Cross Rates
It is possible to back out cross rates given two exchange rates involving three currencies. Consider a foreign exchange market with the exchange rate between the Chinese Yuan and the South African rand (ZAR/CNY). This market can also quote the…
Empirical Vs. Analytical Duration
Analytical duration utilizes mathematical models, assuming credit spreads and government bond yields are uncorrelated and independent. It is a solid method for estimating the bond’s price-yield relationship in numerous situations. On the other hand, empirical duration relies on historical data…
Key Rate Duration
Key rate duration (partial duration) is a financial metric that measures the sensitivity of a bond’s price to changes in interest rates at specific points along the yield curve. On the other hand, effective duration gauges sensitivity to overall parallel…
Bond’s Percentage Price Change Using Curve-based Duration and Convexity
Effective duration and effective convexity are curve-based metrics that are crucial for assessing the interest rate risk of complex instruments, such as those with embedded contingency provisions. These metrics are typically determined from bond prices derived using an option valuation…
Utilizing Effective Duration and Convexity for Option-embedded Bonds
Yield duration and convexity assume predictable bond cash flows. However, bonds with embedded options, e.g., callable or puttable bonds, have future cash flows which are uncertain. The option is exercised based on market interest rates relative to the coupon interest…
Duration and Convexity of a Bond Portfolio
Duration and convexity can be used to measure the interest rate risk of a portfolio of bonds, similar to a single bond. There are two methods to calculate the duration and convexity of a bond portfolio: The first technique is…
Bond Risk and Return Using Duration and Convexity
The percentage price change of a bond, given a specified change in yield, can be more accurately estimated using both the bond’s duration and convexity compared to using duration alone. We will give an example to illustrate this. Consider a…
Convexity and Convexity Adjustment
Duration provides a linear approximation of the change in a bond’s price with respect to changes in yield. On the other hand, convexity measures the non-linear, second-order effect of yield changes on a bond’s price. It captures the curvature of…
Properties of Duration
The sensitivity of a bond’s price to changes in interest rates can be captured using Macaulay duration, modified duration, money duration, and the price value of a basis point (PVBP). Master duration concepts with AnalystPrep’s Free Trial. Relationships Between Bond…
Modified Duration, Money Duration, and Price Value of a Basis Point (PVBP)
Modified Duration Modified duration captures the sensitivity of a bond’s price to fluctuations in its yield-to-maturity (YTM). This relationship provides insight into how bond prices vary with shifts in yield. Specifically, bond prices and yields exhibit an inverse relationship: as…
