Module 11: Measuring the Seesaw - Duration and Convexity

Knowing that interest rates and bond prices move in opposite directions is beginner finance. Knowing exactly how much the price will change is institutional finance. For this, Wall Street uses Duration and Convexity.

1. Macaulay Duration vs. Modified Duration

Macaulay Duration: Measured in years. It calculates the weighted average time it takes for an investor to receive the bond's cash flows. A zero-coupon bond's Macaulay Duration is exactly equal to its maturity.
Modified Duration: A derivative of Macaulay Duration. It provides a direct price sensitivity metric. If a bond has a Modified Duration of 5.0, a 1% increase in interest rates will mathematically cause the bond's price to drop by roughly 5%.

2. The Rules of Duration Risk

Longer Maturity = Higher Duration: A 30-year bond is infinitely more sensitive to Fed rate hikes than a 2-year note.
Lower Coupon = Higher Duration: A bond paying a 1% coupon returns capital much slower than a bond paying an 8% coupon. Therefore, low-coupon bonds possess higher duration and greater price risk.

3. Convexity: The Second Derivative

Duration assumes the relationship between prices and yields is a straight line. In reality, the relationship is curved (Convex).

Convexity measures the curvature of this price-yield relationship. Because of convexity, as yields fall, bond prices rise faster than duration predicts. As yields rise, bond prices fall slower than duration predicts. Institutional managers specifically hunt for high-convexity bonds because they offer mathematically superior downside protection.

Self-Assessment Quiz

If a US Treasury bond has a Modified Duration of 8.5, what is the estimated price impact if the Federal Reserve cuts interest rates by 2%?
Why does a zero-coupon bond possess the highest possible duration for its maturity length?