# The behavior gap: fund return vs user return

> Why the average user earns less than the fund they hold, and who sold at the bottom.

- Course: [Long-Term Investing: Index Funds, Risk and Your Own Behavior](https://productovi.com/courses/long-term-investing.md)
- Module: The users are the risk (and so are we)
- Lesson 25/32, ~27 min
- Source: https://productovi.com/courses/long-term-investing/behavior-gap

## One fund, two numbers

**Alex Tutor:** September at Zapas: the public launch is two months away, and the closed beta has just finished its first full year. You're still the PM, and today Ethan wants a number for the launch page.

**Ethan:** Zapas World Stock made 8.7% this year, after a 22% fall in the spring. Let's write it big: "Our users earned 8.7%."

**Grace:** The fund earned 8.7%. The 200 users who've been in the beta for the whole year earned 6.0% on average. Those are two different numbers, and only one of them is about users.

**Sofia:** Same fund, same year. How can users earn less than the thing they hold?

**Grace:** The fund's return ignores when money came in or left. It answers "how did the fund do?". A user's return weighs every dollar by how long it was invested. It answers "how did my money do?".

![The fund returned 8.7%; users who sold in the fall averaged −6.8%, those who kept investing +10.5%; the average user got 6.0%.](https://productovi.com/courses/long-term-investing/diagrams/m7-l1-two-returns.png)

> **Exercise:** Match each question to the return that answers it.

## The gap in dollars

**Sofia:** So the gap is 8.7 minus 6.0?

**Grace:** Yes, 2.7 points. In money it's clearer. Beta users put in 1,568,900 dol. net and ended with 1,647,711.84. Had all of them simply held the world fund, they'd have 1,733,059.59.

**Dataset (CSV):** [Zapas beta cohort, one year (synthetic)](https://productovi.com/datasets/long-term-investing/behavior-gap/beta_users.csv)

The 200 users in the beta all year: how often they checked the app, deposits, who sold in the drop and when, theme fund buys, withdrawals and the end value in dol.

**One year, one fund, different returns (synthetic)**

| who | Return for the year, % |
| --- | --- |
| Fund | 8.7 |
| Average user | 6 |
| Sold in the drop | -6.8 |
| Never sold | 10.5 |
| Never sold, no theme | 12.7 |

*Fund: time-weighted. Groups of users: average money-weighted return.*

> **Exercise:** Zapas World Stock returned **8.7%** for the year (time-weighted). The 200 full-year beta users averaged **6.0%** (money-weighted). What is the behavior gap, in percentage points?

**Ethan:** 2.7 points sounds like a rounding error.

**Grace:** Then count it in dollars. The same money, simply held, would be worth more at the end of the year. That difference is what behavior cost the cohort.

> **Exercise:** The beta cohort ended the year with **1,647,711.84 dol.** Had every user simply held the world fund with the same deposits and withdrawals, the cohort would have ended with **1,733,059.59 dol.** How much did behavior cost the cohort?

## Who sold at the bottom

**Zapas World Stock, value of 100 dol. through the beta year (synthetic)**

| Month | Zapas World Stock |
| --- | --- |
| 0 | 100 |
| 1 | 103 |
| 2 | 105.1 |
| 3 | 100.9 |
| 4 | 91.8 |
| 5 | 84.4 |
| 6 | 81.9 |
| 7 | 86 |
| 8 | 91.2 |
| 9 | 94.8 |
| 10 | 97.7 |
| 11 | 103.5 |
| 12 | 108.7 |

*Month-end values. The fall from month 2 to month 6 is 22.0%; 52 users sold in months 5 or 6.*

**Grace:** 52 users sold everything in months 5 or 6, close to the bottom. 20 of them came back in month 10 or 11. The rest were still in cash at the end of the year.

**Sofia:** Did the ones who came back at least catch up?

**Grace:** Not even close. They averaged +1.4%; those who stayed out −11.9%. The fund had already recovered most of its fall by the time they returned.

> **Exercise:** **True or false:** beta users who sold in the drop and bought back in month 10 or 11 ended the year roughly level with users who never sold.

## Why the stayers beat the fund

**Sofia:** Wait. Users who never sold got 10.5%. That's more than the fund's 8.7%. How?

**Grace:** Their monthly deposits kept buying during the fall, at cheap prices. The 117 who never sold and never touched the theme fund averaged 12.7%, and every single one beat the fund.

$$
R_{user} \approx \frac{V_{end} - V_{start} - \sum F_m}{V_{start} + \sum F_m \cdot \frac{13 - m}{12}}
$$

*Money-weighted return for one year (a simple approximation): V is the account value, F_m a deposit (+) or withdrawal (−) at the start of month m.*

> **Exercise:** Beta user U001 started with **2,000 dol.**, deposited **150 dol.** at the start of every month (12 deposits), never sold and ended the year with **4,246.39 dol.** Using the formula, what was this user's money-weighted return? The weights (13 − m) ÷ 12 for months 1–12 add up to 6.5. Round to one decimal.

## What goes on the launch page

**Ethan:** Fine. So which number do I put on the page?

**Grace:** The fund's number, labelled as the fund's, synthetic past, no promise. And in the app, each user should see their own money-weighted return next to the fund's.

> **Exercise:** Which line for the Zapas launch page uses the beta numbers honestly?

**Sofia:** What can the product do so the gap shrinks next year?

**Grace:** Make staying the easy path: deposits that keep running in a fall, the user's own plan in view, nothing that rewards nervous checking. Next lessons go deeper.

> **Exercise:** Which product changes are likely to **narrow** the behavior gap for Zapas users? Select all that apply.

## Your turn: the note for Ethan

**Ethan:** Write it up for me in a few lines, so I stop asking.

**Alex Tutor:** Keep it short: the two numbers, what the gap cost in dollars, why, and what goes on the page instead.

> **Exercise:** Write Ethan a 3–4 sentence note: why "Our users earned 8.7%" is wrong, what the beta users actually earned and what behavior cost them, and what the launch page should say instead.

> **Key ideas**
>
> - The fund's **time-weighted** return (+8.7%) measures the fund; the user's **money-weighted** return (average +6.0%) measures what their money did.
> - The **behavior gap** is the difference: 2.7 points, or 85,347.75 dol. for the beta cohort in one year.
> - Users who sold in the drop averaged −6.8%; those who came back +1.4%; those who never sold +10.5%.
> - Deposits that keep running in a fall buy cheap units: the 117 users who never sold or switched all beat the fund (12.7% on average).
> - Put the fund's return on fund pages, labelled; show each user their own return next to it.

> **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. All Zapas and Tessaro data is synthetic. Check the current rules where you live or ask a licensed professional.

**Alex Tutor:** Next time: why checking the app daily and following the crowd into a hot theme lead to the same place.

- Previous lesson: [Case: three model portfolios and the onboarding questions](https://productovi.com/courses/long-term-investing/case-model-portfolios.md)
- Next lesson: [Losses hurt twice: checking, herding, chasing and bubbles](https://productovi.com/courses/long-term-investing/losses-hurt-twice.md)

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