Yield Curves, Spot Rate Curves, and Swap Rate Curves

Summaries

·         Types of shifts in yield curve

1. Parallel shift
2. Non-parallel shift
1. Twists

                                                               i.      upward shift => flatter

                                                             ii.      downward shift =steeper

2. Butterfly

                                                               i.      positive butterfly => less curvature

                                                             ii.      negative butterfly => more curvature

·         95% of the yield curves can be explained by the aforementioned factors

·         Maturities of US Treasury Securities

1. T-bill 4,13, 26 weeks
2. T-note 2,3,5,10 years
3. T-bond 30years

·         Use Bootstrapping method to find spot rates

·         Spot rate => how to discount a future cash flow (yield curve for zero coupon)

·         Construction of spot rate curve (pros and cons)

1. All On-the-run Treasury Securities (updated, missing points)

2. All on-the-run + some off the run (reduced gap, not contain all information, distorted by repo)

3. All Treasury Coupon Securities and Bills (less gap, many yields for same maturities)

4. Treasury Strips (No need bootstrapping, less liquid, tax treatment distortion)

·         Swap rate curve = LIBOR curve

·         LIBOR is dollar-based

·         Each currency has its own swap rate curve

Questions

What is the difference between yield curve and spot rate curves?

Spot rate is telling how to discount a future cash flow. So it is equivalent to the yield of zero-coupon. It is a special case of yield curves. Yield curve is telling the effective “yield” of an instrument with different maturities.