What is the effect on bond price if G spread rises from 168 to 177?
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just to confirm, you’re seeking explanation to the solution assuming the facts given in the question right?
Question doesn’t indicate G-spread change.
Yess… Solution for this question
Solution :
First calculate the weights of treasury bonds that duration match the citigroup bond.
So, using interpolation we have 6.7 duration and 9.1 duration bond….using cross section binary method (as per notes) , we get weights as 87.5% of 7y t-note & 12.5% of 10y t-note. (Hope you get how this calculation this done. Sir has done multiple examples on this in notes).
Now, calculate yield using these weights i.e. yield of a 7y duration tsy bond :
0.875*1.53+ 0.125*1.77 = 1.56%
But yield of 7y duration citi bond is 3.24%, so G-spread effectively is 3.24-1.56 = 1.68%
Now, considering 7y t-note yield decrease 10bp to 1.43%, so now a 7y duration t-note yield will be 0.875*1.43+0.125*1.77 = 1.4725%.
Adding G-spread 1.4725+1.68% = 3.1525% is now the new yield of citi group bond.
so, change in yield is 3.24-3.1525 = 8.75bps.
So, price increase in citi group bond = 8.75*7*0.001 = 0.6125%
so new bond price = 103.64*1.006125 = 104.274