# Volatility and a typical bad year

> Standard deviation of yearly returns, what a typical bad year and the worst year look like for stocks and short bonds.

- Course: [Long-Term Investing: Index Funds, Risk and Your Own Behavior](https://productovi.com/courses/long-term-investing.md)
- Module: How much can you lose, and for how long?
- Lesson 5/32, ~23 min
- Source: https://productovi.com/courses/long-term-investing/volatility-bad-year

## Is −12% normal?

**Grace:** It's March at Zapas, and the beta users are writing to support more often. As the PM you'll answer a lot of these, so let's start with today's top question.

**Ethan:** Here it is: "My balance is −12% this month. Is this normal, or is something broken?" Can we just reply "Don't worry, markets go up on average"?

**Grace:** "On average" is exactly the problem. The average year of Tessaro World in our 40 synthetic years was +10.3%. But almost nobody lives through an average year.

**Grace:** Look at the bars. 9 of the 40 years were negative. The worst, year 22, was −30.0%; the best was +34.0%. Short bonds, by contrast, never had a losing year.

**Tessaro yearly returns, 40 synthetic years**

| Year | World stocks | Short bonds |
| --- | --- | --- |
| 1 | 25.7 | 4.8 |
| 2 | -7.3 | 4.2 |
| 3 | 13.2 | 3.7 |
| 4 | -6.1 | 5.1 |
| 5 | 17.5 | 4.1 |
| 6 | 13.6 | 5 |
| 7 | 20.7 | 4.8 |
| 8 | 9.7 | 4.1 |
| 9 | 18.8 | 4.8 |
| 10 | -4.2 | 3.6 |
| 11 | 6.4 | 4.7 |
| 12 | 14.6 | 4 |
| 13 | 13.1 | 4 |
| 14 | 17.1 | 3.9 |
| 15 | 2.1 | 2.9 |
| 16 | 24.2 | 5.7 |
| 17 | 28.3 | 4.1 |
| 18 | 0.6 | 3.4 |
| 19 | 2.5 | 4.2 |
| 20 | 16 | 3.7 |
| 21 | -22 | 3.9 |
| 22 | -30 | 6.1 |
| 23 | 28 | 4.2 |
| 24 | 18 | 4.4 |
| 25 | 15 | 5.3 |
| 26 | 8.9 | 4.5 |
| 27 | -2 | 5.2 |
| 28 | 14.3 | 4.4 |
| 29 | 11 | 4.4 |
| 30 | -1.9 | 4.1 |
| 31 | 22 | 5.7 |
| 32 | 3.7 | 5.7 |
| 33 | 26.8 | 3.2 |
| 34 | 14 | 3.9 |
| 35 | -4 | 5 |
| 36 | -18 | 6.5 |
| 37 | 6 | 7.5 |
| 38 | 34 | 6.2 |
| 39 | 32.7 | 6 |
| 40 | 29.2 | 4.4 |

*Nominal, in dollars. Dashed lines: the average year of world stocks (+10.3%) and a typical bad year (−4.4%). Synthetic data, not a forecast.*

**Dataset (CSV):** [Tessaro market, 40 synthetic years (nominal %, inflation %)](https://productovi.com/datasets/long-term-investing/volatility-bad-year/market_history.csv)

**Sofia:** So "average +10%" and "lost money in more than one year of five" are both true.

**Grace:** Both true, and a user who hears only the first will feel cheated by the second. Our job is to show both before the money goes in, not after the first red month.

> **Exercise:** In the 40 synthetic years of Tessaro World, how many years ended with a loss?

## Standard deviation and a bad year

**Grace:** To describe the swings in one number we use the **standard deviation**, SD for short. For world stocks it's 14.7 points; for short bonds, 1.0. The [statistics course](/courses/statistics-for-pm-and-marketers) has a whole lesson on it.

**Ethan:** A number like "14.7" won't mean anything to a user.

**Grace:** Agreed. So translate it into years people recognise. A **typical bad year** is the average minus one SD: 10.3 − 14.7 = −4.4%. A typical good year is +25.0%. 28 of our 40 years landed between them.

![World stocks averaged +10.3% a year, most years fell between −4.4% and +25.0% and the worst was −30.0%; short bonds stayed near +3.7% to +5.6% and never lost a year.](https://productovi.com/courses/long-term-investing/diagrams/m2-l1-bad-year-ladder.png)

*One SD each side of the average holds most years, not all of them.*

**Sofia:** And the other 12 years were outside that band, some of them far below.

> **Exercise:** World stocks in the Tessaro history averaged +10.3% a year with a standard deviation of 14.7 points. What is a typical bad year (average minus one SD), in percent?

> **Exercise:** Since the average Tessaro World year was +10.3%, a new user should expect roughly +10% in their first year.

## Calm money, low return

**Ethan:** Then why not put everyone in short bonds? Zero bad years!

**Grace:** Because calm costs return. Short bonds averaged 4.6% a year in dollars, but after inflation only about 1.4% real. Stocks pay for the swings with more growth. Which one fits depends on when the user needs the money.

**Ethan:** So bonds for money needed soon, stocks for money that can sit for years?

**Grace:** That's the rough idea, and we'll build the actual mixes in summer. For now, every screen that shows a return should also show how that same thing behaved in a bad year.

> **Exercise:** Match each Tessaro figure with what it describes.

> **Exercise:** Which risk line should the portfolio screen show a new user?

## Back to the −12% month

**Sofia:** But the user asked about a month, not a year.

**Grace:** Good catch. Months swing less in absolute size but far more often. Over 480 months the average was +0.81% with an SD of 3.62. 25 months were −5% or worse; only one reached −10%, and the worst was −11.15%.

**Dataset (CSV):** [Tessaro World month by month, 40 synthetic years (%)](https://productovi.com/datasets/long-term-investing/volatility-bad-year/world_monthly.csv)

Monthly returns of the world stock fund, nominal, in dollars: 480 months. The average month was +0.81% with an SD of 3.62 points; 25 months lost 5% or more, one lost more than 10%, and the worst was −11.15% (year 22, March). Synthetic data made for this course.

- `year`: Year of the synthetic history, 1 to 40
- `m01`: Return in January, %; m02 to m12 are February to December

**Ethan:** So −12% in a month would be worse than anything in our 40 years.

**Grace:** Yes, so first check the user's portfolio. A world fund alone almost never moves that much; a theme fund or a single company can. If the market really did fall that hard, they deserve a straight answer, not a slogan.

> **Exercise:** Of 480 months of Tessaro World, 25 lost 5% or more. What share of months is that, in percent, to one decimal?

> **Exercise:** Write the support reply to the beta user who asks: "My balance is −12% this month. Is this normal?" Use 2–4 sentences and the Tessaro numbers, without promising anything.

> **Key ideas**
>
> - The average Tessaro World year was +10.3%, but 9 of 40 synthetic years lost money; the worst was −30.0%, the best +34.0%.
> - **Volatility** is how much returns swing; the **standard deviation** puts it in one number: 14.7 points for world stocks, 1.0 for short bonds.
> - A typical bad year = average − 1 SD = −4.4%; a typical good year = +25.0%. 28 of 40 years fell between them.
> - Short bonds never lost a year but earned only about 1.4% a year after inflation.
> - Months are noisier: 25 of 480 months lost 5% or more; the worst month was −11.15%.

> **Educational, not advice**
>
> This course explains how long-term investing works; it never tells 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.

**Grace:** One bad year is the easy part. Tomorrow we look at year 21 and 22 together: how deep the fall went and how long it took to come back.

- Previous lesson: [Case: rewrite the "12% a year" landing page](https://productovi.com/courses/long-term-investing/case-landing-page.md)
- Next lesson: [Drawdown, recovery and time under water](https://productovi.com/courses/long-term-investing/drawdown-recovery.md)

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