A fixed income market index can be viewed as a large set of future cash flows, divisible into any number of intervals. Each interval can be characterized by a forward rate—the implied rate earned over the interval. By measuring the sensitivity of the index to a change in each forward rate (holding all other forward rates constant), the partial derivative approach provides an accurate measure of the index’s exposure to changes in the level and shape of the yield curve.
To apply the PDA, one must first define appropriate yield curve intervals. Because changes in near forward rates have a much greater impact on value than changes in far forward rates, it is reasonable to use shorter intervals for the near term and longer ones for the far term. Next, one calculates the index’s exposure to a series of forward rate changes, making separate calculations for each bond in the index.
Risk exposures are similarly calculated for the bond fund constructed to track the index. The differences between the portfolio’s and the index’s risk exposures define the portfolio’s deviation from the index. The portfolio can then be adjusted to balance the client’s desired degree of risk exposure with the expectation of excess return.