# Bond YTM - clean or dirty price for PV

Hi all,

I notice that most brokers in Bulgaria calculate the YTM of a bond using its dirty price. However, I believe this is incorrect and the clean price should be used. I didn`t find any reference in the CFA curriculum that clarifies this.

If we buy today, 29.06.2018 a bond that matures in 26.03.2035 and pays a coupon of 3.125% once per annum and with a market price of 106.16, we will pay extra for the accrued interest which is 95/365 (act/act) or 0.26 years x 3.125 = 0.813. So, the clean price would be 106.16 - 0.813 = 105.347. That produces a YTM of 2.72%, however if we use the dirty price it would produce a YTM of 2.66% and this appears to be used by most brokers here.

Technically, we pay the interest at settlement and get back this accrued interest plus the interest for the remaining 270 days when the next coupon is paid in full. So, instead of getting 2.312 at the next coupon date, we get 3.125 thus 2.312 + the accrued interest of 0.813. In some extreme cases of a short maturity bond this can produce significant differences.

So, why is dirty used over clean and shouldn`t clean be the appropriate measure?

The clean price is the quoted price, because you want to see how the bond price moves net of accrued coupons (they have a cyclical movement). But what you pay to buy the bond is the dirty price, therefore you want your YTM to be computed using the dirty price (as well as the different duration measures), because that’s your actual investment in the bond. why would you want a measure of return that only takes into account part of the full price that you paid to get in?

They quote the dirty price to start first. Then, I do not believe this is correct, here is why:

I`ll give you a real example which indeed made me think about this:

Type: plain vanilla bond which pays coupon twice per annum

Dealer quote: 100.76 (dirty)

Coupon: 0.5 (paid 17.02/17.08)

Maturity: 17.02.2019

Bond convention: Act/Act

So, PV = -100.76; FV = 100; PMT = 0.5; N = 1.164 (28*/182.5days = 0.153425) ==> YTM = -0.158% this is what the dealer claims.

* There are 30 days but this is on a t+2 basis so actual deal would leave 28 days

The client pays 100.76 and gets back 0.5 on 17.08.2018 and 100.5 on 17.02.2019 so 101 in total. under a very simple ROI approach, we get 0.24% period yield so something is incorrect. If we do clean price, accrued interest is 154.5/182.5 x 0.5 = 0.423288 hence clean price is 100.336712 and if we use it, the YTM comes to 0.207% or 0.414% annual which is much closer to reality.

Another dealer shows the following:

Offer: 101.185 and YTM = -0.411

If we use again PV = -101.185 (clean) so -100.608288 dirty; FV = 100; PMT = 0.5; N = 1.153425 (to be precise), YMT should be -0.881% or -0.508% for the period till maturity. If quote is for dirty, then YTM = -0.522% or -0.301% for the period till maturity.

While my question really is clean vs dirty for PV use - in this short maturity bond the investor would pay accrued interest of 0.42 but he is getting this payment back in 28 days time. Besides, in example one he pays less the nhe gets, yet dealer claims he`d get less then he paid and that I believe is not correct. I get different values from the ones brokers state.