A fundamental principle of investing is that rates of return are key - but most people don't really understand their profound importance. Of course, most savers and investors know that the rate of interest they get on their savings or the rate of return they get on their investments matters a lot, but they are too easily willing to give up valuable return to things such as:
It's important to note that not all of the above fees are bad - you're paying these for a reason. For example, you want the mutual fund to hire a good money manager - this person will need to be compensated well. You clearly understand that administrative fees are going to exist for mutual funds and ETFs. Trading fees obviously are required so that the brokerage is paid for the service they provide you - this is a small price to pay for being able to enter and exit positions with ease.
However, you still don't want to overpay. You will not want your mutual fund or ETF to spend excessively on hiring poor-performing managers, spring money on lots of useless advertising, or running thing so inefficiently that the administrative fees are too high relative to similar funds. You'll obviously want to shop around to find a reputable and high-quality broker, but not one that charges excessive fees relative to what's available on the market. You'll also want to be disciplined and not constantly enter or exit positions so you don't accumulate excessive trading fees that will eat away at your capital. Common sense will dictate that even if the fees are reasonable in principle, they could be unreasonable in practice (meaning in amount).
To illustrate this point well, let's use an example. Examples are often an excellent way to illustrate importance finance principles in ways that are easy to understand - a theory is good but seeing numbers and graphs often allows people to really visualize the concepts being presented and gives the motivation to use the new knowledge they gained.
Let's start with $10,000 in our example and let's invest that money at different rates of return - the return rates will be from 0% to 8% in intervals of 2%. First, we'll break down the possible rates and understand where you might obtain them:
Now, let's see how $10,000 will grow at each of the above rates of return by taking a look at the graph below. From looking at the graph we can see that the 0% return stays constant throughout with all of the non-zero returns separating from it more and more over time. We can also see that each 2% increase does not bring a proportional increase in the final amount - the increase itself increases over time. 2
The 8% portfolio brings the initial $10,000 to almost $500,000 but the 6% doesn't even reach $200,000. We can say how important even a small increase in return can make over the long term. That 2% difference is sadly something too many investors ignore. It makes sense given the human mind's propensities that a person wouldn't be able to totally and intuitively grasp the importance of even a 0.25% difference in return, but through education, we can see that the small differences end up with very big differences in results.
How can a 2% difference result in a greater than 50% difference in the final portfolio value? This doesn't seem to make too much sense at first glances - the 2% difference is only 1/4 of 8%, so shouldn't it result in a 25% difference? The maths of finance don't work this way - this is an incorrect way of thinking through it. The way it works is that the 2% you forgot on the first year doesn't stop there - that 2% you would have gained is no longer able to be around in the second year to earn additional return. For example, by forgoing 2% on the $10,000 investment, you forgo $200 in your first year, BUT it doesn't end there - in the second year that $200 would have been working for you t earn a return. The same is true in the third year, the fourth year, and so on. In effect, the person who invests at 8% is able to not only bring along that extra amount every year but to also keep that amount invested and earning. In effect, changes in investment returns compound over time. This is the underlying principal as to why small differences in return can have tremendous impacts in final portfolio value.
We aren't going deep into the maths here, but you can reference a 2013 article titled "The Arithmetic of Investment Expenses" by William F. Sharpe. The article is accessible to most readers and the title should give you a hint at the complexity of the maths - it's not very complex to calculate nad understand the impact of fees on final returns.
Next, we'll present another graph - this time with the same $10,000 initial investment but now we'll look at a broader spectrum of return rates (0% to 18%).
As we did above, let's take a look at how each of the additional returns can be achieved:
As you can see from the graph, the initial investment returns we plotted on the first graph are made to look minuscule here. Although most investors shouldn't expect to obtain returns over 14% over the long term, this graph clearly represents how important every percentage point is to the final portfolio value.
Finally, to really bring this home, let's go over one more example - this time let's look at two men. One is Benjamin and one is Gerald. Both Benjamin and Gerald invest $10,000 on the birth of their first child - this could be a college fund or a sort of "start of life" fund so that their progeny is financially stable. Clearly, both Benjamin and Gerald are intelligent, prudent, and caring individuals and parents - most people don't do such things. Another thing that's clear is that their children are quite lucky - they have dad's who care enough to put away some money for them at their birth. Both Benjamin and Gerald have $10,000 ready for this investment - they are quite similar in this and many respects. But, let's now see how they're different?
The strange thing is that Benjamin and Gerald are far more similar than different - in the thing that matter (caring, prudence, planning ahead, etc.), they are clearly quite similar. Their differences, as we'll see shortly, will be quite small and trivial if it wasn't for the outcome those differences would lead to.
Benjamin takes his $10,000 and invests it in a fund over the course of one year in a series of 24 purchases, once every month. He shops around for a good brokerage - the makes sure they're reputable and reliable but keeps an eye on trade pricing too. Benjamin chooses a long-term growth fund but looks at expense ratios, loads, and the quality of management in order to make sure that he's choosing the best fund for his strategy.
Gerald takes his $10,000 and invests it in 60 purchases because he is attempting to time the market. Gerald doesn't shop around for a brokerage and chooses the first one he finds. Gerald doesn't shop around for a fund, but instead takes a recommendation from his friend or family member - this fund has the same strategy as Benjamin's fund but isn't managed as well, has a load, and has a higher expense ratio.
Both Benjamin and Gerald leave the money in their account after the first year and never touch it again - they pass it down to their children who also are wise enough to leave it alone and let it grow.
Take a look at the tables above to see the actual numbers Benjamin and Gerald are dealing with. In effect, Benjamin and Gerald end up with different starting amounts and different return rates (9.75% vs. 7.25) due to their different choices. These small differences made in the first year have tremendous impacts on the final portfolio values after 50 years. While Benjamin's portfolio is valued at over $1 million in 50 years, Gerald's is valued at only a bit above $300,000 - this is approximately a 70% difference. This 70% was a result of about a $600 difference in initial investment and a 2.5% difference in return. Most people would probably ignore these differences, but they are clearly extremely important.
If you're interested in further reading, below is a paper titled "The Arithmetic of Investment Expenses" by William F. Sharpe - a paper published by the same William Sharpe who created the famous Sharpe Ratio on how fees and expenses can impact the terminal value of a portfolio.
I love infographics - they can represent interesting and useful data in ways that are easy to understand. Sometimes, the very good infographics can provide you with very useful insight very quickly. The above image is a map but it is also a proper infographic in my opinion because it conveys more than just geographical information - in conveys the density of slaves in the Southern States during Abraham Lincoln's presidency, based on the Census of 1860.
The map, titled Map Showing the Distribution of the Slave Population of the Southern Sates of the United States Compiled from the Census of 1860 specifically focuses on the Southern States and divides each state into counties. The darker the county is shaded in, the higher the density of slaves. It might be hard to see this on the above image (so I've included a downloaded file of a high resolution capture of this infographic), but the darkest square on the bottom left corresponds to a slave density of 80% +. This is astonishing to me. This means that in some counties in the United States, a nation that was founded partly based on a desire for freedom, allowed such perverse things to occur within is boarders. The same nation that wrote what I would argue is the greatest document in testament to humanity's inherent freedom and the inherent right of every individual to self-determination had, one hundred years after its founding, counties where over 80% of the residents were slaves.
Abraham Lincoln referred to this map on more than one occasion in an attempt to see how the cause of freedom and the emancipation of slaves would actually affect the troops on the ground. That makes great sense to me. If I was a general during the Civil War a map such as this might be useful to me. It doesn’t show armies or troop numbers or terrain, but it shows the sentiment of people on the ground. It shows the counties where there are few slaves (and therefore likely little resistance to emancipation) and counties where there are many slaves (and likely much resistance to the cause of emancipation).
Of course, in a county with over 90% of its population composed of slaves, would there be much resistance? I'm not sure what the answer to this is - it's just a question that popped into my head. I would think that as the Northern Army moved down and as the North's victory seemed more likely, counties where slaves outnumbered non-salves by a factor of almost 10 to 1 would quickly overthrow slavery in rebellion. I don't think this occurred, however, in the history of the United States. I'm not a historian or a military expert, so this is pure conjecture.
This is just one example of amazing infographics. We think infographics are a modern phenomenon, but the above map shows that information-rich images existed a long time before the digital age.
Drawn in Paris and dated November 20, 1869, Charles Joseph Minard’s Figurative Map of the Successive Losses in Men of the French Army in the Russian Campaign of 1812 is known by information scientists and data scientists as one of the greatest (if not the greatest) statistical graphic ever created. Edward Tufte calls the graphic "The best statistical graphic ever drawn" in his classic The Visual Display of Quantitative Information. Infographics have become popular ways of representing data, but Minard had the idea a century and a half ago. Mindard’s infographic depicts six data types in an easy-to-understand and elegant fashion.
The data types depicted are as follows:
It's astonishing that such a quality infographic was created over a century ago. The elegance of the graphic is in it's ability to depict so much information in a very intuitive way for the human eye. That is what good data visualization is all about: distilling information so that the important parts are easily accessible to the human mind upon examination without much effort or analysis.
One stunning thing the graph represents is the utter devastation the invasion caused the French army. Looking at the starting and ending points in the lower left, we can see that the French army was annihilated by the extremely cold and difficult journey. That human aspect is left out of the data visualization as it almost always is. It takes the human mind to put that extra human element to the graphic and to the numbers.
Image Source: "Minard map of napoleon" by Iñigo Lopez - Own work. Licensed under CC BY-SA 4.0 via Commons - https://commons.wikimedia.org/wiki/File:Minard_map_of_napoleon.png#/media/File:Minard_map_of_napoleon.png
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