Asset duration and liability duration leading to reinvestment risk

If asset duration is < than liability duration, portfolio is exposed to reinvestment risk:

If ↓I.R we have ↓ reinvested coupon and principal payments. If ↓I.R; ↑ value of bonds.

Losses from reinvested coupon and principal payments are > than gains from appreciation in the value of outstanding bonds. (I get this part). But can someone please explain how the asset is considered the value of the bonds, while the liability is considered the coupon and principal?

You’re misinterpreting.

The asset is the value of the bonds and the reinvestment income (remember, YTM includes reinvestment at the current rate). The liabilities are the absolute value of future payments needed. The future CPN interest and CPN income is considered an asset

I see, so both the coupon and principal payments, and the value of the bond are related to the asset. So when asset duration is < than liability duration (short duration), change in bond price is less sensitive than change in reinvested coupons/principal. Hence why reinvested coupons/principal dominates and you are exposed to reinvestment risk. Is that correct?

What is reinvested principal?

YTM captures most of the effect. Focus on YTM

if coupons are at 5%. And interest rates decline from 5% to 3%.

YTM will decline, ie, Price will increase reflecting the favorable coupons rate in comparison to what the market is offering.

Reinvestment effect: You are reinvesting the coupons. You are getting returns on the coupons. Returns on the coupons went from 5% of 5% to 3% of 5 %. That is: from 0.25% to 0.15% of the Bond’s face value. Less than a cost of a Venti Latte.

Focus on YTM

Hi, all, this is how i understand the question, can someone please confirm if this is correct?