ALM LDI YTM calculation

[Lncognito]

Computing portfolio statistics: Portfolio yield (meaning YTM), duration, dispersion of cash flows, and convexity are commonly computed as weighted averages based on market value weighting of each holding in the portfolio. For ALM, these average computations are less accurate than portfolio statistics computed directly from the portfolio’s aggregate cash flows.

In an upward-sloping yield curve, portfolio duration and IRR will be higher-than-average duration and YTM of the bonds because portfolio statistics reflect all cash flows (and return) to be received and the longer maturity bonds will impact the portfolio for a longer time.

Question:

I understand the YTM will be higher for a portfolio of cashflows relative to the price weighted average of the individual bonds. However. Why would MD be higher? As we scale by the YTM, it should be lower if we divide by a higher YTM? Also the McD of both methods would be equal?

[Lncognito]

See below the calculation I made to check, do I miss something?

[MikeyF]

When you calculated the durations you used the spot rate to discount each cash flow and you should have used the ytm of fthe bond (cash flows)

For example for the 6% coupon bond
you have the first year 6/1.02 = 5.88 but you should have 6/1.0485 = 5.72

Also see this:
https://analystprep.com/cfa-level-1-exam/fixed-income/portfolio-duration-limitations/

[Lncognito]

Thanks! That makes sense.

I will have a look.

Thank you once again for the effort