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 poorperforming 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 highquality 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 nonzero 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 longterm 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.

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