Actively managed mutual funds, as a whole, are designed to achieve lower rates of return than passively managed funds. And the math behind this suggestion will reveal why this is the case.
You see, the reason for this is simple: All stocks need to be owned by somebody.
Two Types of Investors
Now, the total stock market is made up of only two types of investors: active and passive. Active investors are those who try to pick stocks that they hope will beat the market. And they do this by either buying stocks that are underpriced, or selling those that are overpriced.
Passive investors, meanwhile, focus on matching the performance of the market as closely as possible. And they do this by simply buying and holding pretty much the same stocks in the same proportions as the market.
So, to illustrate this point, let’s say that 70 percent of all investors are active, while the remaining 30 percent are passive.
Now, it really doesn’t matter what percentages we use. For instance, it could be that 80 percent of investors are active, while the remaining 20 percent are passive. Or that 60 percent of investors are active, while the other 40 percent are passive. Whatever the case may be, the results will still be the same.
Let’s also suppose that the total stock market achieves a return of 8 percent per year over this period in our example. As such, this 8 percent return is the entire amount that all investors, both active and passive, have to divide among themselves.
Now, with that said, before any costs of investing are deducted, a passive investment strategy, such as owning a total stock market index fund, will earn the exact same return of 8 percent. And the reason for this is because an index fund seeks to reflect the performance of the market.
But here’s a question: What rate of return, before expenses, must all active investors as a group have earned? Well, it turns out that the answer is also 8 percent.
Here’s the simple math that explains why:
The Mathematics of Investing
There are three returns that are relevant in this example.
A = return of the total stock market, B = return earned by active investors, C = return earned by passive investors
And as we’ve just mentioned, we know the return of the total stock market, as well as the return earned by passive investors.
A = 8%, C = 8%
We also know that the total stock market is made up of only active and passive investors.
A = B + C
Now, since we know the values for A and C, as well as the percentage of active and passive investors that make up the total stock market, we can plug them into the formula above.
8% (100%) = B (70%) + 8% (30%)
So, now we know that our goal is to solve for B. And to do that, we’ll first change the values from percentages to numbers.
.08 (1) = B (.7) + .08 (.3)
Finally, all we need to do is some basic multiplication, subtraction, and division.
.08 = .7B + .024
.08 – .024 = .7B
.056 = .7B
B = .08
So, after converting this result back into a percentage, we find that B, which is the rate of return earned by active investors as a group, equals 8 percent.
Active Investors As a Group Are Just Average
“But why is this the case?” you wonder.
Well, the reason for this is because if one active investor beats the market by purchasing more of the winning stocks, then another active investor must have underperformed by not owning those very same stocks. After all, the investor who outperformed had to buy the winning stocks from someone else.
For instance, if the successful investor beats the market by 2 percent, her gain will be offset by the returns of the unsuccessful investor, who falls short by the same 2 percent. So, the winner earns 10 percent (8 + 2 percent), while other investor earns only 6 percent (8 – 2 percent). But when you combine the returns, the average active investor earns an 8 percent [(10 + 6 percent)/2] rate of return.
In other words, before costs are subtracted, active investors as a whole earn the same rate of return as passive investors. But, we haven’t yet mentioned that investors don’t earn gross returns. Instead, they earn returns after expenses are deducted.
So, in order to get the actual, or net returns that investors earn, we need to subtract the costs of investing. And to keep things simple, we’ll just focus on the most obvious cost, which is the fund’s expense ratio.
The Reason Why Actively Managed Funds Underperform
Now, a mutual fund’s expense ratio is the annual fee that investors pay to the fund provider to cover portfolio management, administrative, marketing, legal, accounting, and distribution costs, among others. And this ratio is expressed as a percentage of the value of your investment.
Alright. To be conservative, let’s say that the average actively managed fund has an expense ratio of 0.7 percent per year. Now, many charge more than this, even well over 1 percent per year. You see, these types of funds have a higher expense ratio because they hire financial professionals who conduct research in order to inform their investment decisions.
On the flip side, let’s say that the average passively managed index fund has an expense ratio of 0.3 percent per year. Again, many charge much less than this, and a few even have an expense ratio of zero.
Now, the reason for this is because nobody needs to decide what stocks to buy and sell, or when to buy and sell them. Instead, the fund manager simply replicates the performance of the market. And this is easily done with the help of a computer.
So, from these examples, we see that the cost of carrying out a passive strategy will be less than that of an active one. And for that reason, passive investors will earn a higher net return than active investors as a group. Because once again, they are mathematically set up to do so.
Why Passive Investors Outperform Most Active Investors
Now, to be fair, in a given period, some active investors can beat an appropriate passive strategy. And, they can do this even after costs are subtracted.
But, research has consistently shown that this is difficult to do over long periods of time. For instance, the annual S&P Indices Versus Active (SPIVA) Scorecards are a great example of this.
Now, let’s go back to our example above. The winning investor earns a return of 9.3 percent (10 – 0.7 percent) after expenses are deducted. On the other hand, the loser earns a return of 5.3% (6 – 0.7 percent) after costs are subtracted.
As a group, though, the active investors earn a return of 7.3 percent (8 – 0.7 percent) after expenses are deducted. And to compare, passive investors earn 7.7 percent (8 – 0.3 percent) after costs are accounted for.
But the question is, do you really think that you can identify the top-performing stock funds in advance? And, let’s just suppose that a fund has significantly exceeded market returns in the past. In that case, are you confident that it will continue to be a winning fund in the future?
Key Takeaways
So again, what we’ve learned is three things:
- All investors own the entire stock market, so both active investors as a group and passive investors earn the gross return of the stock market.
- The expense ratios that are charged to active investors are higher than those that are charged to passive investors.
- Since active and passive investors earn the same gross returns, and passive investors have lower expenses than active investors, passive investors must earn the higher net return than active investors as a whole.
With that said, the ideal long-term investing strategy is to own a diversified portfolio of stocks. Or, if you prefer to have more balance, a diversified portfolio of stocks as well as bonds would work too. And either way, its costs should be kept to a minimum. And once you have this portfolio, all you need to do is simply hold on to it throughout the market’s changing seasons.