ch6

• Topics in Risk Management in Banking


  • Credit Risk Management
  • Interest rate risk management
  • Liquidity risk management
  • Market risk management
• Interest Rate Risk Management Techniques


  • Income Gap Analysis
  • Duration Analysis
• Income Gap Analysis


  The difference between interest-sensitive assets and interest-sensitive liabilities
• Income Gap Analysis


  1. Classify assets and liabilities according to maturity/repricing time buckets

  2. Calculate the gap (RSA - RSL) in each bucket

  3. Multiply the gap by the change in interest rate to get the change in net interest income
• Income Gap Analysis


  • Provides a picture of overall balance sheet mismatches
  • Ignores market value effects of interest rate changes
  • Ignores effects of changes in interest rates on off-balance sheet instruments
• Duration Analysis


  Measures the sensitivity of the market value of an asset or liability to changes in interest rates
• Duration Measures


  • Macaulay Duration
  • Modified Duration
  • Duration Gap
• Income Gap Analysis is a book value accounting cash flow analysis, while Duration Analysis is a market value-based model
• If interest rates decrease


  Net interest income decreases due to liabilities repricing faster than assets
• If interest rates increase


  Net interest income increases due to assets repricing faster than liabilities
• Income Gap Analysis ignores the market value effects of interest rate changes
• Income Gap Analysis ignores the rate-sensitive component of rate-insensitive assets and liabilities
• Income Gap Analysis ignores the effects of changes in interest rates on off-balance sheet instruments
• Despite its limitations, Income Gap Analysis is still used by banks, but in conjunction with other risk management tools
• Under the income gap analysis (maturity approach), banks report the gap in each maturity bucket, calculated as the difference between rate-sensitive assets (RSA) and rate-sensitive liability (RSL) on their balance sheets. GAP = RSA – RSL
• A positive GAP implies sensitive assets > sensitive liabilities. The rise in interest rates will cause a bank to have interest revenue rising faster than interest costs; thus the net interest margin and income will increase.
• The decline in interest rates will increase liabilities costs faster than assets returns; as a consequence the net interest margin and income will decrease.
• Bank managers can calculate the income exposure to changes in interest rates in different maturity buckets, by multiplying GAP times the change in the interest rate: ΔI= GAP * Δi
• 3 main problems associated with income gap analysis


  • It ignores market value effects of interest rates changes
  • Even rate-insensitive assets & liabilities (whose interest rates are not re-priced) actually have a component that is rate sensitive (i.e a runoff cash flow)
  • It ignores the effects of the changes in interest rates on off balance sheet instruments
• Macaulay duration


  Measures the average financial life of an asset or liability
• Modified duration


  Expresses the interest sensitivity of an asset or liability's value
• If the durations of designated assets and liabilities are matched (DURgap=0), then the duration gap on that part of the balance sheet is said to be 'immunised against unexpected changes in interest rates'
• Duration gap can be used to calculate the change in the market value of net worth (DNW) as a percentage of total assets induced by a change in interest rates
• The formula for the calculation of the Macaulay duration of any fixed-rate security is: D = ∑CFt x DFt x t / ∑CFt x DFt
• Dividend


  $150 next year with dividend growth expected to be 2.5% per annum thereafter
• US corporate bond


  Annual coupon rate of 5%, par (face) value of $1000, and maturity in 2 years time
• Required return on similar US equities is 10%
• Required return on similar US bonds is 7%
• Macaulay duration calculation


  1. ∑CFt x DFt x t = ∑PVt x t

  2. ∑CFt x DFt

  3. ∑PVt
• Macaulay duration of a portfolio is the weighted average of the durations of the individual securities, with the weights reflecting the proportion of the portfolio invested in each security
• Duration of a zero coupon bond is its maturity
• Macaulay duration of a 4-year 5% coupon bond with market interest rate of 4% and par value of $1000 is 3.7 years
• Investor constructs a bond portfolio of $10,000 in the 4-year 5% coupon bond and $30,000 in a 3-year zero coupon bond
• Macaulay duration increases with the maturity of a bond
• Macaulay duration decreases as market interest rate increases
• Macaulay duration decreases as coupon interest rate increases
• Modified duration


  Direct measure of the interest rate sensitivity of an asset or liability
• The larger the Macaulay duration, the more the price of an asset (or liability) is sensitive to changes in market interest rates
• MD


  D / (1+i)
• Larger Macaulay Duration (D)


  Larger Modified Duration (MD)