Tuckman Chapter 1- How are we deriving the Discount Factor without the Bond Price?

[gargi.adhikari]

Hi,
Please refer to the example in Learning Spreadsheet T4.C Bundle -Tab/Sheet =4c.1 Table 1.3 (rich_cheap).
Thanks to all the help, I understood the previous example but bumped into an issue in the next one. My question is:-
How are we deriving the Discount Factors for the 1 Year and 1.5 Years when we do not have a Bond price for these 2 time periods..?
For ex: for .5 years , we derived the DF to be = .97557 as: 104.080= 106.688* d(.5) => d(.5) = .97557
Similarly we derived the DFs for the 2 year, 2.5 years and so on as we have the Bond Prices available. But we do not have the Bond Price available for 1 year and 1.5 year. :-(

 

[David Harper CFA FRM]

Hi @gargi.adhikari

Sorry, the prices should be displayed (copied forward) from the adjacent tab (which is Tuckman Tables 1.x and 2.2) because, you are correct: I don't think we could solve for a 1.0 or 1.5 year DF with those prices. They are given. In my version, for example (the earlier Tuckman version with higher coupons), the 1.0 year bond price is $108 31.5/32 with 14.250% coupon, such that:

14.250% * 100/2 * 0.97557 + (1 + 14.250%/2)* 100 * df(1.0) = $108.9844, such that:
df(1.0) = $108.9844 - (14.250% * 100/2 * 0.97557) / (1 + 14.250%/2)* 100 = 0.95247

And so it goes, each step is "bootstrapped" by finding the df(.) that solves for the price. I hope that explains!

 

[gargi.adhikari]

@David Harper CFA FRM Thanks so very David ! That helps a lot