# Bonds: yield, rate risk and the year both fell

> What a bond is, why its price moves with interest rates, short vs long bonds, and a year when stocks and bonds fell together.

- Course: [Long-Term Investing: Index Funds, Risk and Your Own Behavior](https://productovi.com/courses/long-term-investing.md)
- Module: Building the model portfolios
- Lesson 21/32, ~22 min
- Source: https://productovi.com/courses/long-term-investing/bonds-rate-risk

## Is the safe part really safe?

**Alex Tutor:** July 2027 at Zapas. June settled the fund line-up and what each fund really costs; now, four months before the launch, you start building the model portfolios, beginning with the "safe" part.

**Ethan:** The Careful portfolio is mostly bonds, right? Bonds can't lose, so let's call it "safe" on the screen.

**Grace:** First, what a bond is: a loan. You lend \$1,000 to a government or a company, it pays you a fixed 4% a year, \$40, and returns the \$1,000 at the end.

**Sofia:** If I hold it to the end, I get exactly that. Where's the risk?

**Grace:** In the price along the way. If new bonds start paying 6%, nobody pays full price for your 4% bond. Its price drops until its yield matches the new ones.

**Grace:** How far it drops depends on **duration**, roughly how many years until you get your money back on average. A good estimate: price change ≈ −duration × change in yield.

$$
\Delta P \approx -D \times \Delta y
$$

*Price change (%) ≈ −duration (years) × change in yield (points).*

![When yields rise by 2 points, a short bond with duration 2 loses about 4% and a long bond with duration 15 loses about 30%.](https://productovi.com/courses/long-term-investing/diagrams/m6-l1-rate-seesaw.png)

*The longer the bond, the harder rate moves hit its price.*

**Grace:** Take a long bond with duration 15. Yields jump by 2 points. What happens to its price?

> **Exercise:** A long bond has a duration of 15 years. Market yields rise by 2 percentage points. Using price change ≈ −duration × change in yield, by how many percent does its price change? Enter a negative number for a fall.

**Sofia:** Minus 30%. But it still pays the 4% coupon that year, doesn't it?

**Grace:** It does. So that year's return is roughly the coupon plus the price change. Work it out.

> **Exercise:** A \$1,000 long bond pays a 4% coupon (\$40 a year) and has a duration of 15. During the year market yields rise by 2 points. Roughly what is its total return for that year, in %? Use coupon + price change.

**Sofia:** So if the user doesn't sell, the −30% is only on paper?

**Grace:** For one bond held to the end, yes. A fund never "ends": it keeps buying new bonds. Its loss is real for anyone who sells, but it also starts earning the new, higher yields.

**Grace:** Here are both bonds side by side, for rises and a fall in yields.

**Price change of a short and a long bond when yields move**

| Change in yield, points | Short bond | Long bond |
| --- | --- | --- |
| Yield +1 point | -2 | -15 |
| Yield +2 points | -4 | -30 |
| Yield −1 point | 2 | 15 |

*Short bond: duration 2; long bond: duration 15. Estimate: −duration × change in yield.*

> **Exercise:** A short bond has duration 2, a long bond duration 15. Match each case to its approximate price change.

**Sofia:** The long bond moves seven and a half times as much. Why would anyone hold it?

**Ethan:** So the Careful portfolio gets short bonds only?

**Grace:** Depends on the job. Long bonds sometimes help: in the crash of years 21–22, world stocks fell 45.4% while long bonds gained 26.5% and short bonds 10.2%.

**Grace:** But look at year 36. Inflation hit 9.1%, rates rose, and world stocks fell 18.0% while long bonds fell 16.0%. Only short bonds rose, 6.5%, and even they lost 2.4% after inflation.

**Tessaro market in three bad years (synthetic)**

| Year | World stocks | Long bonds | Short bonds |
| --- | --- | --- | --- |
| Year 21, crash | -22 | 14 | 3.9 |
| Year 22, crash | -30 | 11 | 6.1 |
| Year 36, inflation 9.1% | -18 | -16 | 6.5 |

*Nominal returns. Synthetic data.*

> **Exercise:** A user saves for a flat deposit needed in 2 years. Which bond fund suits that money better?

> **Exercise:** In the synthetic Tessaro history, bonds always rose when stocks fell, so a stock-and-bond mix never had a year where both parts lost money.

**Ethan:** So bonds aren't a shield at all?

**Grace:** They are a shield against some storms. Against a crash with falling rates, long bonds helped a lot. Against inflation and rising rates, only short bonds held up, and only in money terms.

**Sofia:** So what do we put on the Careful screen instead of "safe"?

**Grace:** Numbers. In the worst year here, a 60/40 mix with our bond blend lost 12.7%, and that was a bond year, not a stock crash.

> **Exercise:** Look at the three bad years of the synthetic Tessaro history. Which conclusions are supported? Select all that apply.

**Ethan:** Fine, no "safe". Write me the line for the Careful card.

> **Exercise:** Ethan wanted to label the bond-heavy Careful portfolio "safe, bonds can't lose". In 2–3 sentences, explain why that is wrong using the bond numbers from this lesson, and write a more honest one-line label.

**Grace:** Good. Next we mix stocks and bonds and see what each mix did over forty years, including the worst stretch for each.

> **Key ideas**
>
> - A bond is a loan: fixed coupons and the face value back at the end. Its price moves the other way from market yields.
> - Price change ≈ −duration × change in yield: duration 2 and +2 points ≈ −4%; duration 15 ≈ −30%.
> - A year's return ≈ coupon + price change: 4 − 30 = −26%.
> - Bonds helped in the crash of years 21–22 (long +26.5%) but fell with stocks in year 36 (long −16.0%, stocks −18.0%).
> - Choose bond duration by when the money is needed, and describe bonds by their worst real year, not as "safe".

> **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: pick the fund line-up from six factsheets](https://productovi.com/courses/long-term-investing/case-fund-lineup.md)
- Next lesson: [Stocks vs bonds: risk capacity, tolerance and the job you have](https://productovi.com/courses/long-term-investing/stocks-bonds-mix.md)

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