The stock market is a device to transfer money from the impatient to the patient.
Warren Buffett
The Marshmellow test is probably one of the most famous studies in psychology. During an experiment in the 1970s, kids at age five were given a marshmallow and told that they would receive a second one 15 minutes later if they managed not to eat it until then. The behavioral study initially attempted to study the development of a human's sense of delayed gratification. However, it became hugely influential for a different reason. Subsequent studies in the 1980s and 1990s indicated that kids who showed the ability to resist the temptation of eating the first marshmallow fared better in school and experienced fewer behavioral problems. Thus, the idea that accepting delayed gratification leads to a healthier and more successful life was born. Unfortunately, the broader public tends to adopt academic research findings in a reduced, incomprehensive way. Concerning the marshmallow test, there is often the notion that some people are just born with the precious deferred-gratification gene.
More recent studies have challenged the marshmallow test and its interpretation and brought hope for people who find themselves to be somewhat impatient. A 2018 conceptual replication of the test used a larger sample size and controlled for socioeconomic factors and the environment in which the test was conducted. It found that the correlation between patience at the age of 4 and success later in life is way lower than implied by the papers from the 1990s. Secondly, the experiment found no correlation between the outcome of the marshmallow test and people's behavior later in life. As this article summarized, "people who say they are good at self-control are often people who live in environments with fewer temptations."
There are situations in life where the benefits of waiting for delayed gratification are hard to quantify, but one discipline where patience is vital is investing. Fortunately, as the behavioral research quote above shows, even if you belong to the people who "just can't stand to wait," you may not need to "work very hard to overcome that," as Charlie Munger pointed out. Instead, approaching the task with the right mindset and a favorable environment may dot the heavy lifting.
One starting point is to correctly formulate investment goals and become aware of time's role in achieving them. It is well known that compound interest is a mighty force in the long term, but it is often hard to get one's mind around it. It gets even more challenging once uncertainty (volatility) is added. I think visualizations come in extremely handy in this context, which is why I uploaded another small interactive tool to the quantamental platform. The Monte Carlo application enables the flexible simulation of portfolio returns based on user specifications assuming a Geometric Brownian Motion (GBM). It builds on the R script published by Kris Longmore on Robot Wealth but wraps it in an intuitive Shiny application and adds a couple of visualization options. The app also offers the possibility to model savings plans. The resulting charts are frequently used by the new breed of digital wealth managers that have come up over the past decade.
The tool enables investors to quickly assess the likely development of their wealth under various risk/return assumptions and the benefits of investing for the long term. However, it is also interesting to look beyond the return component and learn a few lessons about volatility and its impact on the long-term cumulative return distribution.
The chart below shows the realized distribution of the annualized total return over rolling 25-year windows of the S&P 500 Index since 1926.
Over this time, the mean return was 9.4%, with a standard deviation of 15.5%. This must not be confused with the mean and standard deviation of the index over the entire sample period from 1926 to 2021. Instead, I am using the mean return, and standard deviation experienced across all rolling window samples. However, investors could also realize an annualized return of more than 15% or close to zero depending on the holding period.
.png)
It is a shortcoming of the application that it usually assumes distributed returns and doesn't yet consider the fat tails observable in reality. The below chart was produced with the Monte Carlo simulation app and showed the GBM simulated distribution of annualized returns using the same expected return and average standard deviation.
It is important to remember that the underlying simulation is based on 10.000 iterations while the empirical sample contains only 900 rolling windows (95 years of monthly returns). However, the results are reasonably close. Most importantly, the simulation is actually more conservative on the downside.
.png)
The 1st and 3rd Quantile are still pretty close to those of the realized distribution. According to the simulation, the lowest annual return, achieved with 75% confidence, is 6.3%, while the empirical distribution yields a value of 6.42%.
So what does all this imply for your retirement investments? The below chart, produced with the application, illustrates the development of the ending wealth of a hypothetical savings account. It assumes that it is funded with 10.000 at initiation and topped up at the beginning of each month with 1.000.
The result is pretty impressive and demonstrates how much it pays to eat your marshmallows later and how wide the distribution of ending wealth is. Of course, patience is valuable but whether you end up with 500k or 2m is likely a function of luck. Funny enough, this is also the key finding of replication studies on the marshmallow test.
The superior success of the children who patiently waited during the first experiment in 1970 could eventually be attributed to factors such as intelligence, parent's education, and home environment.
Of course, the application can be extended and enhanced a lot. My next step will be to add the simulation of a Glide Path to obtain a more realistic view of the risk and return profile of pension savings accounts. I have attached the PDF version of the Watts et al. (2018) study for readers interested in psychology.
.jpg)
