35:null 36:["$","title",null,{"children":"“Bonds Aren’t Safe” — Rate Rises Hurt More Than You Think | Etienne Pema Lafleur | Observable"}] 3c:T41e,## Why does this happen? A bond pays a **fixed** coupon. If you own a 4% bond and new bonds start paying 7%, nobody will pay full price for yours — its price has to drop until its yield matches the market. The longer your bond has left to run, the more years you're stuck earning below-market interest, so the bigger the price drop. Bond pros call this sensitivity **duration**. **The math (pure formula, no data download):** `P = C × [1 − (1 + r)^−n] / r + FV × (1 + r)^−n` - `C` = annual coupon ($40 on a 4% bond) - `r` = new market yield (4% + the slider) - `n` = years to maturity - `FV` = face value ($1,000) **Assumptions:** annual compounding, every bond issued at par with a 4% coupon, an instant parallel shift in rates. Real bonds and bond funds differ in coupon, compounding and convexity, but the lesson holds: *long bonds are not low-risk when rates can rise.* *Context: in 2022, the 10-year Treasury yield rose about 2.5 points, and long-dated Treasury funds lost roughly 30% — one of the worst years for bonds on record.*3d:[] 3a:{"id":"2a3524c76105758a","slug":"bonds-arent-safe-rate-rises-hurt-more-than-you-think","title":"“Bonds Aren’t Safe” — Rate Rises Hurt More Than You Think","thumbnail":"062e4be2ba2391b16fcb72fc94a93cc327d37e6e4a46bdc5d449d3cb4d7f5557","access_level":"public","create_time":"$D2026-10-19T15:30:38.972Z","update_time":"$D2026-10-19T15:35:05.558Z","view_time":null,"first_public_time":"$D2026-10-19T15:35:51.724Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"217b00e487e758d3","login":"etienne-pema-lafleur","name":"Etienne Pema Lafleur","avatar_url":"https://avatars-next.observableusercontent.com/b09275e7b6b3576ac1a1f4c68e1b8ce25afb4b108c78fab2bdadfe497f992b62","tier":"starter_2024","bio":"","following":false},"version":23,"publish_version":23,"role":null,"authored":false,"authors":[{"type":"individual","id":"2e1cc15858c34694","login":"epema","name":"Etienne Pema Lafleur","avatar_url":"https://avatars-next.observableusercontent.com/b09275e7b6b3576ac1a1f4c68e1b8ce25afb4b108c78fab2bdadfe497f992b62","tier":null,"bio":"","following":false}],"members":[{"type":"team","id":"217b00e487e758d3","login":"etienne-pema-lafleur","name":"Etienne Pema Lafleur","avatar_url":"https://avatars-next.observableusercontent.com/b09275e7b6b3576ac1a1f4c68e1b8ce25afb4b108c78fab2bdadfe497f992b62","tier":"starter_2024","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"“Bonds Aren’t Safe” — Rate Rises Hurt More Than You Think","cells":[{"id":1,"value":"# \"Bonds Aren't Safe\" — Rate Rises Hurt More Than You Think\n\n*Drag one slider and watch your \"safe\" long-term bond lose a huge chunk of its value.*\n\nMost people treat bonds as the \"safe\" part of a portfolio. But when interest rates rise, existing bonds lose value — and the longer the bond, the bigger the hit. Drag the slider right (rates up) to see losses, or left (rates down) to see gains.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2,"value":"// The one interaction: how much do interest rates move? (percentage points)\nconst rateChange = view(Inputs.range([-3, 5], {\n step: 0.25,\n value: 3,\n label: \"Rate change (pp)\"\n}));","pinned":true,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":4,"value":"// The chart: one bar per maturity, red = loss, green = gain\nconst label = (d) => (d.change > 0 ? \"+\" : \"\") + (d.change * 100).toFixed(1) + \"%\";\n\ndisplay(Plot.plot({\n width: 680,\n height: 380,\n marginLeft: 56,\n x: {label: \"Bond maturity\", domain: bonds.map((d) => d.maturity), padding: 0.2},\n y: {label: \"Price change (%)\", domain: [-0.6, 0.8], tickFormat: \"+.0%\", grid: true},\n color: {domain: [\"loss\", \"gain\"], range: [\"#d1495b\", \"#2a9d8f\"]},\n marks: [\n Plot.barY(bonds, {x: \"maturity\", y: \"change\", fill: (d) => (d.change < 0 ? \"loss\" : \"gain\"), tip: true}),\n // value labels: below the bar end for losses, above it for gains\n Plot.text(bonds.filter((d) => d.change < 0), {x: \"maturity\", y: \"change\", text: label, dy: 14, textAnchor: \"middle\", fontWeight: \"bold\", fontSize: 13}),\n Plot.text(bonds.filter((d) => d.change >= 0), {x: \"maturity\", y: \"change\", text: label, dy: -10, textAnchor: \"middle\", fontWeight: \"bold\", fontSize: 13}),\n Plot.ruleY([0])\n ]\n}));","pinned":true,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"// A live, plain-English takeaway that updates with the slider\nconst long = bonds.at(-1), short = bonds[0];\nconst pct = (x) => (x > 0 ? \"+\" : \"\") + (x * 100).toFixed(1) + \"%\";\nconst dollars = (x) => \"$\" + Math.round(x).toLocaleString();\n\ndisplay(rateChange === 0\n ? html`

Rates unchanged: every bond is still worth its $1,000 face value. Drag the slider to move rates.

`\n : html`

If rates ${rateChange > 0 ? \"rise\" : \"fall\"} by ${Math.abs(rateChange)} points (4% → ${(newYield * 100).toFixed(2)}%),\n a $1,000 30-year bond becomes worth ${dollars(long.price)} (${pct(long.change)}),\n while a 2-year bond moves only ${pct(short.change)}.\n ${rateChange > 0 ? \"The longer you lock in a fixed rate, the more it hurts when new bonds pay more.\" : \"Falling rates make your locked-in 4% coupon more valuable — the longer the bond, the bigger the gain.\"}

`);","pinned":true,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":6,"value":"// The numbers behind the bars\nInputs.table(bonds, {\n columns: [\"maturity\", \"price\", \"change\"],\n header: {maturity: \"Maturity\", price: \"Price of a $1,000 bond\", change: \"Change\"},\n format: {\n price: (x) => \"$\" + x.toFixed(2),\n change: (x) => (x > 0 ? \"+\" : \"\") + (x * 100).toFixed(1) + \"%\"\n },\n select: false\n})","pinned":true,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"$3c","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3,"value":"// Bond pricing math — no data download needed.\n// P = C × [1 − (1+r)^−n] / r + FV × (1+r)^−n (annual compounding)\nconst FACE = 1000; // face value\nconst COUPON = 0.04; // 4% annual coupon, issued at par (starting yield = 4%)\nconst maturities = [2, 5, 10, 20, 30];\n\nfunction bondPrice(yieldRate, years, coupon = COUPON, face = FACE) {\n const c = coupon * face;\n if (Math.abs(yieldRate) < 1e-9) return c * years + face;\n const disc = Math.pow(1 + yieldRate, -years);\n return c * (1 - disc) / yieldRate + face * disc;\n}\n\nconst newYield = COUPON + rateChange / 100;\n\nconst bonds = maturities.map((years) => {\n const price = bondPrice(newYield, years);\n return {maturity: years + \"-year\", years, price, change: (price - FACE) / FACE};\n});","pinned":true,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W3d","stdlib":"2"}} 3b:"$3a:body"