Dispersion - Fixed Income

Would anyone be able to explain dispersion as it relates to Fixed Income in plain English?

CFAI defines it is “weighted variance of the times to receipt of cash flow” and I could just memorize this but in the spirit of the curriculum I would like to make the effort to fully understand the concept.

Much thanks in advance!

Say you are trying to immunize a 7 year duration liability and have two options, a zero coupon bond with 7 years to Maturity or a combination of a 2 year zcb and a 9 year zcb They both have duration 7,but the 7 year has zero dispersion of its cash flows around its duration because there is just one payment. The two combined zcbs have one payment before the duration and one after, so there are some cash flows that don’t lie on the duration. Think of it like a fulcrum and the two payments are balancing out at 7 years.

Now, if spot rates change at the 7 year, the single payment is affected the same way as the liability so the portfolio remains immunised,it moves in the same way. But the 2 year and 9 year spot rates might move differently and we will have to adjust the portfolio to re immunise.

The dispersion is higher than zero so we have more spot rate moves to monitor to keep our portfolio immunised.

Higher dispersion means more cash flows spaced away from the duration, so a higher effect from yield changes.

Plot the cash flows on a chart and see how spaced out they are. Then imagine having to discount each cash flow with spot rates.

But it is better if assets have a HIGHER dispersion than liabilities right? To avoid both reinvestment and immunization risk. In your example for 7y bullet a one time asset may be desirable, but I believe with several cash flows an asset with with greater dispersion is desirable. Agree?

Rule for single liability is minimize dispersion to avoid structural risk. You’re comparing a single liability to a multitude of assets to match it so that’s more risky in terms of yield curve changes.

Rule for multiple liabilities is have dispersion be somewhat higher than liabilities. Not significantly higher as that introduces too much structural risk. But some dispersion (convexity) allows the portfolio to profit more from larger parallel movements.

Moonbourne is straight cash with all his answers. Always on point dude.

Thanks. I get to help fellow candidates while rehearsing the concepts myself! Win-win.

Convexity is a measure of dispersion of cash flows, maturities or durations?

For example CFA exam 2017 q 9C: portfolio B is selected as best to immunise multiple liabilities because its convexity is higher based on asset bonds durations and not maturities.

Thank you.