1. Tutorial. Measuring Interest Rate Risk
Repricing Model
Duration

2. Contents
A quick review
Some exercises

3. What is Interest Rate Risk?
Potential loss due to the fluctuation of interest rate
Faced by a financial institution
Because it may possess specific assets or liabilities, like bonds
A FI is said to be exposed of interest rate risk if the FI faces a potential loss due to the fluctuation of interest rate.

4. 1. Repricing Model Applied to a balance sheet
Rate sensitive assets (RSA):the total book value of all FI’s assets which the first repricing at current market interest rates is within the maturity backets.
Rate sensitive liabilities (RSL):the total book value of all FI’s liabilities which the first repricing at current market interest rates is within the maturity backets.

5. 1. Repricing Model Assets or Liabilities: First repricing: cash
3-month U.S. Treasury bills
20-year U.S. Treasury bonds
30-year floating-rate mortgages with repricing every two years
30-year floating-rate mortgages with repricing every six months
Overnight fed funds
1-year fixed-rate CDs
5-year floating-rate CDs with annual repricing
Common stock

6. 1. Repricing Model Assets or Liabilities: First repricing: cash
3-month U.S. Treasury bills
20-year U.S. Treasury bonds
30-year floating-rate mortgages with repricing every two years
30-year floating-rate mortgages with repricing every six months
Overnight fed funds
1-year fixed-rate CDs
5-year floating-rate CDs with annual repricing
Common stock
N.A.
3 months
20 years
2 years
6 months
1 day
1 year

7. 1. Repricing Model Assets or Liabilities: First repricing: cash
3-month U.S. Treasury bills
20-year U.S. Treasury bonds
30-year floating-rate mortgages with repricing every two years
30-year floating-rate mortgages with repricing every six months
Overnight fed funds
1-year fixed-rate CDs
5-year floating-rate CDs with annual repricing
Common stock
N.A.
3 months
20 years
2 years
6 months
1 day
1 year
RSA/RSL (time period, e.g., [0, 1 year])

8. 1. Repricing Model Assets or Liabilities: First repricing: cash
3-month U.S. Treasury bills
20-year U.S. Treasury bonds
30-year floating-rate mortgages with repricing every two years
30-year floating-rate mortgages with repricing every six months
Overnight fed funds
1-year fixed-rate CDs
5-year floating-rate CDs with annual repricing
Common stock
N.A.
3 months
20 years
2 years
6 months
1 day
1 year
RSA/RSL (time period, e.g., [0, 1 year])

9. 1. Repricing Model
Gap Analysis : It is based on the book values of asset and liabilities on a balance sheet.
Formula:
Under unequal changes in interest rates:

10. 2. Duration Measure sensitivity of bond price to interest rate Bond:
time
1 year
2 year
3 year
Price (P)
Face Value ---- F
Annual Coupon Rate ---- c
Coupon Frequency ---- m (m=1,2,4)
Maturity ---- N years

11. 2. Duration If interest rate is R, what is the price P?
If R+∆R, what about P+∆P?
Remember the first order derivative:

12. 2. Duration
Formula of Duration:
Furthermore

13. 2. Duration
Formula of Duration:

14. 2. Duration
Zero-Coupon Bond – Duration is equal to its time to maturity. 
Vanilla Bond - Duration will always be less than its time to maturity.

15. 2. Duration
For a zero-coupon bond:
For a vanilla bond:

16. Exercise Calculate the duration (required, by hand) Bond information:
Maturity 4
Coupon 8%
Yield (R) 10%
Frequency 2
FaceValue 1000

17. Thanks! Q&A