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Duration refers to a linear relationship between the price of the bond with its yield, i.e., what will be the change in the price of the bond if the interest rate changes. Duration helps in quantifying the impact of credit risk (default), and interest rate risk (interest rate fluctuations) on a bond's price as these risks affect a bond's expected YTM. For example, if a companyâs credit quality declines, the bond becomes risky for which investors will demand a higher yield which will ultimately lead to the fall in the prices of the bond and vis-Ã -vis.
There are two types of durations:
The Macaulay duration: It is the weighted average of the bonds cash flow over the life of the bond calculated by dividing the present value of the bondâs cash flow by its price. It helps the investor to compare and analyse the bonds without taking their time to maturity into consideration. A bond which has a higher duration will have a high interest-rate risk or reward.
The Modified duration: It is the other form of duration which calculates the change in the price of the bond (expected change) if the interest rates change by 1%. As the bondâs price have an inverse relation with the interest rates, so the price of the bond will rise in a declining interest rate environment and vis-Ã -vis. For a bond paying a semi-annual coupon, it is calculated by dividing the Macaulay duration with 1+(YTM/2).
Convexity refers to a non-linear relationship between the price of the bond with its yield, i.e., what will be the change in the price of the bond if the interest rate changes. It measures the curvature of the duration and shows how the duration of a bond changes as the interest rate changes. It is used to measure and manage the amount of market risk the portfolio is exposed to.
Compared to Duration, Convexity is a better measure to determine the interest rate risk as duration assumes a linear relationship between yield and bond prices whereas convexity takes the convex relationship between bond prices and yields. But duration provides a better picture of change in bond prices if the interest rates change suddenly. Generally, it is considered that a bond with a higher coupon rate usually have a low convexity as market rates would have to increase at a more substantial pace to surpass the coupon rate.
A bond is said to have a negative convexity if the bond duration as well as the yield increases, as the shape of the bond is concave. This means that the price of the bond would increase in value as interest rates rise and vis-Ã -vis. Bonds with a traditional call provision, most mortgage-backed securities (MBS) and preferred bonds usually have negative convexity.
A bond is said to have a positive convexity if the bond duration increased, but the yield decreases. A positive convexity means that if the yield falls, the price of the bond will experience a more significant increase in the price. Non-callable bonds and bonds with make-whole call provisions usually have positive convexity.
The bonds which have higher coupon rate have a low degree of convexity, and Zero-coupon bonds (bonds which do not pay coupons) have the highest degree of convexity.
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