R31.P1.T4.Tuckman-Chapter 3- Spread Of a Bond

[gargi.adhikari]

In reference to Tuckman-Chapter 3
Topic : Spread Of a Bond
In reference to the screenshot below, wanted to see how we arrived at the value of Spread = 0.0440%
I tried subtracting the Bond Market Price of 100.190 from the Discounted PV of the Bond of 100.255....but not quite arriving at the .0440 number....

 

[ShaktiRathore]

100.255=0.375/(1+0.001492/2)+0.375/((1+0.005561/2)*(1+0.001492/2))+100.375/((1+0.005561/2)*(1+0.001492/2)*(1+0.010356/2))
0.375/(1+0.001492/2+.00044/2)+0.375/((1+0.005561/2+.00044/2)*(1+0.001492/2+.00044/2))+100.375/((1+0.005561/2+.00044/2)*(1+0.001492/2+.00044/2)*(1+0.010356/2+.00044/2))= 100.190 which is coming correct.
The yield .0440% IS GIVEN IN ANNUAL TERMS.
thanks

 

[gargi.adhikari]

Thanks @ShaktiRathore I did understand the calculation of the PV of the Bond = 100.255 and the subsequent calculation of theMarket Price of the Bond= 100.190.

I was wondering if we calculated the Spread to be 0.0440 % as the Tuckman Chapter 3 , pg 29 ( please refer the screenshot-circled in Green ) says that " We solve for the spread"

 

[David Harper CFA FRM]

Hi @gargi.adhikari

@ShaktiRathore 's answer is actually on point: there is not an analytical solution (just like there isn't for yield). The spreadsheet is goal-seeking to solve for the spread (the first spread of 0.0440% is literally an input cell) that contributes to a discounted present value equal to the market price. So, it's not a formula, it's an iteration until we find the number. It's similar to finding the bond yield (which is iterative) except, in the case of yield (YTM) we are "solving for" (ie, finding) the single constant value used to discount all the cash flows, in this case, we already know the forward rates (which explain most of the price) and we are just finding the small but constant gap. Nevertheless, in both cases it amounts to solving for a number (i.e., yield, or the spread in addition to a forward rate) that produces a discounted cash flow price equal to the observed market price. I hope that helps,

 

[gargi.adhikari]

@David Harper CFA FRM @ShaktiRathore Thanks much to both of you for the clarifications