[Verse 1] Treasury bonds are puzzle pieces, prices scattered on the floor Each maturity tells secrets of the rates we're searching for Start with shortest-term instruments, six months or maybe one Calculate their implied returns, the bootstrapping has begun [Chorus] Bootstrap up the curve, bond by bond we climb Short to long maturity, building rates through time Strip away the coupons, find the zero yield Spot rates emerge like diamonds from the pricing field [Verse 2] Take a two-year government bond, it pays you twice a year Discount back the first coupon with the one-year rate that's clear What remains is principal plus that final interest flow Solve for what discount rate makes present value equal what we know [Chorus] Bootstrap up the curve, bond by bond we climb Short to long maturity, building rates through time Strip away the coupons, find the zero yield Spot rates emerge like diamonds from the pricing field [Bridge] Iteration after iteration, each new rate unlocks the next Three-year bonds need one and two-year rates to be perplexed Five years needs the previous four, it's mathematical cascade Risk-free curve takes shape before us, foundation rates we've made [Verse 3] Government securities only, credit risk we must exclude Corporate bonds have extra spread, they'd make our curve skewed Pure time value of money, that's what spot rates should reveal Bootstrap method guarantees our zero-coupon curve is real [Outro] From the shortest bills to longest bonds The spot rate curve responds Bootstrap methodology Creates our yield harmony
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