CFA : Fixed Income: Concept of Z- Spread - YouTube

So let's say we have a bond

the face value of Bond is thousand

coupon rate lets assume is 12%

let's a life of the bond is four years

so what will we do is step number one we will plot the cash of bond

1,2,3,4 so let me plot the cash

120 120 120 and 1120

so these are my cash

now what we would do is we would put down

Treasury spot rates

so ideally its a risky bond and risky bond should be dicounded with risky bond cashloss

risky band discount rate

but we're going to discount this with Treasury spot rates

let's assume that Treasury spot rate for year one

come out to be 10%

let's say this is 5% this was 6%

this was 6.5 percent

and let's say this was 7% these are

the different Treasury spot rates

what I am doing now

is that we would calculate discounted cash row

so discounted cash row 120 divided by 1+5% raise to one

discount first year cash log with 1

then take total followup them

then we got value of bond

by using this technique the value of the bond

came out to be 1175 but actually

this is a very high value because in the market the market the market prize of this bond

was only 975

the bond in the market was selling as a 975

the reason why we getting a value very high because we used Treasury spot rates

so what is that one rate that I add

to each of the Treasury spot rate

so that the value of the bond comes out to be exactly 975

so that rate is called Z - Spread

as of now I'm going to assume Z - Spread of 0%

just revise the formula

discounted cash flow is equal to

120 divided by one-plus

5 percent plus a constant

Z-Spread which as if now 0 then raise to 1

and now replicate the formula

but as of now the value would be zero

if I keep this number as 1% then it's coming out to be 1135 let's increase furder

if we keep this 3 we are going closer

5 even closer

6 very close so that means on average we are earning about 6 percent more

then the Treasure is spot rate cough

if you want to exactly how much we can use simple

goal seek function where we want this value

become how much 975 by changing what cell by changing

this cell and the correct answer is

5.99891% so this is your Z-Spread

and that this is the spread to you have to earning over and obove the Treasure is spot rates

cleared ... any Question to ask

so interpretation nominal spread and Z-Spread is correct

the only difference being the nominal spread was simply a difference between

right teams

which is nothing but mathematical average of spot mathematical

average of

rates for the risky bond

we're just finding out that one rate that is to be added to each of the

Treasury spot rates cough in such a way present value cash clause would be equal to

that

market prize of the bond and why are you giving Z-Spread 3 reasons again

one why do you get that extra spread

for taking three-risk one credit risk then

re-query risk and finally Option risk