Key Rate Duration and Convexity in Fixed-Income Curve Returns

# Factor Model - Fixed Incom


# Factor Model - Fixed Incom












I am reading Bloomberg's fixed income fundamental factor model doc. And they define their curve factor (motivation for this factor: most fixed income securities' prices are largely impacted by the movement of the yield curve):

$$R_{yc} = - \sum_{i=1}^9 KRD_i \cdot \Delta y_i + \frac{1}{2} OAC \cdot(\overline{\Delta y})^2$$

And here are the explanations of what each term means:

- curve factors are nine par rate changes along the 6M, 1Y, 2Y, 3Y, 5Y, 7Y, 10Y, 20Y and 30Y tenors and the square of the average curve change. The exposures of these factors are key rate durations and the option-adjusted convexity.

$R_{yc}$ is the return due to curve change, $\Delta y_i$ is the reate change of the par swap curce at i-th tenor point and $\overline{\Delta y}$ is the simple average of changes across all tenor points.

To be honest, the above is not very clear for me. I am looking to incorporate this curve factor, as one of the factors in my model. I am trying to understand how each component is computed and whether $R_{yc}$ is a global value or dependent on each bond.

Here is what I think:

- $KRD_i$ is calculated on the sovereign curve/swap curve. $\left(KRD_i = \frac{P_--P_+}{2 \cdot 1\% \cdot P_0} \right)$

- $\Delta y_i$ is calculated from a swap curve (it says it is a rate change, so I am not sure how exactly to calculate this).

What I do not know:

- How to compute $\Delta y_i$

- How to compute OAC

- Do I then include this $R_{yc}$ as a factor (dependent variable) in my linear factor models for bonds and try and find exposure (slope/sensitivity to this param)? (Because clearly, it looks like this $R_{yc}$ is not calculated per bond; i.e. you need 9 tenors, and your bond's maturity may be 2 years, for example).