Question

In a recent trading session, the benchmark 30-year Treasury bond’s market price went up $8.25 dollars per $1000 face value to $1032.75 dollars, while its yield fell from .07 to .068. The bond’s market price then went up another $7.25 dollars per $1000 face value as the yield fell further to .0665 from .068. Report answers for the following (using average of latest two bond prices for duration and average of latest three bond prices for convexity):

1. Convexity,usingtheaverageofallthreemarketpricesofthebondinthedenominator of the formula.

2. First modified duration, using average of first two market prices of the bond in the denominator of the formula.

3. Second modified duration, using average of second and third prices of the bond.

4. The expected rise in bond price if the interest rate were to fall another 20 basis points (.002) from .0665, using the average of two modified durations and convexity.

PLEASE SHOW WORK THANK YOU!

Answer 1

Soln : Duration is a measure of change in bond prices, with the change in yield and convexity is the measure of change in duration due to change in yield.

Now, as it is given that price changed by $8.25 by changing yield from 0.07 to 0.068 i.e. for change in 0.002.

As, first modified duration is to be calculated using first 2 mkt price average i.e. = $(1032.75*2- 8.25)/2 = $1028.625

2) First Modified duration = (8.25/1028.625)/0.002 = 4.01

3) 2nd Modified duration = (7.25/(1032.75*2+7.25)/2)/(0.068-0.0665) = 4.664

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