Managing Interest Rate Risk: Duration and Market Value of Equity

1
Managing Interest Rate Risk Duration and Market
Value of Equity

• FINC 4320
• Fall 2004

2
Measuring Interest Rate Risk

• The Maturity Model
• Note that all values are market values!
• The basic accounting identity yields
• A L E
• or
• E A - L
• But, we are really concerned about the changes
• DE DA - DL
• How does maturity affect this?

3
Measuring Interest Rate Risk

• IF MA¹ MA then as rates change
• DA ¹ DL and DE ltgt0
• PROBLEM Even if we match the maturities, we
  will not eliminate interest rate risk! That is,
• MA ML does not imply DE 0
• WHY?

4
Measuring Interest Rate Risk

• The Concept of Duration
• Duration is the weighted average maturity of a
  promised stream of future cash flows.

5
Measuring Interest Rate Risk

• Why do we want to use this measure? What does it
  tells us about interest rate risk exposure?

6
Duration and Interest Rate Exposure

• How do we apply this concept to the bank? The
  key idea is that we should look to duration
  matching, not maturity matching! To do this, we
  need the weighted average duration of the assets
  and liabilities.
• But, WE DO NOT TRY TO SET THESE EQUAL! Why?

7
Duration and Interest Rate Exposure

• Recall,
• A L E
• E A - L
• so that
• DE DA - DL
• Now apply the duration ideas

8
Duration and Interest Rate Exposure

• Substitute these relationships into the one
  above, and for now assume the rate changes on
  assets and liabilities are the same. This yields
• which provides us with a measure of rate
  exposure, the banks DGAP.

9
Positive and negative DGAPs

• Positive DGAP indicates that assets are more
  price sensitive than liabilities, on average.
• Thus, when interest rates rise (fall), assets
  will fall proportionately more (less) in value
  than liabilities and the MVE will fall (rise)
  accordingly.
• Negative DGAP indicates that weighted
  liabilities are more price sensitive than assets.
  
• Thus, when interest rates rise (fall), assets
  will fall proportionately less (more) in value
  that liabilities and the MVE will rise (fall).

10
Using the DGAP Model

• Immunizing changes in equity cannot occur
  simultaneously with immunizing changes in the
  ratio of E/A (a regulatory concern)
• Using duration is difficult and costly (?)
• The duration and price relationship is
  approximate due to convexity
• The term structure is not really flat
• What is the duration of a floating rate security?
• What is the duration of demand deposits and
  passbook savings?

11
Effective Duration

• used to estimate a securities price sensitivity
  when the security contains embedded options.
• Effective duration is
• Where Pi- price if rates fall, Pi price if
  rates rise P0 initial (current) price i
  initial market rate plus the increase in rate
  i- initial market rate minus the decrease in
  rate.
• Effective duration compares a securitys
  estimated price in a falling and rising rate
  environment.

12
Effective duration example

• Consider a 3-year, 9.4 percent coupon bond
  selling for 10,000 par to yield 9.4 percent to
  maturity. The Macaulays duration for the
  option-free version of this bond with semiannual
  coupons and compounding is 5.36 semiannual
  periods, or 2.68 years at the market rate of 4.7
  percent semiannually. The modified duration is
  5.12 semiannual periods or 2.56 years. A 30 basis
  point increase in rate to 5 percent semiannually
  will lower the price to 9,847.72.
• The callable bonds effective duration for a 30
  basis point (0.30 percent) semiannual movement in
  rates either up or down is 2.54

13
Immunized portfolio
DGAP 2.88 0.92 (3.11) 0
14
Market value of equity sensitivity analysis

• MVE sensitivity analysis effectively involves the
  same steps as earnings sensitivity analysis.
• In MVE analysis, however, the bank focuses on
• the relative durations of assets and liabilities,
  
• how much the durations change in different
  interest rate environments, and
• what happens to the market value of equity across
  different rate environments.

15
Embedded options

• sharply influence the estimated volatility in
  MVE
• Prepayments that exceed (fall short of) that
  expected will shorten (lengthen) duration.
• A bond being called will shorten duration.
• A deposit that is withdrawn early will shorten
  duration.
• A deposit that is not withdrawn as expected will
  lengthen duration.

16
Sensitivity of economic value of equity (MVE)
versus most likely (zero shock) interest rate
scenario
Sensitivity of Economic Value of Equity measures
the change in the economic value of the
corporations equity under various changes in
interest rates. Rate changes are instantaneous
changes from current rates. The change in
economic value of equity is derived from the
difference between changes in the market value of
assets and changes in the market value of
liabilities.
17
Asset / liability sensitivity and DGAP

• Funding GAP and Duration GAP are not directly
  comparable.
• Funding GAP examines various time buckets while
  DGAP represents the entire balance sheet.
• Generally, if a bank is liability (asset)
  sensitive in the sense that net interest income
  falls (rises) when rates rise and vice versa, it
  will likely have a positive (negative) DGAP
  suggesting that assets are more price sensitive
  than liabilities, on average.

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Advantages of DGAP over Funding GAP

• DGAP analysis has the advantage of focusing on
  all cash flows from the underlying assets and
  liabilities and not just cash flows that are
  expected to arise over short time intervals.
• Interest rate risk can be summarized in one
  measure for the entire portfolio.

19
Speculating on DGAP

• It is difficult to consistently alter either GAP
  or DGAP on the balance sheet and increase
  earnings or the market value of stockholders'
  equity.
• Whenever management chooses to change asset and
  liability maturities and/or durations in
  anticipation of rate changes, it is placing a bet
  against forward rates from the yield curve.