentially demonstrating exponential growth characteristic of compounding. 9

One relevant application of compound learning today is with machine learning and artificial intelligence. Gartner, a technological consulting firm, describes how "compound learning comes as the Al software learns from each interaction and the algorithms improve over time." Gartner continues to highlight the importance of compound learning in machines by explaining how all "robots from one vendor can share knowledge and grow collectively." Therefore, compound learning isn't only a concept humans can utilize but will be important for the future of improving machine learning and artificial intelligence technologies. 

Finally, let's analyze compounding through another lens. Upon researching compounding, I stumbled upon a poem titled "Just a Drop" by Dallin Candland. Candland writes in the opening stanza:

Just a drop of kindness can lead to an ocean of hope Just a drop of forgiveness can lift a soul struggling to cope Just a drop of courage can set the captive free Just a drop of peace can help me to feel more like me

He continues to explain applications of the ripple effect, which is basically another term for compounding. The idea that "a drop of kindness can lead to an ocean of hope" isn't just an artistic, poetic line, but backed by science. Researchers at the Stanford Social Neuroscience Lab found that kindness is actually contagious, meaning that if you see or are the subject of an act of kindness, you are more likely to spread it. This effect of "paying it forward" is yet another example of the power of compounding outside of a financial context. To summarize, we should understand that compounding is a powerful idea that we can take advantage of, not only when looking to invest financially, but also when looking to invest in our pursuit of knowledge or in making the world a happier place.

The Importance of Diversification and Calculated Risk

My presentation focused on diversification and managing risk. First, it was important to lay out the facts about diversification. Figure 6.2 from the textbook shows how diversification within a single financial asset (in this case stocks) can reduce the risk of a portfolio. Adding more stocks in a portfolio composed of only stocks reduces the risk of the subsequent portfolio compared to a single stock portfolio. The reason for this is because diversification within one type of financial asset helps eliminate unique risk - the risk faced by an individual company. For example, a portfolio that only consists of Chipotle stock will be fully exposed to the risk of a salmonella outbreak, versus a portfolio of Chipotle, Apple, and Walgreens, which is much less exposed to this "unique risk." 

While diversifying within a single financial asset reduces risk, risk is further reduced when diversifying among multiple asset classes. Figure 6.1 showcases how a portfolio faces unique risk and market risk. The latter is risk that can be mitigated through a portfolio of different types of assets. One important realization is that diversification among more types of assets reduces risk as long as the assets aren't perfectly correlated. Mathematically, this equates to the correlation coefficient, rho, not being equal to one in the variance equation. An eye-opening example is the thought of being able to reduce risk by investing in riskier assets. For example, we saw in class how the minimum variance portfolio for investing in stocks and bonds is a combination of both of the assets, not simply investing in bonds (the less risky of the two). The textbook explains the intuition behind this as "in a recession, stocks fare poorly, but this is offset by the good performance of the bond fund. Conversely, in a boom scenario, bonds fall, but stocks do well. Therefore, the portfolio of the two risky assets is less risky than either asset individually." Therefore, we can conclude that to reduce risk, it's important to diversify across multiple asset classes and within the individual asset classes.

Following the overview of how diversification reduces variance, I expanded on investment strategies and their relation to diversification. We started with a brief analysis of day trading, which has gotten extremely popular over the last couple years, especially through social media platforms. However, even though daytrading may seem appealing because of its fast paced and exciting nature, the average investor should stay away from it. A UC Berkeley study found that 80% of day traders lose money and 75% of professional day traders quit within two years. Evidently, these statistics indicate that daytrading is rarely a profitable endeavor, much less one that consistently beats the market. It's also important to recognize that the top day traders spend considerable amounts of time and effort to turn a profit and still rely on luck.

While day trading is clearly a venture to avoid, less obvious are the pitfalls of investing in active management. An article from CNBC describes how "Every year, S&P Dow Jones Indices does a study on active versus passive management. Last year, they found that after 10 years, 85% of large-cap funds underperformed the S&P 500, and after 15 years, nearly 92 percent were trailing the index." To summarize, active management rarely outperforms the market. The article even states that active management "is bad and it's getting worse." A cool story related to the superiority of passive management in most cases is that in 2007 Warren Buffett bet hedge fund manager Ted Seides one million dollars that an S&P Index fund would outperform a basket of hedge funds in 10 years and he was right. Thus, it's best to avoid active management as well.

I went on to discuss why it's generally not a great idea to pick individual stocks and try to time the market. A Forbes article states that "A JPMorgan report found that if investors missed the top 10 best days of investing over a two-decade period from January 1999 to December 2018, it cut their portfolio return in half. If investors missed the top 20 best investing days, their return turned negative, meaning that they lost money over that two-decade period." Trying to time the market and consequently missing out on the best investing days can be extremely costly. Also consider the positive market sentiment leading up to the Great Depression. The problem with hand picking individual stocks is that it goes against the importance of diversification in reducing risk, as we described earlier. It's difficult to predict the future for individual stocks, and to illustrate this, we can think about what happened with GameStop.

We also touched on portfolio allocation and lump-sum versus dollar cost averaging investing. Theory tells us to hold a combination of risk free assets and a portfolio of all possible risky assets, which we termed "O." We learned that while it is virtually impossible to actually invest in "O," index funds that track things like the Russel 3000 or the MSCI world index. I explained some typical asset allocation rules, such as the rule of 110 where an individual subtracts their age from 110 to get the percentage of stocks they should hold. I also touched on Ray-Dalio's All Weather Portfolio designed to mitigate large losses through diversification among commodities, gold, stocks, and bonds. In regards to lump-sum versus dollar cost averaging, the main benefit of lump-sum investing is that we take into account the opportunity cost of holding cash, which generally leads to higher returns. However, dollar cost averaging is better for a more risk averse investor that wants to take emotion out of their investment strategy and maintain a constant routine. The main takeaway should be to practice either of the philosophies, but do so in the context of investing in a diversified portfolio that likely includes low fee ETFs. 

What I wanted to spend longer on, and the second lesson to take away from financial markets and apply in a broader context, is the importance of taking calculated risks. Calculated risks are especially important for younger people as they have more time to overcome potential failures. It's important to stress intelligent risk-taking because of how much emphasis we place on reducing risk through diversification. While we don't want to encourage unnecessary risk taking, we want to also avoid encouraging latency due to excessive risk aversion.

One of, if not the most important theory in behavioral economics is called prospect theory. It was developed by Nobel Prize winners Daniel Kahneman and Amos Tversky and confirmed by Columbia researchers in 2020. They describe how "For most people, the fear of losing $100 is more intense than the hope of gaining $150," which is called loss aversion. This leads the average person to be risk averse. Risk aversion isn't inherently good or bad; one can be risk averse and still take risks when the payoff is high enough, and there are numerous benefits to taking risks. A UCLA study found that "a surprising or unexpected reward causes an extra dopamine release. So every time we do something with an uncertain outcome-taking a "risk" increased dopamine is released while we are determining what happens." Furthermore, the Milwaukee Journal states that "Most procrastinators are what we call "risk averse." Brain studies show they are more likely to have a fear center in the brain (amygdala) that is both larger and more active than folks who are doers. So risk-taking has neurological benefits and procrastination is tied to risk-aversion. Procrastination is bad in the context of studying, but terrible when we think about long-term procrastination on things with no deadlines like getting in shape. Being too risk averse should not be taken lightly.

Broadening the scope even further, we should understand that without risk-taking, innovation and advancement is hindered greatly. By stepping out of our comfort zone, we are inevitably introducing the potential for failure, but also allowing for the possibility of discovery. The Journal of Labor Economics describes how risk-taking has led to success. They say "the empirical results suggest that the returns to human capital investments are much higher among college-educated workers who are risk takers." In short, risk-taking has led to better self improvement and gain. Finally, to provide a more emotional appeal, by diversifying across many fields and taking risks, one becomes a more interesting, well-rounded, and cultured person. Therefore, diversification and intelligent risk taking isn't only important when investing, but also for one's character, or should I say, human portfolio.


Looking to the Long Term

In the study of financial markets, the importance of considering time cannot be understated. As students, we must understand that time is on our side (one of the most entertaining moments from the course was seeing my life expectancy). An Investopedia article on age as a factor in investment strategy explains that "An investor's age affects how much risk they can take on. A young investor can seek out bigger returns by taking bigger risks. This is because if a young investor loses money, they have time to recover the losses through income generation." This idea is the foundation for portfolio allocation philosophies like the Rule of 110 which we explained earlier. In addition, making meaningful returns and to maximize the power of compounding, having a long term investment horizon is vital. As previously explained, the benefits of compounding increase exponentially with time. 

Investing over the long term is also important for reducing risk. I spent the last couple paragraphs arguing that taking calculated risk and investing over the long term is one way a more risk averse individual can be persuaded to invest in riskier assets like stocks. A McKinsey article states, "Short-term measures of volatility can fluctuate wildly. But over the long term the market has been remarkably stable." With increased volatility in the short term, there is increased risk, but as the article explains, volatility decreases when investing across a longer time horizon. Let’s backtrack and go over important facts about volatility. According to Investopedia, volatility is “a measure of the variance bounded by a specific time period.” Therefore, volatility is inherently tied to variance and in turn, diversification and risk. Riskier assets tend to be more volatile as there is a greater standard deviation of returns because these types of assets are capable of producing large gains or large losses. For example, we saw in class and in our textbook that small cap stocks tend to have higher variance. Investopedia provides a reason for this, saying, “Large caps tend to be more mature companies, and so are less volatile during rough markets as investors fly to quality and become more risk-averse.” This makes sense because in times of economic downturn, the companies that individuals should be most worried about suffering massive losses are smaller companies that aren’t able to weather the storm as well as more established ones. 29

The size of companies isn’t the only factor in affecting volatility, another factor is the type of company. Different sectors have varying levels of volatility. An article from Markets Insider on the most volatile sectors explains that “technology, known for its innovation and rapid growth, is often the epicenter of market volatility. Investors in FAANG and other tech have experienced significant price swings over the years. This is due to many factors, not the least of which is the rapidly changing nature of tech itself.” To summarize, technology tends to be one of the most volatile sectors in the market because of how the sector is based on innovation, growth, and change. In addition, investors in tech tend to be looking for high returns because they feel they are able to predict the next groundbreaking technology. Also, trends and hype surrounding the technology sector increases volatility. The NASDAQ tends to be more volatile than the S&P 500, and one of the reasons for this is because the NASDAQ is tech heavy. 

Now that we have outlined basic principles surrounding volatility, we can revisit how volatility and risk decrease with a long investment horizon to support the argument that time is on our side. A Morgan Stanley article titled “Good Things Come to Those Who Wait: An Argument for Long-term Thinking” does a phenomenal job of providing statistics to demonstrate the benefits of long term investing. For example, the article states, “If you were to invest in the MSCI World Index between 1970 and 2023, 23% of months were negative for a one-year investment horizon, whereas the negative return figure drops to 11% on a five-year view and just 3% for 10-year periods.” It goes on to argue against timing the market with similar examples to the ones I gave earlier in this paper. Clearly, the risk of losing money decreases when investing over many years as opposed to a month for example. An easy way to see this is to look at charts of the S&P 500 or most other market tracking index. Zooming in on a specific month will likely show many peaks and troughs; however, zooming out will show consistency. Expanding on the previous example, something that is probably familiar is when headlines will read DOW falls X amount of points when there is a large downturn in a given day. In the short term, these declines seem major, but in the long term, they will represent a small dip in an overall upward trend (if we are speaking about a well-diversified market-tracking ETF), as long as the decline or gain isn’t super major (like in the case of COVID or 2008 Financial Crisis). 

Investing in stocks and bonds is just one of the ways where we must take time into account. I will briefly touch on an important concept: the opportunity cost. Opportunity cost refers to the cost of the next best alternative. In financial markets, opportunity cost is closely tied with time. For starters, there is an opportunity cost of holding cash, which is the zero-risk rate because instead of getting no return on our cash, we could be investing in zero-risk assets and getting a premium. This cost increases exponentially the longer you hold cash (due to how the return you would be getting compounds). Therefore, one should be focused on investing for a long period of time, but also not waiting to invest, as by investing sooner rather than later, the investor reduces risk by having a longer term investment, but also reduces the opportunity cost of not investing at all. 

Volatility may be the most applicable financial concept to life that encapsulates the other two lessons provided earlier. Some of the most important qualities that we associate with successful athletes, revolutionaries, and business people are intrinsically connected to continuous long term growth despite short term failures. Numerous CEOs have spoken on how they have gone bankrupt or experienced major setbacks, yet persevered over time to achieve long term goals. Perhaps a more relatable example may be practicing a sport or learning to play an instrument. While each day you may not notice much improvement, or even believe you are getting worse, looking back over the long term usually tells a different story. This is why many Psychologists emphasize the importance of long term goal setting, but having short term checkpoints to reach. 

Two of the most important concepts in strength training are muscular failure and progressive overload. According to Healthline, “Progressive overload is when you gradually increase the weight, frequency, or number of repetitions in your strength training routine. This challenges your body and allows your musculoskeletal system to get stronger.” Strength training involves pushing your body close to muscular failure in order to make your body adapt to get stronger. Professional bodybuilders and powerlifters have explained that in the short-term many workouts may feel better or worse than others, but across a longer time horizon, they see progression. Thus the ideas of having a long term investing horizon and short term volatility are applicable not only to mental improvement, but also physical. 

I will leave the reader with a quote from Atomic Habits written by James Clear and one of the most popular self-improvement books today. Clear writes, “Making a choice that is 1 percent better or 1 percent worse seems insignificant in the moment, but over the span of who you could be. Success is the product of daily habits—not once-in-a-lifetime transformations.” While choices we make today may seem minor, or setbacks may seem insurmountable, making small amounts of progress in spite of difficulties makes a major difference in the long run. 

SOURCES:

• Monetary Control Law - I. INTEREST RATES AND THE LAW: A HISTORY OF USURY

• What Is The Average Annual Return Of The S&P 500?

• Power of Compounding: How to Make Your Money Work for You

• Interest Rates (English)

• A Short Review of the Historical Critique of Usury

• Why Einstein Considered Compound Interest "Most Powerful Force In Universe"

• Compound Learning: The Most Powerful Tool for Acquiring Skills Faster

• The Power of Compound Learning: Robotics in the Warehouse of the Future

• Just a Drop: A Poem About Compounding

• Stanford Social Neuroscience Lab

• The Science of Kindness

• The long and the short of stock market volatility

• What Is The Best Measure Of A Given Stock's Volatility?

• Volatility

• Sector-Specific Volatility: Which Industries Are Most Prone And What To Do About It

• Good Things Come to Those Who Wait: An Argument for Long-term Thinking

• The Psychology Behind Motivation: Staying Focused on Long-Term Goals

• Goal Setting Psychology

• Atomic Habits by James Clear Quote

• Progressive Overload

ps. This is probably the most important post scriptum I have ever written in the blog. The text above was the best final paper of the 2024 "Introduction to financial markets" of the Ca' Foscari Harvard Summer School. It was written by Luke Chung and he kindly permitted me to publish it here (even though I took almost one year to make it public). It is simply a stunning reflection on what can be learned in a course (but my lectures were just instrumental to unleash wisdom, curiosity and brilliance that would have flourished anyway).
I tried, with the help of Gemini, to translate the original pdf text into a formast suitable for the blog editor. The readers and Luke should excuse me for the typos that I may have inadvertently introduced, links were particularly hard to clean. Hope you will like this essay as much as I did. Thank you Luke!