Foreign currency bank accounts

(MD).

Modified duration is an estimate of the market price sensitivity of an instrument, to small changes in yield.

It is the related proportionate price change of a market instrument or portfolio.

The estimate of change in market price is given by:

Modified duration x Starting Market price x Change in yield

Often - but not always - the relevant yield is defined as the annual effective yield (EAR).

For changes in EAR, modified duration is calculated from Macaulay’s duration as:

MD = Duration / (1 + EAR)

For changes in simple nominal annual yields (R), modified duration is calculated as:

MD = Duration / (1 + (R / n) )

where n = number of compounding periods per year.

Example: Modified duration calculations

Duration = 5.00 years.

Semiannual yield R = 6.00% (so n = 2)

and so EAR = 6.09%.

(i) With respect to the EAR:

MD = 5.00 / 1.0609

= 4.71

(ii) With respect to the Semiannual yield:

MD = 5.00 / 1.03

= 4.85

This shows that there would be a greater proportionate change in price for a 1% change in the Semiannual yield, than for a 1% change in the EAR.

See also

• Convexity
• Duration
• Effective annual rate
• Macaulay duration
• Matching
• Modified convexity
• Price value of a basis point
• Semi-annual rate
• Volatility