Government Bond
Also known as: Treasury, Bund, Gilt, Sovereign
A loan to a state, and the reference price of money itself — the yardstick every other asset is measured against.
1 · SnapshotThe one idea to remember
2 · BeginnerWhat is it, really?
A government bond is an IOU from a country: lend the state money today, and it promises fixed interest payments (coupons) every period and your money back (the principal or face value) at maturity.
Because rich-country governments can tax — and, in their own currency, print — their bonds are treated as the closest thing markets have to a risk-free asset. That makes their yields the baseline price of money: mortgages, corporate loans and stock valuations all key off them.
One rule to internalise: prices and yields move in opposite directions. If new bonds pay 4% and yours pays 2%, nobody buys yours at full price — it must get cheaper until its effective return matches. Rates up, bond prices down; rates down, prices up.
- Asset class
- Fixed income
- Instrument type
- Sovereign coupon bond
- Traded
- OTC dealer market, huge and liquid
- Typical users
- Central banks, pensions, banks, everyone
3 · IntermediateHow it works in practice
Reading a bond quote
- Coupon: annual interest as % of face (paid semi-annually for Treasuries, annually for Bunds).
- Yield to maturity (YTM): the single discount rate equating price to promised cash flows — the "internal rate of return" if held to maturity.
- Clean vs. dirty price: quotes exclude accrued interest; you pay clean + accrued ("dirty").
The yield curve
Plot yields against maturities and you get the yield curve — normally upward-sloping (long lending pays more), inverting when markets expect rate cuts, which is why inversion is a famous recession signal. The curve embodies expected policy rates plus a term premium.
Duration: the risk number
Duration measures price sensitivity: a bond with duration 7 loses ≈ 7% of its price per 1 percentage point rise in yield. Longer maturity and lower coupons → higher duration. This is the single number bond portfolios are managed around.
4 · AdvancedPricing & valuation
Pricing off the curve
The price is the sum of discounted cash flows; the honest version discounts each flow at its own maturity's rate (the zero/spot curve \(z_t\)):
What the symbols mean
- Pa price, or a present value
- ta point in time
- Tmaturity, in years
- cthe coupon rate
- Cthe price of a call option
- Fthe forward or futures price
YTM \(y\) is the flat-rate shortcut. Zero curves are bootstrapped from bond prices; forward rates \(f(t_1,t_2)\) follow from no-arbitrage between zeros.
Duration and convexity, precisely
What the symbols mean
- Dduration: how far a bond's cash flows sit in the future
- Pa price, or a present value
- ythe yield to maturity
- Cthe price of a call option
- Deltahow much a derivative moves when the underlying moves
Convexity is why the price–yield curve bows: losses decelerate and gains accelerate — valuable, hence low-coupon long bonds (high convexity) trade at slightly lower yields, other things equal.
Beyond one factor
Curve risk is multi-dimensional; desks hedge key-rate durations (sensitivity to each maturity bucket) and trade level/slope/curvature factors, which explain ~99% of curve variance in PCA. Term-structure models (Vasicek, Hull–White, HJM) impose no-arbitrage dynamics for pricing derivatives on these curves.
The plumbing premia
Even sovereigns have basis effects: on-the-run vs. off-the-run liquidity, repo specialness, and the futures delivery cycle all create yield wedges unrelated to credit — the raw material of relative-value trading.
The formulas above are standard textbook formulations, simplified for teaching. They explain the mechanism — they are not a valuation tool, and they will not reproduce a dealer’s price.
5 · Desk notesHow practitioners think about it
Where this instrument shows up elsewhere
- Why does a bond lose value when interest rates rise?Start hereQuestionsNobody will pay full price for last year's interest rate when this year's is higher
- The Yield CurveSome background helpsConceptsOne line, drawn from overnight to 30 years — the bond market's forecast, the economy's mood ring, and a P&L engine…