Tutorial. Measuring Interest Rate Risk

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Presentation transcript:

Tutorial. Measuring Interest Rate Risk Repricing Model Duration

Contents A quick review Some exercises

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.

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.

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

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

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])

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])

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:

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

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

2. Duration Formula of Duration: Furthermore

2. Duration Formula of Duration:

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.

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

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

Thanks! Q&A