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Chapter 9 part B Portfolio Immunization Using Duration

Chapter 9 part B Portfolio Immunization Using Duration. Economic Interpretation. Duration is a measure of interest rate sensitivity or elasticity of a liability or asset: Δ P/P = -D[ Δ R/(1+R)] = -MD × Δ R where MD is modified duration. More simply MD = D/(1+r). Economic Interpretation.

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Chapter 9 part B Portfolio Immunization Using Duration

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  1. Chapter 9 part B Portfolio Immunization Using Duration

  2. Economic Interpretation • Duration is a measure of interest rate sensitivity or elasticity of a liability or asset: ΔP/P = -D[ΔR/(1+R)] = -MD × ΔR where MD is modified duration. More simply MD = D/(1+r)

  3. Economic Interpretation • To estimate the change in price, we can rewrite this as: ΔP = -D[ΔR/(1+R)]P = -(MD) × (ΔR) × (P) ΔP = -MD X ΔR X P • Note the direct linear relationship between ΔP and -D.

  4. Immunizing the Balance Sheet of an FI in $ -DA xA x DR/(1+R)=-MDAA x DR -DLL x DR/(1+R)=-MDLL x DR Assets $1000, MD = 4% Liabilities $800, MD = 5% Equity $200, MD = NA (treat as zero) .04 x $1000 x 1 = $40 for a 1% rate change .05 x $800 x 1 = $40 for a 1% rate change Institution is matched.

  5. Immunizing the Balance Sheet of an FI in $ • -DAA x DR/(1+R)=-MDAA x DR = $ gain/loss on assets for DR • -DLL x DR/(1+R)=-MDLL x DR = $ gain/loss on liabilities for DR • Equity does not need to be considered since all $ gains/losses on assets & liabilities are accounted for

  6. Immunizing the Balance Sheet of an FI • Duration Gap: • From the balance sheet, E=A-L. Therefore, DE=DA-DL. In the same manner used to determine the change in bond prices, we can find the change in value of equity using duration. • DE = [-DAA + DLL] DR/(1+R) or • DE = -[DA - DLk]A(DR/(1+R)) or, more simply • DE$ = -[MDA - MDLk] x A x DR • Note that k = Liabilities/Assets

  7. Immunizing the Balance Sheet of an FI in % • DE = -[DA - MDLk]A x DR • k=L/A • k x MDL = unlevered MDL = L/A x MDL

  8. Duration and Immunizing • The formula shows 3 effects: • Leverage-adjusted Duration-Gap • The size of the FI • The size of the interest rate shock

  9. Immunizing the Balance Sheet of an FI in % • DE = -[DA - MDLk]A x DR • k=L/A • k x MDL = unlevered MDL = L/A x MDL Assets $1000, MD = 4% Liabilities $800, MD = 5% Equity $200, MD = NA MDA = 4% Unlevered MDL = 5% x 800/1000 =4% Institution is matched.

  10. *Limitations of Duration • Immunizing the entire balance sheet need not be costly. Duration can be employed in combination with hedge positions to immunize. • Immunization is a dynamic process since duration depends on instantaneous R. • Large interest rate change effects not accurately captured. • Convexity • More complex if nonparallel shift in yield curve.

  11. *Duration Measure: Other Issues • Default risk • Floating-rate loans and bonds • Duration of demand deposits and passbook savings • Mortgage-backed securities and mortgages • Duration relationship affected by call or prepayment provisions.

  12. *Contingent Claims • Interest rate changes also affect value of off-balance sheet claims. • Duration gap hedging strategy must include the effects on off-balance sheet items such as futures, options, swaps, caps, and other contingent claims.

  13. Residential Mortgages • Typical term is 360 months • Rate can be fixed or floating • Classic ARM adjusts every year • Hybrid ARMs now very popular • Fixed first 3, 5 7 or 10 years • Fully amortizing loans • No prepayment penalty (call price =100) • Prepayments accelerate cash flows, so they reduce duration • Duration can move dramatically due to rate changes (loan rate – new loan rate)

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