- Compound interest accrues by reinvesting previously earned profits.
- Investors should not only seek to maximize their gross return subject to a level of risk, but also to minimize their total costs.
- Then, they will be maximizing the net return on their investments.
- A difference in costs that may appear small creates a significant gap in net profits over time for the investor.
In this article, we explain how to calculate the net return on investments and how total costs affect the profits that investors actually obtain.
What is compound interest?
Usually, investment managers do not deposit the profits earned by our investments into our checking accounts: the assets (stocks, bonds, or others) are held in the portfolio and are not liquidated, while stock dividends are reinvested.
Let's assume we decide to invest in a fund with an expected return of 10% per year. Then, over time, that 10% that would be gained per year will translate into higher profits in absolute terms, since the 10% return will be applied to an increasingly larger amount of assets. The process we just described is known as compound interest.
Compound interest is obtained by reinvesting previously earned profits.
As an example, if USD 100,000 are invested with an expected return of 10% per year, the return would not be of USD 10,000 every year. Profits would be USD 10,000 in the first year and USD 11,000 in the second year, jumping to USD 21,436 in the ninth year and USD 23,259 in the tenth year.
As it can be seen, capital grows over time, partly because an increasingly larger amount is reinvested every year.
Impact of total costs on net return
The real goal of investors should not be to maximize the expected gross return of the instruments they decide to buy (although this is important), but rather to maximize the expected net return, adjusted for factors such as investment horizon and risk tolerance. To do this, they must also minimize total costs. In this way, they will be maximizing the net return on their investments, which is the variable that should really be of concern.
While costs are certain, returns are uncertain. In other words, it is a fact that costs will be paid for investing, while positive returns cannot be counted on. Therefore, the first step in maximizing the net return on an investment is to minimize explicit costs, which can be anticipated and controlled. This is much simpler than maximizing expected gross return. For example, if an investor has decided to invest in stocks of large US companies, what is the best way to do it from a cost perspective?
The role of total costs associated with an investment is fundamental. The higher the total costs of a fund (explicit plus implicit), the slower the capital will compound and the lower the net return will be for the investor. This is important: the higher cost this year will have consequences not only during the current year, but in all subsequent years. The true cost is greater than what is apparent at first glance.
Moreover, high costs substantially affect the risk-return relationship offered by a fund. As mentioned above, riskier investments offer a higher expected return to make them more attractive to investors. However, high total costs distort this relationship, resulting in a risky asset that does not offer a high enough expected return for the investor.
What is the effect of fees on profitability?
The following example is useful to understand the effect of fees on profitability.
Suppose an investor has USD 100,000 to invest and two institutions offer similar funds, but with different total costs. Institution A offers to invest in a mutual fund with a total annual cost of 6%, while institution E offers to invest in a similar mutual fund, but with a total annual cost of 0.75%.
Both funds could be considered substitutes, as they invest in US stocks and their expected annual return is 12.5% (which corresponds to the average historical annual return of the S&P 500 between 1988 and 2021, including dividends reinvested).
In Figure 1, we can see the cumulative gains that an investor would obtain in both cases (investing in institution A and institution E). Although they invest in the same instruments, which obviously have the same return, the cumulative gains after 10 years in fund A are USD 74,906, while in fund E they are USD 201,183. The difference in cumulative gains up to year 10 is, therefore, USD 126,277 in favor of the less expensive fund. This is simply because in institution A, which charges a higher expense ratio for management, the capital compounds at a slower rate.
The lesson is that a difference in costs, which may seem small, creates a significant gap in cumulative gains: those who invest in institution E will have obtained gains 2.7 times higher, despite not incurring greater risks.
Figure 2 shows the total size of assets over a 10-year period. At the end of year 10, those who invested in institution E will have a total of USD 301,183, while those who chose institution A will have only USD 174,906.
Once again, the lesson is the same: small differences in portfolio management costs create large differences in results for investors. The instruments’ yield is the same, but in one case the investor simply keeps a larger fraction of the returns.
It is useful to analyze this by observing the evolution of fees.
Figure 3 shows accumulated fees over 10 years, that is, the total costs that the individual has paid up to the corresponding year. After 10 years, whoever invests in institution A will have paid USD 78,162 in fees, while those who invest in institution E only pay USD 12,945. This means that total costs are 6 times higher in institution A than in institution E. Even more importantly, the cost is even higher if we consider that this capital could have been reinvested, generating returns. In other words, there is an opportunity cost that the investor may not be considering: there is money that is lost by not compounding. The true cost is higher than what is perceived at first glance.
Figure 4 shows that commissions paid year after year are also substantially higher in institution A. At the end of year 10, they are more than 6 times higher in institution A than in institution E.
Finally, Figure 5 shows the ratio between total costs paid after 10 years (see Figure 3) and the accumulated gains after the same time (see Figure 2). In institution E’s fund, total fees paid after 10 years represent 6.4% of the profits gained during the same period; in the more expensive A fund, this number rises to 104%, meaning that an investor, after 10 years, would have paid more in fees than what the assets actually grew. At this point, the investor would have been better off not investing at all.
What should really concern investors is maximizing the net return on their investments: gross return minus total cost. Many people focus on the gross return of their assets and do not consider the total costs (implicit and explicit) of their investments. Returns are uncertain and that is why we talk about "expected returns", while costs are certain. That is, it is a fact that investing will carry a cost, while it is not certain that returns will be positive. Hence, to maximize the net return on an investment, the first step is to minimize its explicit costs and find out about the implicit ones, to minimize them as well.
Compound interest is obtained by reinvesting previously obtained gains. One way to maximize it is to minimize the cost of investing, so that more capital is kept in the hands of the investor. In this article, we have showed that a difference of 5.25 percentage points in annual costs generates large impacts on total assets after 10 years.
Consult with your financial advisor to find out which investment strategies best suit your objectives, risk level, and investment horizon. Because costs affect the risk-return relationship of assets, it may happen that, for the same level of risk, funds with a lower expected return turn out to be more convenient than funds with a higher expected return. This can happen if the costs of investing in the fund with higher expected return are large enough. What matters for an investor, after all, is net return.