Key rate duration (or partial duration) is a measure of a bond’s sensitivity to a change in the benchmark yield at a specific maturity. Such a measure is important to isolate the price responses of bonds to changes in the rates of key maturities on the benchmark yield curve. Key rate durations define a security’s price…
Just as with yield-based interest rate risk measures, effective duration and effective convexity can be used to estimate the percentage change in a bond’s full price for a given shift in the benchmark yield curve (∆Curve),
Yield duration and convexity assume a bond’s cash flows are certain. However, if a bond has contingency features, such as embedded options, as with a callable (or puttable) bond, then future cash flows are uncertain since option exercise depends on the level of market interest rates relative to coupon interest being paid (or received). For example, the…
There are two ways to calculate the duration and convexity of a bond portfolio:
Money convexity (MoneyCon) captures the second-order effect in currency terms and is the annual convexity multiplied by the full price, Similar to estimating the percentage change in a bond’s full price, MoneyDur and MoneyCon are combined to achieve a more accurate, thus less risky, estimate of the change in a bond’s full price,
Convexity is a complementary risk metric that measures the second-order (non-linear) effect of yield changes on price for an option-free fixed-rate bond. The true relationship between a bond’s price and its yield-to-maturity is the curved (convex) line that shows the actual bond price given its market discount rate. Duration (i.e., money duration) estimates the change in…
Modified duration is used to measure the percentage price change of a bond given a change in its yield-to-maturity. A related statistic is money duration. The money duration of a bond is a measure of the price change in currency units. Money duration (MoneyDur) is the product of the annualized modified duration and the full price (PVFull) of the…
or Without the negative sign, this is known as a bond’s modified duration, or ModDur: The change in annualised yield-to-maturity: Approximate Modified Duration
The general calculation of Macaulay duration, MacDur, that also accounts for partial coupon periods if the calculation is done between coupon dates where Finally, another approach to calculating Macaulay duration is to use a closed-form equation derived using calculus and algebra, where
