Module: | MODULE C: TREASURY MANAGEMENT
Q491: Consider the following statements regarding the measurement of interest rate sensitivity using Duration and Convexity:
1. Macaulay Duration measures the weighted average time required to recover a bond's internal rate of return, and it is mathematically identical to the maturity period for a zero-coupon bond.
2. Treasuries predominantly utilize Modified Duration to directly calculate the approximate percentage change in a bond's price resulting from a 100 basis point shift in the underlying yield.
3. The structural mathematical relationship between a fixed-income security's price and its yield is strictly inverse, meaning an upward yield curve shift invariably causes portfolio valuation losses.
4. Convexity measures the exact curvature in the price-yield relationship, serving as a second-order derivative metric that adjusts Modified Duration to predict accurate prices for massive yield shocks.
2. Treasuries predominantly utilize Modified Duration to directly calculate the approximate percentage change in a bond's price resulting from a 100 basis point shift in the underlying yield.
3. The structural mathematical relationship between a fixed-income security's price and its yield is strictly inverse, meaning an upward yield curve shift invariably causes portfolio valuation losses.
4. Convexity measures the exact curvature in the price-yield relationship, serving as a second-order derivative metric that adjusts Modified Duration to predict accurate prices for massive yield shocks.
✅ Correct Answer: B
Treasuries rely on complex metrics to manage the interest rate risk embedded in their fixed-income portfolios.
The foundational rule of bond pricing is the inverse relationship: when market yields rise, the price of existing bonds must fall to remain competitive. "Macaulay Duration" expresses this risk in years, calculating the weighted average time an investor needs to recover the bond's total cash flows (coupons and principal). Because a zero-coupon bond pays no intermediate coupons and only a single lump sum at maturity, its Macaulay Duration is mathematically exactly equal to its maturity length, making it highly sensitive to rate changes.
For active risk management, treasuries use "Modified Duration," which converts Macaulay's time metric into a percentage price sensitivity.
Specifically, Modified Duration calculates the approximate percentage drop in a bond's price for a 1% (100 basis points) increase in yield.
However, Modified Duration assumes the price-yield relationship is a straight linear line, which is false; the relationship is actually a curved line.
For massive yield shocks (e.g., a 300 bps hike), Modified Duration becomes inaccurate. "Convexity" measures this curvature.
By adding the Convexity adjustment (a second-order derivative) to the linear Modified Duration estimate, the treasury achieves a highly accurate bond price prediction regardless of the shock size.
A: This option incorrectly excludes statement 3. The inverse mathematical relationship between bond prices and market yields is the absolute foundational law of fixed-income treasury management.
B: This is the correct option.
All four statements perfectly define Macaulay Duration's zero-coupon dynamic, Modified Duration's 100 bps sensitivity, the inverse price-yield law, and the Convexity curvature adjustment.
C: This option incorrectly excludes statement 1. The definition of Macaulay Duration and its unique equivalence to the maturity of a zero-coupon bond is a tested, highly specific mathematical rule.
D: This option incorrectly excludes statement 2. Modified Duration is the primary, actionable metric used daily by traders to estimate percentage price drops for 100 basis point yield shifts.
The foundational rule of bond pricing is the inverse relationship: when market yields rise, the price of existing bonds must fall to remain competitive. "Macaulay Duration" expresses this risk in years, calculating the weighted average time an investor needs to recover the bond's total cash flows (coupons and principal). Because a zero-coupon bond pays no intermediate coupons and only a single lump sum at maturity, its Macaulay Duration is mathematically exactly equal to its maturity length, making it highly sensitive to rate changes.
For active risk management, treasuries use "Modified Duration," which converts Macaulay's time metric into a percentage price sensitivity.
Specifically, Modified Duration calculates the approximate percentage drop in a bond's price for a 1% (100 basis points) increase in yield.
However, Modified Duration assumes the price-yield relationship is a straight linear line, which is false; the relationship is actually a curved line.
For massive yield shocks (e.g., a 300 bps hike), Modified Duration becomes inaccurate. "Convexity" measures this curvature.
By adding the Convexity adjustment (a second-order derivative) to the linear Modified Duration estimate, the treasury achieves a highly accurate bond price prediction regardless of the shock size.
A: This option incorrectly excludes statement 3. The inverse mathematical relationship between bond prices and market yields is the absolute foundational law of fixed-income treasury management.
B: This is the correct option.
All four statements perfectly define Macaulay Duration's zero-coupon dynamic, Modified Duration's 100 bps sensitivity, the inverse price-yield law, and the Convexity curvature adjustment.
C: This option incorrectly excludes statement 1. The definition of Macaulay Duration and its unique equivalence to the maturity of a zero-coupon bond is a tested, highly specific mathematical rule.
D: This option incorrectly excludes statement 2. Modified Duration is the primary, actionable metric used daily by traders to estimate percentage price drops for 100 basis point yield shifts.