"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.

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