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I keep reading that floating rate notes trade on par on coupon reset days.

Is this always true, regardless of changes in the issuer's credit quality since the FRN was issued?

It seems probably that a change in the issuer's perceived credit quality should be visible in the price, but I am a novice in this area...

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your concern about issuer's credit quality deterioration is valid. price would be par when a spread over reference index for the purpose of coupon determination is the same as a spread used for discounting (subject reference curve and discount curves are the same) - i.e. reset margin equals discount margin.

have a look at seminal paper Salomon Brothers - An Investor's guide to FRNs

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