Having passed Level II however, still somewhat not clear about bond’s yield concept and its use in duration calculation. Here I have a real transaction of a zero-coupon bond:
Issue date: Mar 08, 2018
Maturity date: Sep 09, 2018
Trade date: Mar 12, 2018
Settlement date: Mar 13, 2018
Purchase price: 97.60771522
Here are my question:
For example, I wish to calculate the Modified Duration as of Aug 30, 2018, so I have to know the YTM. The YTM is just the discount rate when price is set equal to the market price, so I retrieved the historical price on Bloomberg Terminal:
Date, Mid Line
Th 08/30/18 97.612
We 08/29/18 97.619
Tu 08/28/18 97.648
Mo 08/27/18 97.656
So I used 97.612 as current market price to calculate a new YTM for the bond using the Excel function Yield:
=YIELD(“8/30/2018”,“9/09/2018”,0,97.612,100,1,1), but I get 89.29%!
So here are my questions:
I’m not sure whether this process for calculating Modified Duration is correct or not? Usually the question will just ask you to calculate a Modified duration given YTM, or ask if interest rate changes, what’s the change in price, etc. But here the problem is what’s the impact on duration as passage of time. A bond was bought, and after sometime, what would the bond modified duration be?
I don’t know if it’s correct to calculate a new YTM as if I were to buy such a bond today in order to calculate the Modified Duration, because YTM is the yield you get if you buy the bond and hold it to maturity, so it should not change, and so a “new YTM” is meaningless? Or should I use some sort of interest rate from the market to calculate the Modified Duration?
I usually get confused when it says “the Yield of the bond” on the book or financial news, or someone asks what’s the yield on the bond, I think that’s just the YTM but I’m not sure… Sometimes the book also mentioned “the market interest rate”, seems that’s also referring to YTM when doing practice questions, but YTM always depends on the market price, looks like that’s not a rate that’s from the market, it’s an implied rate, and it needs not to be estimated, it’s a always a certain value because you can always find the market price for the traded bond. On the other hand, when using spot rate to discount the bond to get a price, that’s valuation purpose, to assess if the market price is overvalued or undervalue, and that has nothing to do with YTM. Is my understanding about YTM correct?
The per hundred price is 97.6077, and I think the face value may be just 100, but there is a notional of $150,000,000, before when I saw notional I would think of it as the synonym of face value, but here looks like it’s not, but the total amount of money invested, so does that mean 150,000 bonds were bought?
Thanks for your help!