Tell me the difference between bond convexity and duration. Why does it matter?
Yep – these are extremely important concept for anyone trying to go for a job position in the fixed income domain. Duration measures the linear relationship between bond prices and interest rate movements. For example, if the duration for a bond is 2 years, then it implies that the bond’s price will decrease by approximately 2% if the interest rate increases by 1% (always remember when the interest rate drops, bond price will increase). But let’s keep in mind that the relationship between bond prices and interest rate movements is not linear. Specifically, bond prices usually don’t fall at the same magnitude as the interest rate interests (same for when rates decrease).
In other words, the duration of a bond will change as the interest rate level changes, especially when such interest rate movement is large and that makes it an unreliable metric to examine when the rate movement is large. As an example, when the interest rate on the previous bond increases by 8%, bond’s price will not quite decrease by 8% since the duration of the bond will change as the magnitude of the interest rate movement enlarge.
As such, convexity matters much more here as we can see that is the measurement that explains for the accurate relationship between bond prices and interest rate movements. More importantly, duration does not taking into consideration the impact of any embedded derivatives on the bond’s cash flows while convexity can accurately reflects the payoff structure of the bond even with the presence of these options (i.e., negative convexity demonstrates the effect of a call option on the bond’s price).
Duration is a measure of the sensitivity of the price of a bond to a change in interest rates. Duration is expressed as a number of years. When interest rates rise, bond prices fall, and falling interest rates mean rising bond prices. Formally, duration is the “weighted average maturity of cash flows”. In simple terms, it is the price sensitivity to changes in interest rates. If cash flows occur faster or sooner, duration is lower and vice versa. In other words, a 4 year bond with semi-annual coupons will have a lower duration than a 10 year zero-coupon bond. The larger the duration number, the greater the impact of interest-rate fluctuations on bond prices.
Convexity measures the relationship between bond prices and bond yields. It is used as a tool to manage risk and measure the amount of exposure on a portfolio of bonds. If bond A has a higher convexity than bond B, bond A will have a higher price than bond B. As the convexity of a bond portfolio increases, the systematic risk to that portfolio increases. This means that the higher the convexity of the portfolio, the more sensitive it is to overall fluctuations in interest rates. As a general rule, the higher the coupon rate, the lower the convexity of a bond.
All in all, duration is the first derivative of the bond price function with respect to the interest rate while convexity represents the second derivative, which means that duration assumes a linear relationship between bond prices and interest rate changes when the reality is that this relationship is not linear at all.