- CFA Exams
- 2024 Level I
- Topic 7. Fixed Income
- Learning Module 9. The Term Structure of Interest Rates: Spot, Par, and Forward Curves
- Subject 1. Maturity Structure of Interest Rates and Spot Rates
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Subject 1. Maturity Structure of Interest Rates and Spot Rates PDF Download
A yield curve is typically constructed on the basis of observed yields and maturities. There are different types of yield curves.
The most common type is the upward-sloping yield curve. The longer maturity issues have higher yields than the shorter maturity issues.
A spot rate is the yield on a zero-coupon bond. A series of spot rates (spot curve) can be used to discount the cash flows of a bond.
Default-free spot rates can be derived from the Treasury par yield curve by a method called bootstrapping. The basic principle of bootstrapping is that the value of a Treasury coupon security should be equal to the value of the package of zero-coupon Treasury securities that duplicate the coupon bond's cash flows.
Example
Determine the spot rate for the fourth period cash flow. The coupon rate is 4.11%, paid semi-annually.
The coupon for each period should be discounted at the corresponding spot rate.
100 = 2.055/(1+0.03/2)1 + 2.055/(1+0.033/2)2 + 2.055/(1+0.035053/2)3 + 102.055/(1+i/2)4 = 2.0246 + 1.9888 + 1.9506 + 102.055/(1+i/2)4
i = 2.0669% and the annualized spot rate is 4.1339%.
A par curve is a sequence of yields-to-maturity in which each bond is priced at par value. A par curve is obtained from a spot curve. All bonds used to derive the par curve are assumed to have the same credit risk, periodicity, currency, liquidity, tax status, and annual yields.
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