What major weakness of the repricing gap model does the duration model solve?
The repricing gap model ignores market value changes due to interest rate movements, while the duration model measures market value sensitivity to interest rate changes.
What is duration?
Duration is the weighted average time to maturity of an investment, where the weights are the present values of the cash flows.
Why is duration a better measure of interest rate risk than maturity?
Because it considers:
Timing of all cash flows
Present values of payments
The full cash flow structure of the instrument
What are the three steps to calculate duration conceptually?
Convert future cash flows into present values
Calculate weights for each cash flow
Multiply each weight by the time period and sum
What does duration measure economically?
The interest rate elasticity of a bond’s price (price sensitivity to interest rate changes).
What is the relationship between interest rates and bond prices?
They are inversely related:
Interest rates ↑ → bond prices ↓
Interest rates ↓ → bond prices ↑
What is Modified Duration (MD)?
Modified duration measures the percentage change in bond price for a 1% change in interest rates.
Formula for modified duration?
MD = D / (1 + R)
Where
D = Macaulay duration
R = yield to maturity
Formula for approximate bond price change using duration?
ΔP / P = − MD × ΔR
What happens to price sensitivity when duration increases?
Higher duration → larger price changes when interest rates change.
How does maturity affect duration?
Duration increases with maturity, but at a decreasing rate.
How does yield affect duration?
Higher yield → lower duration.
How does the coupon rate affect duration?
Higher coupon rate → lower duration, because more cash flows occur earlier.
What is balance sheet immunization?
A strategy where asset duration equals liability duration, protecting a financial institution’s net worth from small interest rate changes.
What is the duration gap?
DGAP = Duration of Assets − Duration of Liabilities
What does a non-zero duration gap mean?
Interest rate changes will affect the market value of the financial institution’s equity.
What is the leverage ratio in duration gap analysis?
k = L / A
Where
L = liabilities
A = assets
What three factors determine the change in a financial institution’s net worth after an interest rate shock?
Leverage-adjusted duration gap
Size of assets
Size of interest rate change
What condition fully immunizes a financial institution from interest rate changes?
DA − kDL = 0
(Leverage-adjusted duration gap equals zero)
What is convexity?
Convexity describes the curvature of the bond price–yield relationship, meaning the relationship is not perfectly linear.
Why is convexity important?
Because duration only approximates price changes for small interest rate movements.
Convexity improves accuracy for large interest rate changes.
What is the convexity-adjusted price change formula?
ΔP / P = −MD(ΔR) + ½ CX(ΔR²)
Where CX = convexity.
What are two major challenges of the duration gap method?
Balance sheet restructuring can be costly
Duration approximations become inaccurate for large rate changes
