chapter 9 part b portfolio immunization using duration
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
9-1
Chapter 9 part B
Portfolio Immunization Using
Duration
9-2
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)
9-3
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.
9-4
Immunizing the Balance Sheet of an FI in $
-DA x A x R/(1+R)=-MDAA x R-DLL x R/(1+R)=-MDLL x R
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 changeInstitution is matched.
9-5
Immunizing the Balance Sheet of an FI in $
-DAA x R/(1+R)=-MDAA x R
= $ gain/loss on assets for R
-DLL x R/(1+R)=-MDLL x R
= $ gain/loss on liabilities for R
Equity does not need to be considered since all $ gains/losses on assets & liabilities are accounted for
9-6
Immunizing the Balance Sheet of an FI
Duration Gap: From the balance sheet, E=A-L. Therefore,
E=A-L. In the same manner used to determine the change in bond prices, we can find the change in value of equity using duration.
E = [-DAA + DLL] R/(1+R) or
EDA - DLk]A(R/(1+R)) or, more simply
E$DA - MDLk] x A x R
Note that k = Liabilities/Assets
9-7
Immunizing the Balance Sheet of an FI in %
EDA - MDLk]A x R k=L/A k x MDL = unlevered MDL = L/A x MDL
9-8
Duration and Immunizing
The formula shows 3 effects: Leverage-adjusted Duration-Gap The size of the FI The size of the interest rate shock
9-9
Immunizing the Balance Sheet of an FI in %
EDA - MDLk]A x R 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.
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*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.
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*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.
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*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.
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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)