1. Lecture 7 Part B: Interest Rate Risk
Finance 562: Enterprise Risk Management Professor Stephen P. D’Arcy and Professor Weili Lu
Lecture 7 Part B:
Interest Rate Risk

2. Applications of Duration
ALM evaluates the interaction of asset and liability movements
Insurers attempt to equate interest sensitivity of assets and liabilities so that surplus is unaffected
Surplus is “immunized” against interest rate risk
Immunization is the technique of matching asset duration and liability duration 34

3. Why Worry About Interest Rate Risk?
The 1970s Savings & Loan industry didn’t
Asset-liability “mismatch”
Interest rates can and do fluctuate substantially
Examples of 7 Year U.S. T-bond interest rates:
r at r at
t t-12 months t i
March % % 3.85%
July
Oct
May
April
Dec

4. Assumptions Underlying Macaulay and Modified Duration
Cash flows do not change with interest rates
This does not hold for:
Collateralized Mortgage Obligations (CMOs)
Callable bonds
P-L loss reserves – due to inflation-interest rate correlation
Flat yield curve
Generally, yield curves are upward-sloping
Interest rates shift in parallel fashion
Short term interest rates tend to be more volatile
than longer term rates

5. Surplus Duration
Sensitivity of an insurer’s surplus to changes in interest rates
DS S = DA A - DL L
DS = (DA - DL)(A/S) + DL
where D = duration
S = surplus
A = assets
L = liabilities

6. Surplus Duration and Asset-Liability Management
To “immunize” surplus from interest rate risk, set DS = 0
Then, asset duration should be:
DA = DL L / A
Thus, an accurate estimate of the duration of liabilities is critical for ALM

7. Are Insurers Exposed to Interest Rate Risk?
Absolutely!!
Long term liabilities
Life insurers
Whole life policies
Annuities
Property-Liability Insurers
Medical malpractice
Workers’ compensation
General liability
Assets
Significant portion of assets invested in long term bonds

8. Term Structure Shapes
Normal upward sloping
Inverted
Level
Humped

9. How Do Curves Shift?
Litterman and Scheinkmann (1991) investigated the factors that affect yield movements
Over 95% of yield changes are explained by a combination of three different factors
Level
Steepness
Curvature

10. Level Shifts
Rates of maturities shift by approximately the same amount
Also called a parallel shift

11. Steepness Shifts
Short rates move more (or less) than longer term interest rates
Changes the slope of the yield curve

12. Curvature Shifts Shape of curve is altered
Short and long rates move in one direction, intermediate rates move in the other

13. Parameterizing the Yield Curve
Level = 6 month yield
Steepness (or slope) = 10 year yield – 6 month yield
Curvature = 6 month yield + 10 year yield
– 2 x 2 year yield
Based on Brandt and Chapman (2002)

14. Example If Treasury interest rates are as follows: Then
6 month rate = 0.25%
2 year rate = 1.00%
10 year rate = 4.00%
Then
Level = 0.25%
Steepness = 3.75% (or 4.00%-0.25%)
Curvature = 2.25% (or 0.25%+4.00%-2x1.00%)

15. Conclusion
Most organizations, especially financial services firms, face interest rate risk
ALM is a risk management approach to reduce financial risk
Interest rate sensitivity measures include
Duration
Convexity
Term structure of interest rates can take different shapes