Tutorial. Measuring Interest Rate Risk Repricing Model Duration SEEM 3580, 2016 YAN, Xing xyan@se.cuhk.edu.hk

Contents A quick review Some exercises Excel

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

1. Repricing Model Applied to a balance sheet Rate sensitive assets (RSA) Rate sensitive liabilities (RSL)

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

2. Duration Exercise： Calculate the duration (required, by hand) Bond information: Need Excel? https://support.office.com/en-US/article/overview-of-formulas-7abfda78-eff3-4cc6-b4a7-6350d512d2dc Maturity 4 Coupon 8% Yield (R) 10% Frequency 2 FaceValue 1000

3. Excel Some shortcuts without mouse: F2 ---- enter the editing mode Esc ---- exit the editing mode Shift (pressed) ---- select multiple cells (can be used with Ctrl+C, Ctrl+V)

3. Excel Some functions: IF(logical_expression, ture_do_this, false_do_this) e.g., =IF(2+2>3,1,0) =AND(____,____) =OR(____,____) =SUM(B1:B8) =AVERAGE($C$3:$C$9) $C$3 is absolute reference C3 is relative reference (relative location, applied when you copy formula to a new cell)

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Thanks! Q&A