I am having troubles studying about Modified duration and Money duration, and hoping to get some helps.
Modified duration can be used to measure the percentage price change upon absolute change in YTM. I am confused about YTM here. Modified duration can be shown as
Modified duration = (dP/P)/d(1+r)
And I think the r here represents periodic interest rate.
So，suppose there is a semiannually paid bond has a modified duration of 5, and the YTM declines 0.25%. In calculating the price percentage change, why use 5*0.25%, instead of 5*0.25%/2 as the periodic interest rate?
If there is no any statement, is money duration per bps, per 1% or per 1 YTM? For example, if the money duration is $10,000, and the YTM increases 25 bps, the value of the bond would change 10000*25, 10000*0.25, or 10000*0.0025?