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# Tuckman Table 5.4: First Five Rows

#### ankit4685

##### New Member
Subscriber
Hi David,

I'm working to understand the calculation we have in Tuckman Table 5.4: Row (vi). But not very much sure why we used below formula to get the dollar amount :

For 2 year : =$E28*10000*F$23
where F$23 = (0.0010) and$E28 = -100.000 mn

#### David Harper CFA FRM

##### David Harper CFA FRM (test)
Staff member
Hi @ankit4685 (you don't need to follow-up post: both Nicole and check the forum daily, if we don't respond immediately, it's only because either we have excess backlog or the question requires much time to answer. In fact I prefer that you not double- or triple-tap as a courtesy to us, thank you!).

As Tuckman explains (emphasis mine)...
"The sums of the key-rate ’01s for each of the bonds in rows (i) through (v) are given in the rightmost column of Table 5.4. The trader uses these sums for initial hedging, which, as discussed previously, is very much like single-factor, hedging. So, the trader bought $72.4 million of the five-year against the$40 mm short of the 10-year because

(5.5) .0869/.0480 × $40 mm =$72.4 mm

Similarly, the trader bought $47.1 million of 30-year bonds against the$100 million short of 30-year STRIPS because

(5.6) .0829/.1760 × $100 mm =$47.1 mm

Row (vi) of Table 5.4 gives the key-rate ’01 profile, in dollars, of the trader’s position recorded in column (2) of Table 5.3. The five-year key-rate ’01 in millions of dollars, for example, is calculated as ...

72.446 × .048/100 - 40 × (-.0001/100) - 100 × (-.0035/100) + 47.077 × .0001/100 = .038361

which is $38,361. ... so with respect to the cell in my XLS that you cite: the 30-year zero coupon bond (i.e., which "the trader shorted$100 million face amount of a 30-year STRIPS to a customer") has itself a KR01[2 year] of -0.0010 but we must always remember that DV01/KR01 are expressed in terms of "per 100 face value" such that this represents -0.0010/100. The short position is $100.0 million, which of course is -100,000,000, so the KR01[2-year] of this trade is given by -0.0010/100 * -$100,000,000 = +\$1,000. But the cell values are given by -0.0010 * - 100.0 such that the un-scaled (actual) dollars is given by -0.0010 / 100 * - 100.0 * 1,000,000 = -0.0010 * - 100.0 * 1,000,000 / 100 = -0.0010 * - 100.0 * 10,000. I hope that explains!

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