What Is Convexity?
Let me explain convexity directly: it's the curvature in the relationship between bond prices and interest rates. It shows you how the duration of a bond shifts as those rates change. In the bond market, this ties into risk and reward, since rates often reflect potential risks.
Key Takeaways
You need to know that convexity helps measure a portfolio's exposure to market risk. It's essentially the curvature between bond prices and yields. It reveals how bond duration adjusts with interest rate changes. If a bond's duration increases as yields rise, that's negative convexity. On the flip side, if duration rises while yields fall, it's positive convexity.
How Convexity Works
Convexity shows you exactly how a bond's duration alters with interest rate shifts. As a portfolio manager, I use it to measure and control exposure to interest rate risk. Consider this: if one bond has higher convexity than another, all else equal, it will maintain a higher price regardless of whether rates rise or fall.
When interest rates drop, bond prices climb, and the reverse happens when rates go up. The bond yield is what you earn by holding the security, and its price fluctuates based on market rates and other factors. If rates rise, new bonds offer higher yields to attract investors, so older bonds with lower yields see their prices drop until they match the market.
Bond Duration
Bond duration tells you how much a bond's price changes with interest rate fluctuations. A high duration means the price moves significantly in the opposite direction of rates. For instance, if rates rise by 1%, a bond with a five-year duration might lose about 5% in value. Lower duration means less sensitivity.
Higher duration equals bigger price swings and more interest rate risk. If you think rates will rise, go for lower-duration bonds. Don't mix this up with maturity—duration measures price sensitivity, while maturity is just the time until principal repayment. As a rule, for each year to maturity, a 1% rate rise drops the price by about 1%.
Convexity and Risk
Convexity expands on duration by tracking how duration itself changes with yields, making it a superior gauge of interest rate risk. Duration assumes a straight-line relationship, but convexity accounts for the curve. It's fine for small rate changes, but for big swings, convexity gives the real picture.
As convexity rises, so does the portfolio's systemic risk. Rising rates make fixed-rate bonds less appealing. Lower convexity reduces rate exposure, acting like a hedge. Generally, higher coupon rates mean lower convexity and less market risk.
Example of Convexity
Take XYZ Corp. with two bonds: both $100,000 face value, 5% coupon. Bond A matures in five years, Bond B in ten. Duration for A is four years, for B it's 5.5 years. A 1% rate change moves A's price by 4%, B's by 5.5%.
For a 2% rate increase, duration predicts an 8% drop for A and 11% for B. But convexity adjusts this—B's higher convexity (due to longer maturity) buffers the drop, so it's less than 11%.
Negative and Positive Convexity
If duration increases with rising yields, that's negative convexity—the price falls more sharply than it would rise. For positive convexity, duration rises as yields fall, boosting price increases more than decreases. Higher yields typically mean lower convexity, reducing risk as rates would need to surge to make the bond unattractive.
Explain Like I'm 5
Convexity checks how a bond's price reacts to interest rate changes. Rates up, price down—and vice versa. It measures sensitivity, telling you if the reaction is more or less than expected. Duration gives a basic estimate, but convexity refines it for bigger shifts, giving a fuller view of risk.
How Will I Use This in Real Life?
Grasping convexity makes you a smarter investor. Match bonds to your risk tolerance—high convexity for more reaction to rate drops, low for stability. It helps manage your portfolio's exposure to economic rate changes and predict reactions.
The Bottom Line
Convexity measures the curve in bond duration and price-yield relationships. It shows duration changes with rates, affecting investment value. Factors like coupon, maturity, and credit quality influence it. Use it to optimize your bond portfolio against rate shifts.
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