Clean Price/Full Price Question

Maybe I’m over-thinking this and that’s why I just can’t wrap my head around it. If anyone can explain, I would really appreciate it. My question is, why do we SUBTRACT accrued interest from full price to compensate the seller? Since the buyer will receive the next coupon payment from the issuer, shouldn’t we ADD the accrued interest since the seller would not be able to get this from the issuer and instead, the buyer gets it? The following is my take. If you find a fault, please let me know! Ex) A-------------------B--------------------C last coupon settlement next coupon paid date payment Full price = PV at settlement date (does not include period between A-B) A-B = accrued interest Clean price = full price - accrued interest But, buyer will get coupon payment between A-C from the issuer Since seller earned the coupon payment from A-B, buyer should compensate the seller by ADDING accrued interest to the full price, no? ***PLEASE HELP!

This may be wrong, but my guess is you’re calculating the full price from the time immediately after payment of A, so A-B is already figured into the price, and you are subtracting that time period out to find the value at time B.

Ok, I was thinking about this the whole day today and I think I understand where my reasoning was illogical, and this is consistent with your explanation, swe30. I think I assumed that when we find the PV of the future payments, it was PV AT SETTLEMENT DATE, but what you’re saying is that it’s NOT PV at settlement date, it’s PV basically at the time of last coupon payment, right? If that’s the case, then I can go to sleep tonight…

rockstar you are correct. If the buyer buys the bond at B, we subract the interest off from A to B because at B the bond is worth less than at point A because its closer to maturity. So we can value the bond at A, which is the dirty price, then subtract off how much interest accrued from A to B to arrive at the clean price. Think of it this way. at A seller gets payment. immediately it begins earning interest. at B, that coupon at A has already been earining interest, so by deducting the accrued interest from the buyer, the seller isn’t losing out. Dirty price includes interest from A to B the seller already earned.

Thanks for the confirmation, BayStreet… Then, I have a part 2 question for you… If you say that we value the bond at A (=dirty price) then subtract the accrued interest, then how come according to the book, the computation of the full price is discounting back only TO settlement date? Ex) A--------------------B---------------C --pr.0-----------------78days----------182days => PV(full price) = CF/(1+r)^(78/182) Since we discounted it back 78/182 days rather than the full year, doesn’t that mean the PV of the future CF is at B?? This is what has been confusing me… I want to punch accrued interest in the face.

hold on a second, the 78 days at B. is that 78 days until C, or 78 days from A? That makes a huge difference in solving the question. If its 78 days until C, then at B, the PV of tha payment at C is CF/(1+r)^(78/182). basically you calculate the bond at the last coupon payment, then bring it to where you are today using FV (dirty price), THEN subtract the accrued interest (you dont subtract it from point A, that was my typo if I said you did before), which in this case is the amount of payment you would have earned to date. See if the below link helps clarify. So for your example, say you sell the bond at B. Find the PV at A, bring it forward to B using PVatA*(1+r)^(days to B/days between coupons), then subtract the accrued coupon interest which is CF at C*(days from A to B/ days between coupons). Are you using the CFAI books? If so what page? This link is really good for bond valuation. also tells you how to use a BAII the following is just a side note about accrued interest just to make sure we’re talking about the same accrual here. Im sitting at my desk eating lunch and have nothing else to do lol. Accrued interest and accrued bond interest on coupons are different. For example. If I invest 100 at 10% per year, halfway through the year I will have accrued 100*(1.1)^.5 - 100 = 4.88 of interest, this assumed compounding. The thing with bonds is they dont compound interest, bonds earn interest equally each day up until the coupon payment. The interest in this case is the amount of coupon you earned from A to B. so for halfway through the year for a bond that pays 100 annually, your accrued interest is 100 (180/360) = 50, using the 360 rule. Two very different amounts. The compounding occurs when you invest the coupons in the market at the going rate

What is confusing me is why the full price is calculated using fractions of a power, over all future payments to calculate the PV. If you look at the stream of payments it’s a number of coupons discounted at (1.04)^0.4286 or x.42.86. I thought only the upcoming coupon – but NONE of the others – would be subject to the fraction of a power treatment. After all, other coupons are NOT involved in accrued price calculation, so this doesn’t make sense to me. I am not sure I have couched this query in understandable terms, perhaps a function of the lack of explanation in the reading I am trying to understand.

I haven’t touched this since the last message I posted, but coming back to it now and with your detailed explanation, Baystreet(that you so generously shared with me your work lunch hour for), I think I finally understand why I had troubles with this. Thanks a lot! G’luck on your studying! Fyi, the page I was referring to is Reading 64 page 412-413. Cheers

petess99, if I may answer (as the student who has become the master,… not really…=)) , I believe you discount the future payments as a fraction as well b/c the fraction is not implying that it is only for accruals, rather, the fractional power represents to what point future payments are discounted to. ex again) A------------------B--------------------------------C-----------------------------D---------------E… -----------last------78d til next coupon------------------next coupon Coupon at C, then coupon at D, then E, etc. are discounted to settlement date at B. If we don’t use a fraction as a power, there would be no way to discount D,E,… CF’s to settlement B.