Can someone please explain the first part of the 5E solution in MM Exam 1 AM? It states that a barbell structure with a modified duration of 7 years will have an average maturity of about 10 years. The rest of the solution makes sense to me. I’m lost on how a 7-year duration equates to approximately 10-year maturity…
Thanks!!
You may recall the rule of thumb for swaps that the duration of the fixed leg is approximately 75% of the swap’s tenor.
Well, the fixed leg of the swap is nothing more nor less than a fixed-rate bond. So that rule of thumb is equivalent to saying that the duration of a fixed-rate bond is approximately 75% of its maturity. So,
0.75 × maturity = 7 years
maturity = 7 years / 0.75 = 9.33 years
For the purposes of that question, that’s pretty close to 10 years.
As an actual example, a 10-year, semiannual pay, 6% coupon bond yielding 6% has a modified duration of 7.44 years (according to Excel’s MDURATION function, which I have verified several times).