Imagine a company wants to reduce its sensitivity to interest rates.
It has 4 options. Assume duration of fixed is 75% of its maturity.
3 year quarterly swap. Receive fix, pay float. Duration = 2.25 - 0.125 = 2.125
1 year quarterly swap. Receive float, pay fix. Duration = 0.125 - 0.75 = -0.625
2 year quarterly swap. Receive fix, pay float. Duration = 1.5 - 0.125 = 1.375
2 year quarterly swap. Receive float, pay fix. Duration = 0.125 - 1.5 = -1.375
Which one should the company pick?
#4
I’d go with #4. If rates are going up you want to shorten up duration as much as possible.
D(FLOATING) = .5 x Reset Period = .5 x .25 = .125
D(FIXED) = .75 x Maturity = .75 x 2 = 1.5 years.
If we want to reduce duration, we want to pay fixed(-); receive floating (+), so .125 - 1.5 = -1.375 would reduce the company’s sensitivity to rates moving higher the most.
I’m thinking 2 because you want duration to be close to 0 to have the least amount of interest rate sensitivity.
My understanding is negative duration will give you the same amount of sensitivity to a position with the same positive amount of duration. The only difference is that the negative duration will mean your position value increases with rate increases and decreases with rate decreases.
I realize I didn’t make mention of the company’s original portfolio. But it is assumed to be 0.
CFA Institute’s historical position has been that you want the swap with the smallest notional value; that’s the one with the longest net duration.
Coincidentally or not, your understanding is correct.
@S2000magician what’s the intuition for the relationship between the swap with the smallest notional value corresponding to the longest net duration?
I don’t know anything about intuition, but I can give you some understanding.
Changing the duration of a fixed income portfolio involves adding or subtracting a given amount of money duration. For a given amount of money duration, if the duration increases, the money (value) must decrease, and vice versa.