Campisi Fixed Income Attribution - Income Contribution Explained

Recall from my previous posting, the steps to executing the Campisi fixed income attribution model are:

1. Decompose the benchmark return into:
   - income contribution
   - Treasury contribution (i.e., price change due to changes in Treasury rates)
   - spread contribution (i.e., price change due to changes in the average spreads of a risky bond class
    
2. Decompose the index portfolio return into:
   - income contribution
   - Treasury contribution (i.e., price change due to changes in Treasury rates)
   - spread contribution (i.e., price change due to changes in the average spreads of a risky bond class
3. Calculate the index portfolio spread change.  This is the change in interest rates that will be used to calculate the spread contribution of the portfolio (more on this in a subsequent blog post).
4. Decompose the portfolio return into:
   - income contribution
   - Treasury contribution (i.e., price change due to changes in Treasury rates)
   - spread contribution (i.e., price change due to changes in the average spreads of a risky bond class
   - security specific contribution
5. Calculate the attribution effects as the value added contributions:
   - income effect = portfolio income contribution minus the benchmark income contribution
   - Treasury effect = portfolio Treasury contribution minus the benchmark Treasury contribution
   - spread effect = portfolio spread contribution minus the benchmark spread contribution
   - selection effect = portfolio selection contribution (note - the benchmark has no selection contribution)

The first step under items 1, 2 and 4 above are to calculate an income contribution (for the benchmark, index portfolio and portfolio, respectively).

The income contribution is how much of the return comes from the income paid by the bonds in the portfolio or benchmark.  We express this income contribution as a rate of return, which has a numerator and a denominator.  The formula for this contribution is simply:

For example, in your reading, the portfolio's weighted average coupon is 7.118% and the  portfolio's weighted average price is 98.1.  Thus, the contribution of income to the total return of the portfoli may be calculated as:

To say it differently, out of the portfolio return of 0.31%, the portion that comes from income is the weighted average coupon divided by the weighted average price which is 7.26% in total.  Thus, obviously the sum of the other contributions must be negative.

The income contribution can also be calculated from money amounts:

Essentially, the income contribution is a form of current yield, comparing interest earned by the manager's portfolio to the market value invested to earn that income. 

Given, then, that the portfolio return may be decomposed into income and price change, we have decomposed the income portion of the return.  All remaining elements are part of the price change component.  We'll tackle that subject next!

Happy studying!