Key Concepts
The primary yield curve risk factors are level, slope, and shape. Yield curve changes can be decomposed into these factors by principal components analysis.
\[ \begin{split} \text{butterfly spread} = &\ 2\cdot \text{medium-term yield} \\ &-\text{short term yield} \\ &- \text{long term yield} \end{split} \]
Taylor approximation of present value for change in yield: \[ \%\Delta PV ^{\text{Full}} \approx -(\text{ModDur}\cdot \Delta \text{Yield})+(\frac{1}{2} \cdot \text{Convexity} \cdot \left(\Delta \text{yield})^2 \right) \]
A bond with higher convexity will gain more from a rate decrease and lose less from a rate increase.
Yield Curve Strategies
An investor who believes the yield curve is static can increase returns by increasing duration or leverage of the portfolio.
Buying a bond with a maturity longer than the investment horizon will yield more than one that matches the investment horizon by rolling down the yield curve.
Financing a long term purchase at repo rates generates a repo carry return if the rolldown yield exceeds the financing cost.
A receive-fixed swap is like a repo carry but pays a market reference rate instead of the repo rate.
- Bull Steepening
- Short term rates fall more than long term rates
- Bear Steepening
- Long term rates rise more than short term rates
Bear steepening scenario should short duration, bull should long duration.
A butterfly position combines an intermediate bullet position with a long and short term barbell position.
Active Fixed-Income Management Across Currencies
- Covered interest rate parity
- \[ F(\frac{DC}{FC}, \ T) = S_0(\frac{DC}{FC})\frac{(1+r_{DC})^{T}}{(1+r_{FC})^{T}} \]
- Butterfly spread
- Twice the intermediate term rate minus the short term and long term rates