Duration

Duration measures a bond's price sensitivity to interest rate changes.

Duration is calculated as:

Duration = Price if yields fall - Price if yields rise

(2)(Initial Price)(Yield change in decimal form)

The calculated duration value is read as a percentage price movement for a 100 basis point rate change. A duration of 8.5 translates into an 8.5% price change for a 100 basis point movement.

For a given change in yield and given duration, one can estimate a bond's % price change. Approximate % of price change is calculated as:

Approx % price change = (-duration)(change in yield)(100)

Other measures of duration are modified duration and Macaulay duration. Modified duration measures the approximate percentage price change in a bond given a 100 basis point change while assuming expected cash flows from the bond do not change with the yield. Modified duration only makes sense for option-free bonds.

Modified duration can be expressed using Macaulay duration.

Specifically, modified duration is calculated as:

Modified duration = (Macaulay duration) / (1 + yield/number of payment periods)

Since Macaulay duration suffers from the same options adjustment problem as modified duration, it is considered a less attractive methodology compared with effective duration.

Effective duration, or options-adjusted duration, accounts for changes to expected cash flows based on yield changes. Because effective duration factors in the effects of embedded options, it is considered the more attractive method.

The duration calculation is not an exact predictor. For larger change in yields, duration tends to underestimate the new price. Duration also suffers from rate shocks associated with embedded options.

Bonds with embedded options require another adjustment in addition to duration. Convexity helps explain the approximate price change of a bond that duration does not.

Convexity is calculated as:

Convexity = Price if yields increase + price if yields decrease - (2)(Original price)

(2)(Original price)(Yield change in decimal form)

Combining duration and convexity gives the forecaster a more accurate depiction of a bond's sensitivity to changes in interest rates. In general, a bond with less convexity is said to have a better price estimate.

A related valuation technique measuring price volatility for interest rate changes is the price value of a basis point (PVBP) estimate.

Price value of a basis point is calculated as:

PVBP = | initial price - price if yield changes by 1 basis point |

Financial Terms by BetterTrades