# Before and after costs: the arithmetic of the average investor

> Why the average active dollar earns the market before costs and lags it by its costs after them.

- Course: [Long-Term Investing: Index Funds, Risk and Your Own Behavior](https://productovi.com/courses/long-term-investing.md)
- Module: Can anyone beat the market?
- Lesson 13/32, ~22 min
- Source: https://productovi.com/courses/long-term-investing/average-investor-arithmetic

## Can we beat the market?

**Alex Tutor:** May 2027, your fourth month as Zapas's product manager. April's work on diversification is done, and Ethan catches you before the morning stand-up with a new idea.

**Ethan:** A partner wants to list their active fund in the app. Their line is "Why settle for the market when you can beat it?" Users love that. Why should we offer only index funds?

**Grace:** Before we argue about one fund, let's do the arithmetic for everyone at once. It takes five minutes and it doesn't depend on who is clever.

**Grace:** A toy market: shares worth \$100,000 in total, returning 6% after inflation this year. Three investors own all of it. The passive one holds half, \$50,000, in an index fund that costs 0.1% a year.

**Grace:** Two active investors own \$25,000 each and pay 1.5% a year in fees and trading costs. Active A had a great year: 10% before costs. What did active B earn before costs?

> **Exercise:** A market of shares worth \$100,000 returns 6% this year. A passive investor owns \$50,000 of it; two active investors own \$25,000 each. Active A earned 10% before costs. What did active B earn before costs, in %?

**Sofia:** So B gets only what's left over, 2%. A's great year came out of B's pocket?

**Grace:** Before costs, yes. Every share has an owner, so all owners together earn exactly the market. The passive half earns it by design, so the active half must earn it too: (10 + 2) ÷ 2 = 6%.

![The three owners split the market's 6,000 dollar gain exactly; after 800 dollars of costs they keep 5,200, and the active pair averages 4.5% vs 5.9% passive.](https://productovi.com/courses/long-term-investing/diagrams/m4-l1-market-split.png)

*Before costs the owners split the market; costs come off the top.*

**Ethan:** Fine, but nobody promised the average. Our partner's fund could be A.

**Grace:** It could. Now the part the slogan leaves out: costs. Every investor pays them, winner or loser, and that money never comes back to the investors.

**Grace:** Subtract each investor's costs from their return before costs. The passive investor pays 0.1%, both actives pay 1.5%.

**Toy market: return before and after costs**

| Investor | Before costs | After costs |
| --- | --- | --- |
| P, passive | 6 | 5.9 |
| A, active | 10 | 8.5 |
| B, active | 2 | 0.5 |
| Active average | 6 | 4.5 |

*Costs: passive 0.1%, active 1.5%. Market 6% this year.*

> **Exercise:** Toy market: shares return 6% this year. The passive investor pays 0.1% a year in costs; active A and active B pay 1.5% each. Before costs, passive earned 6%, A 10% and B 2%. Match each investor to the return after costs.

**Sofia:** So the passive investor beats the average active one by 1.4 points, and that's just 1.5 minus 0.1?

**Grace:** Exactly. The average active dollar trails the average passive dollar by its extra cost. It holds every year, in rising and falling markets.

$$
\text{average active return after costs} = \text{market return} - \text{average active costs}
$$

*Holds for active investors as a group, in any year. Here: 6% − 1.5% = 4.5%.*

**Ethan:** In a crash active managers can move to cash. That's when they earn their fee, isn't it?

**Grace:** Someone has to buy the shares they sell. In a falling market every share is still owned by someone. If some actives dodge the fall, other actives bought it from them and took it instead.

> **Exercise:** In a falling market, active investors as a group lose less than the market before costs, because they can sell and wait in cash.

**Sofia:** How much did the three of them pay in costs altogether?

**Grace:** Work it out in dollars from their holdings, then compare it with the market's \$6,000 gain.

> **Exercise:** Toy market: the passive investor holds \$50,000 at 0.1% a year in costs; active A and active B hold \$25,000 each at 1.5% a year. How many dollars do the three pay in costs this year in total?

**Ethan:** So you're saying nobody should ever pick an active fund?

**Grace:** I'm saying the average active dollar starts behind by its costs. Some funds still win in a given year, like A. The question for the app is what we can honestly promise in advance.

> **Exercise:** Zapas is writing a "Why index funds?" screen. Which sentence can it honestly put there?

> **Exercise:** Which statements follow from the arithmetic of the average investor? Select all that apply.

**Ethan:** Give me two lines for the partner call. I'll read them out.

> **Exercise:** Ethan will tell the partner: "Our users deserve a chance to beat the market." In 2–3 sentences, explain what the toy market shows about active investors as a group and what Zapas can honestly offer instead.

**Grace:** Good. Tomorrow Ethan will ask the natural follow-up: fine for the average, but can't we just find the funds that win? That needs real fund records.

> **Key ideas**
>
> - All owners of a market together earn exactly the market's return, before costs.
> - Passive investors earn the market by design, so active investors as a group earn it too. One active investor's gain is another's shortfall.
> - After costs the average active dollar trails the market by its costs: 6% − 1.5% = 4.5% vs 5.9% passive.
> - Costs are the only part of the result known in advance.

> **Educational, not advice**
>
> This lesson explains how investing works; it doesn't tell you what to buy. Investments can fall and you can get back less than you put in. Check the current rules where you live or ask a licensed professional.

- Previous lesson: [Case: a user with everything in two bets](https://productovi.com/courses/long-term-investing/case-concentrated-user.md)
- Next lesson: [Winners that don't repeat: luck, skill and closed funds](https://productovi.com/courses/long-term-investing/winners-dont-repeat.md)

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