Can anyone explain the intuition behind following answer? I was tripped up about breaking the problem into two parts. Is there a simpler way to do this in one step? Looking at answer I can see that it makes sense to have the first part increasing duration from 6 to 8 and the second part increasing the notional exposure by 50mm.
You can just go in one step.
Current 100,000,000 x 6 x 0.01% = 60,000
Want 150,000,000 x 8 x 0.01% = 120,000
[(120,000 - 60,000)/117 ] x 0.98 = 502
Intuition means you get the right answer without understanding why.
Intuition cannot be explained.
It sounds as though you want understanding, not intuition.
Historically, CFA Institute has done problems such as this in two steps: first you change the value, then you change the duration (on the new value). Think of it as trying to get from (1, 1) to (4, 7) in Cartesian coördinates: first you go from (1, 1) to (4, 1), then you go from (4, 1) to (4, 7). It works, but it’s inefficient.
(Note that you could also change the duration on the existing portfolio first, then change the value of the new portfolio: (1, 1) to (1, 7), then (1, 7) to (4, 7). It’s still inefficient.)
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