What is the unit of measure ascribed to effective duration –
i) XX% of bond price OR
ii) years
Case in point, under reading 37, section 4.1.1, the author illustrates an example with the solution being, “an effective duration of 1.97 indicates that a 100-bps increase in interest rate would reduce the value of the three-year 4.25% callable bond by 1.97%.”
However, in a side bar titled “EFFECTIVE DURATION IN PRACTICE”, the author explains that “a bond’s effective duration does not exceed its maturity”. The term maturity logically begets the measure of time or years.
Can anyone shed some light on these two contexts of effective duration – % of value or years ? Or have I been studying so long that I am losing my grasp of the English language ? LOL
All types of duration – Macaulay duration, modified duration, effective duration, spread duration, key rate duration, empirical duration, whatever – have years as their units.
Most of these measures (except Macaulay duration) measure interest rate sensitivity. But their units are still years. So the author properly should have said, “an effective duration of 1.97 _ years _ indicates . . . .”
The author is correct in implying that effective duration is measured in years, but his statement is wrong. Inverse floating-rate bonds can have effective durations that are longer – sometimes _ much _ longer – than their time to maturity. For example, a 10-year semiannual-pay bond whose coupon rate is 15% minus 6-month LIBOR will have an effective duration of approximately 15 years.
Think about the ratio of % price change to yield change. Percent price change has units of %. Yield has units of % _ per year _. (The per year is the part that everyone forgets.) Thus, the ratio has units of % ÷ (% / year) = years.
Thank you again Mr./Ms. S2M for answering my questions. So in the CFA syllabus, the cited example might have been improved by saying 1.97% price change per year…?
Interesting point you make with the duration of inverse floating rate bonds being longer than maturity. I am going do the math with the effective duration formula and see what happens…BTW, where can one get her hands on a bond with a 15% coupon ? LOL
And, for whatever reason, it’s typically abbreviated S2_ K _. Not my fault.
And you’re quite welcome.
Nope.
The price change is just 1.97%. The _ duration _ is 1.97 years. When you multiply the duration of 1.97 years by the yield change of 1% _ per year _, the years in the numerator cancel with the years in the denominator and you’re left with 1.97%.
The key is that when the yield drops, so the discount rate drops, the payments increase. So the increase in price is compounded by higher payments and a lower discount rate. I refer to inverse floaters as twitchy bonds. And if they’re leveraged – say, the coupon is 15% − 2×LIBOR, or 20% − 3×LIBOR – the effective duration is even longer: 20 years or 30 years or more on a 10-year bond. Super twitchy.
Turkey, maybe. Or the Philippines, I’m told. Or Brazil, perhaps.
Of course, LIBOR would have to be 0% to get a 15% coupon payment.
