# Duration confusion

Why is is so that effective Duration is used for bonds with options while modified duration can be used with no option bond.

I understand it is something related to curve duration and yield duration. But I just cannot get Why?

Also do we expect to see questions on calculating Macaulay duration in the exam? That formula is dreadful. Or can we use the theory of duration which says “it is the time in which you get your initial investment back” to calculate Macaulay duration step wise.

When a bond has embedded options, the cash flows an investor receives partly reflect the payoffs of those options. As an example, when interest rates drop, a callable bond could get called, in which case the investor would receive not the remaining coupons, but the call price. Effective duration accounts for those cash flow changes, while modified duration does not (it assumes that cash flows are fixed).

As for calculating Macauley duration, the LOS states that you should be able to calculate it. So it’s fair game. Anyone who tells you that it is or isn’t likely to be tested is merely guessing. So to be safe, learn how to do it - its really not that complicated (just the present value-weighted maturity). Having made a comment about guessing what’s on the exam, I will say that you are given on average 90 seconds per question, so if they did give you a Macauley calculation, it would most likely be one with only 2-3 periods.

Another possibility, I suppose, is that you could be given the modified duration and the (annual) yield and asked to compute the Macaulay duration; if the annual yield were y, then, assuming semiannual coupon payments,

DurMac = DurMod × (1 + y/2).