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It is stated on P.38 of CFAI Text, Vol 4 as follows.

An asset (here, shall be a bond or a bond portfolio) that "MAKES" floating payments will typically have caps associated with the floating rate. The manager is at risk of the level of market rates rising while the asset returns are capped. This event may severely affect the value of the assets.

My question : Shall it be that : An asset (here, shall be a bond or a bond portfolio) that "RECEIVES" floating payments ?

You got it right.

If a manager with a floating rate liability invests in a floating rate bond that has a cap, there will be a risk to the manager. The liability will reprice to 100 as the coupon payment reset to reflect the new market rates. However when the asset is capped and interest rates rises above the cap rate, the coupon will be fixed to the cap and it has a twin negative effect.

1. Coupon received will be lower than coupon paid
2. While liability reprices to 100 due to flexibility asset will be repriced downwards because the floating rate note has been effectively converted to a fixed rate note (at the cap rate) and experience a downward pricing because of duration.

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It depends whether you are holding that asset or you are the issuer. If you are holding it, then you have cap risk. If you are the issuer, caps work in your favor.

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