What is Duration
That metric is as crucial a measure for assessing bond interest rate sensitivity, demonstrating how the weighted average maturity of a bond and its linear response to shifts in benchmark rates. Higher duration means a bond price will react to interest rates in a greater magnitude. For that reason, duration is primarily used to estimate the price change in bonds as interest rates shift. Normally, the longer a bond’s duration, the more its price will fall (rise) during periods of higher (lower) interest rates. Conversely, bonds with shorter durations are less sensitive to changes in interest rates.
Duration is commonly split into Macaulay Duration and Modified Duration. Macaulay Duration measures the weighted average time to receive a bond’s cash flows, making it useful for gauging how changes in interest rates can affect returns on bonds held until maturity. Modified Duration is actually an amendment to Macaulay Duration, which tries its best to reflect faster change of a bond in reply to the interest rates fluctuation.
Practical Application of Duration
Investors typically match bond portfolio durations in line with their sensitivity to interest rate changes. Given that interest rates typically rise, investors tend to shorten their portfolio duration in an effort to minimize the risk of falling bond prices. Conversely, increasing the length when interest rates are decreasing will result in increased capital gains.
Duration can also be applied to matching the duration of liabilities on a balance sheet for example, so that changes in interest rates have less impact upon the bond portfolio. An example of this is insurance companies or pension funds that use duration-matching strategies to mitigate the interest rate risk of their long-term liabilities.
What is Convexity
Convexity is an adjunct to duration, which describes how the price of a bond might not change linearly as interest rates fluctuate. In both cases, a convex curve reflects the reality that how bond prices and interest rates relate to each other can become non-linear, particularly after large changes in one direction or another. Convexity accounts for this non-linear adjustment and accentuates the second-order effect of interest rate changes on bond prices.
If interest rates move, in general, bonds with higher convexity will be less volatile because their price elasticity to large changes in bond yield increase. This is important because bonds that have greater convexity are better insulated from extreme market conditions, especially those with very volatile prices.
Practical Application of Convexity
Convexity is more scrutinized in the market for bonds when interest rate sensitivity is expected to increase significantly at some future point on account of investors. Higher convexity bonds are less affected by interest rate changes because their price or yield reacts more steadily in the presence of unexpected rate increases (or falls). Convexity either dampens or limits the potential losses that can occur from price fluctuations.
Numerous bond fund managers believe convexity is a key component in optimizing their portfolios. Where higher convexity in bonds can help to buffer the portfolio is during extended periods of market volatility, especially involving wide swings and changes in interest rates. Convexity is particularly important when managing large bond portfolios because it can better capture the significant non-linear aspects of interest rate risk, which are extremely relevant to asset-liability management and derivative hedging.
Combined Use of Duration and Convexity
Both measures, duration and convexity, are the tools that supplement each other in measuring the interest rate risk. Duration represents the straight-line sensitivity of bond prices to interest rate movements, whereas convexity is a measure of the non-linear reaction. We have seen that duration is a good approximation of the bond price change in case interest rates fluctuate within a small range. When interest rates change by a lot, duration on its own is inaccurate (because it estimates linearly) and convexity gives you the correct estimate of how bond prices have changed.
