# Winners that don't repeat: luck, skill and closed funds

> Where yesterday's top funds rank later, how dropping closed funds flatters the average and how long it takes to tell skill from luck.

- 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 14/32, ~24 min
- Source: https://productovi.com/courses/long-term-investing/winners-dont-repeat

## Last period's winners

**Alex Tutor:** Still May at Zapas. Yesterday Grace showed that the average active dollar trails the market by its costs; today Ethan arrives with a spreadsheet.

**Ethan:** Fine, the average loses. So we skip the average. I found 20 active funds with 14-year records. We list the top five and let users ride the winners.

**Grace:** Good test. Split the record in two: years 1–7 to pick the winners, years 8–14 to see what happened to them. Picking on the past and checking on the future is the only fair way.

**Grace:** One warning about this data: it is synthetic, and we built it with no skill at all. Each fund's return is the index plus luck minus its fee, with fresh luck in each period. Let's see if that matters.

**Dataset (CSV):** [20 fictional active funds and the index fund, real returns a year (synthetic)](https://productovi.com/datasets/long-term-investing/winners-dont-repeat/active_funds.csv)

p1_return_pct: average yearly real return in years 1–7; p2_return_pct: years 8–14, or until the fund closed (status closed, closed_year). IDX is the Tessaro World index fund after its 0.2% costs.

**The top 5 of years 1–7, and what they did in years 8–14**

| Fund | Years 1–7 | Years 8–14 |
| --- | --- | --- |
| F19 Star Growth | 9.88 | 4.1 |
| F02 Ottervale Focus | 8.58 | 5.21 |
| F16 Tallowmere Opportunities | 8.18 | 4.52 |
| F18 Fernhollow Select | 7.78 | 5.43 |
| F04 Brackwater Dynamic | 7.67 | 0.56 |
| Index fund | 7 | 6 |

*Real return, % a year. F04 Brackwater Dynamic closed in year 9.*

**Sofia:** In the first period seven funds beat the index's 7%, and Star Growth is top with 9.88%. In the second period it drops to 4.10%.

> **Exercise:** In the fund data, Star Growth ranked 1st of 20 in years 1–7 with 9.88% a year. Where did it rank in years 8–14?

**Ethan:** Fine, Star Growth slipped. Maybe the other four held up?

**Grace:** Average them. The period-1 top five earned 4.10, 5.21, 4.52, 5.43 and 0.56% a year in period 2. Brackwater's 0.56 runs until it closed in year 9.

> **Exercise:** The five best funds of years 1–7 earned 4.10, 5.21, 4.52, 5.43 and 0.56% a year in years 8–14 (the last one until it closed). What is their simple average in years 8–14, in % a year? The index fund earned 6.00%.

## Funds that disappear

**Sofia:** Wait. Brackwater closed in year 9. If a user opens a fund list today, Brackwater isn't on it at all.

**Grace:** Right, and it wasn't the only one. Five funds closed in years 9–13, merged into other funds, and they were the five worst of period 2. A list of funds that exist today quietly drops them.

![Of 20 active funds, 5 closed; the 15 survivors average 5.13% a year in years 8–14, all 20 only 4.20%, and the index fund 6.00%.](https://productovi.com/courses/long-term-investing/diagrams/m4-l2-survivors.png)

*Survivors only: +0.93 points that no investor earned.*

> **Exercise:** In years 8–14, all 20 active funds averaged 4.20% a year, counting the five that closed. The 15 funds still open averaged 5.13%. By how many percentage points does dropping the closed funds flatter the average?

> **Exercise:** Zapas wants to show users how active funds compare with the index fund over years 8–14. Which list should the comparison use?

## How long to tell skill from luck?

**Ethan:** Some managers must be good, though. How would we ever know?

**Grace:** Do the sum. Say a manager truly beats the index by 1 point a year, but their yearly result wanders around the index by 6 points. How many years until that edge stands out from the noise?

**Grace:** The noise in an average shrinks with the square root of the years: 6 ÷ √n. We want the edge to be at least two of those: 1 ≥ 2 × 6 ÷ √n. The statistics course calls 6 ÷ √n the standard error.

$$
n = \left(\frac{2 \times \text{tracking error}}{\text{true edge}}\right)^2 = \left(\frac{2 \times 6}{1}\right)^2
$$

*Years of data for a true edge to reach two standard errors*

> **Exercise:** A manager truly beats the index by 1 point a year, with a tracking error of 6 points (how far their yearly result typically wanders from the index). Using n = (2 × tracking error ÷ edge)², how many years of data does it take for that edge to reach two standard errors?

**Sofia:** So a seven-year lead like Star Growth's 9.88 against 7.00 is well inside the noise.

**Grace:** Yes. And one more trap: some funds don't hold the whole market on purpose. They lean towards cheap companies, small ones or recent winners. That's called a factor tilt.

**Grace:** Such tilts have had long good and long bad stretches. A tilted fund isn't the market; it's an active bet that the tilt pays more than its extra cost. We keep global and market-weighted as the default.

> **Exercise:** A fund holds only the cheapest third of the world's companies by price compared with profits, and charges 0.5% a year. How should Zapas describe it?

**Ethan:** Then help me answer the partner. Star Growth beat the index for seven years. Why isn't that skill?

> **Exercise:** Star Growth earned 9.88% a year in years 1–7 against the index fund's 7.00%. In 2–3 sentences, explain to Ethan why this record doesn't show skill and what happened next in the data.

**Grace:** Good. Notice that none of this needed us to know who is skilled. Records this short can't tell us, so the app shouldn't pretend they can.

> **Key ideas**
>
> - Rank on one period, check on the next. The top 5 of years 1–7 ranked 13, 8, 9, 7 and 20 (closed) in years 8–14, averaging 3.96% vs the index's 6.00%.
> - Survivorship: dropping the 5 closed funds lifts the average from 4.20% to 5.13%, 0.93 points no investor earned.
> - Telling a 1-point edge from luck with a 6-point tracking error takes (2 × 6 ÷ 1)² = 144 years.
> - A factor tilt is an active bet; the default stays global and market-weighted.

> **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: [Before and after costs: the arithmetic of the average investor](https://productovi.com/courses/long-term-investing/average-investor-arithmetic.md)
- Next lesson: [Timing the market and the best months you miss](https://productovi.com/courses/long-term-investing/timing-best-months.md)

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