Modified duration and Mac duration formulas....

[sridhar]

David:

There is a (1 + yield/2) factor in both D_mod and D_mac. Is the "yield / 2" applicable even to ANNUAL bonds and not just to semi-annual bonds.

In other words, the formula:

D_mod = (1/P) * (1 + y/2) * (sum of time-weighted cash flows)

applicable to computation of duration of ANY bond?

--sridhar

 

[David Harper CFA FRM]

Sridhar -

Not any, the term is (1+y/k) where k is the number of periods per year (k = 1 for annual, = 12 for monthly). In practice, as the (Tuckman-inspired) bonds tend to be semi-annual, the most common is yield/2 but it's really yield/(number of compound periods in the year)

David

 

[sridhar]

That clears it up, thanks...Another related quesry:

If I've a question that asks to calculate D_modified of a 5 year zero-coupon bond, priced to yield 5%, (without any further info), do I do:

D_modified = D_mac / (1 + 0.05/2)

--sridhar

 

[David Harper CFA FRM]

sridhar,

Imprecise question. Note the Macaulay duration of a zero is its maturity, so D_mac = 5. If the 5% yield is bond-equivalent basis (i.e., six-month yield is 2.5% so bond-equivalent yield is 5%), then yes, as you have it would be my default answer. If they mean annual pay bond, then 5/(1+5%)

David