### Key Points

- Over long periods, a
approach in index funds is more likely to lead to an outcome that falls in line with a given*passive*investing**benchmark**. - With an
approach, where*active*investing**mutual fund****fees**are higher, outcomes are far less certain. - As such, the long-term
**opportunity cost**of an*active*approach can be significant, and perhaps even disastrous.

### Twenty, Again

We introduced the notion of opportunity cost in Part 1 of my series, The World’s Most Expensive Hobby, so in this post we’ll take this notion one step further and explore this phenomenon as it relates to choosing an *active* investing fund over a *passive* investing one.

Opportunity cost represents the benefits an individual, investor or business misses out on when choosing one alternative over another. While financial reports do not show opportunity cost, business owners can use it to make educated decisions when they have multiple options before them. —Investopedia

Let’s say your benchmark is the S&P 500** ^{®}** Index and once again you have $10,000 to invest for your

**retirement**that is many (many) years away. This time you are determined to invest the funds until you retire in 45 years (doesn’t it feel great to be 20 again?). Given this, let’s consider the following five scenarios:

Scenario 1: You invest in the S&P 500** ^{®}** Index with no fees. This scenario represents the theoretical closest that you can come to your benchmark.

Scenario 2: You invest in a *passive* S&P 500** ^{®}** Index fund with an annual

**expense ratio**of 0.08%, and as expected this investment performs in line with the S&P 500

**Index minus expenses.**

^{®}Scenario 3: You invest in an *active* index fund, which has the S&P 500** ^{®}** Index as its benchmark (with an annual expense ratio of 0.67%), and to your non-surprise, its performance generates an annual return that is in line with your benchmark minus fees.

Scenario 4: You invest in an *active* index fund, which has the S&P 500** ^{®}** Index as its benchmark (with an annual expense ratio of 0.67%), and to your jubilation, its performance generates an annual return that is 2% greater than your benchmark minus fees.

Scenario 5: You invest in an *active* index fund, which has the S&P 500** ^{®}** Index as its benchmark (with an annual expense ratio of 0.67%), and to your distress, its performance generates an annual return that is 2% less than your benchmark minus fees.

*Note: these fees are just the average expense ratios for these two categories of funds (passive and active large-cap mutual funds), as discussed in **Part 3** of this series.*

The notion here is that with a *passive* fund (Scenario 2) you pretty much know what you’re getting. But with an *active* fund (Scenarios 3, 4, and 5), your future is more uncertain. So once again, let’s use history as our guide to rerun our simulation from Part 5 with an understanding of this more ambiguous set of outcomes for an *active* fund. In Part 5 we considered the growth of $1,728.03 (which would be worth about $10,000 in today’s dollars after adjusting **inflation**) over the past 45 years after investing this initial sum in the S&P 500** ^{®}** Index and then reinvesting all

**dividends**back into the index.

### The Results

Over a 45-year period, in Part 5, we showed that this initial sum of $,728.03 could have grown to about $149k if you didn’t have to pay any fees (Scenario 1), or about $144k if you paid the average fees of a *passively* managed large-cap fund, or 0.08% per year (Scenario 2). We then noted that you would only be left with $111k if you paid the average fees of an *actively* managed fund, 0.67% per year (Scenario 3).

However, this $111k figure assumes this actively managed fund provides no value beyond the return of the S&P 500** ^{®}** Index before taking fees into account. But of course, an actively managed fund can do far better than its benchmark (Scenario 4), or it can do far worse (Scenario 5). Given all this, let’s check out the five scenarios from above in

**Figure 1**below

**.**

*Note: in this hypothetical simulation, I used S&P 500*^{®}* Total Return data (which includes reinvested dividends) provided by **S&P Dow Jones Indices**, and to adjust for the fees, I reduced each month’s return by a monthly estimate of the annual fee determined by taking each annual expense ratio and dividing by 12. To adjust for annual outperformance, I reduced each month’s return by a monthly estimate for the annual outperformance also determined by taking each annual outperformance and dividing by 12. For simplicity I also used January 1, 1973 as the start-date and December 31, 2017 as the end-date for this 45 year peri*od.

In this chart, the blue line still represents an investment in the S&P 500** ^{®}** Total Return sans fees (Scenario 1); while the yellow line represents the same return but with low fees (Scenario 2). In addition, the red line represents the same return but with a no outperformance and the larger 0.67% annual fee (Scenario 3); the purple line represents the same return but with a 2% annual outperformance with the same 0.67% annual fee (Scenario 4); while the black line represents the same return but now with a 2% annual underperformance with the same 0.67% annual fee (Scenario 5).

### Back to Opportunity Cost

In **Table 1** below, we summarize these results for deeper insight. The difference is incredible, right? After 45 years, the purple line leaves an investor with around $271k, while the red is only left with around $45k.

So now your hypothetical investment decision might come down to the following: would you rather have the opportunity to end up with around $144k (Scenario 2) by investing in a *passive* fund; or would you rather take a gamble and potentially end up with around $271k (Scenario 4) at the **risk** of ending up with only $45k (Scenario 5), with the most likely outcome being around $111k (Scenario 3) by investing in an *active* fund?

Now, let’s apply our understanding of **opportunity cost** to these five scenarios. If your benchmark is the S&P 500** ^{®}** Index, in order to minimize your opportunity cost you would go with Scenario 2 to end up with around $144k given that this scenario represents the closest to your benchmark that you can obtain in the marketplace (give or take, depending on your particular passive fund). According to

**Table 1**, with Scenario 3, your opportunity cost is around $34k. Yipe. But it gets worse; with Scenario 5, your opportunity cost is around $99k. which is around 69% less wealth than Scenario 2. Oh my. However, it’s important to note that with Scenario 4, your opportunity cost is around

*negative*$127k (this would actually be an

*opportunity benefit*if you could pull it off, by the way), which represents around an 88% improvement over Scenario 2.

At first pass, it might seem like the decision between an *active* fund and a *passive* one are equally compelling. After all, $271k is quite a large amount of money. But what are the chances that Scenario 4 actually transpires? If the odds are greater than 50%, you might think the gamble would be worth it. But what if the odds were much lower? What if the odds of outperforming a *passive* strategy were closer to zero? In that case, clearly Scenario 2 would be more sensible. So let’s investigate further before we make up our minds on this. As such, in Part 7, we’ll dig into this important line of questioning by highlighting what some academic research has to say about all this.