0
Bank Management, 6th edition.
           Timothy W. Koch and S. Scott MacDonald
           Copyright © 2006 by South-Weste...
Measuring Interest Rate Risk with Duration
GAP
 Economic Value of Equity Analysis
   Focuses   on changes in stockholder...
Recall from Chapter 4

 Duration is a measure of the effective
 maturity of a security.
   Duration  incorporates the ti...
Duration and Price Volatility
 Duration as an Elasticity Measure
   Duration   versus Maturity
     Consider the cash f...
Duration versus Maturity
 The maturity of both is 20 years
      Maturity does not account for the differences in
      ...
Duration versus Maturity

Duration is an approximate measure of
 the price elasticity of demand


                        ...
Duration versus Maturity

 The longer the duration, the larger the
 change in price for a given change in
 interest rates...
Measuring Duration

 Duration is a weighted average of the
 time until the expected cash flows
 from a security will be r...
Measuring Duration

 Example
    What  is the duration of a bond with a
      $1,000 face value, 10% annual coupon
     ...
Measuring Duration

  Example
      What is the duration of a bond with a
       $1,000 face value, 10% coupon, 3 years
...
Measuring Duration

  Example
      What is the duration of a bond with a
       $1,000 face value, 10% coupon, 3 years
...
Measuring Duration

 Example
   Whatis the duration of a zero coupon
   bond with a $1,000 face value, 3 years
   to mat...
Duration and Modified Duration

 The greater the duration, the greater
  the price sensitivity
 Modified Duration gives ...
Effective Duration

 Effective Duration
   Used   to estimate a security’s price
    sensitivity when the security conta...
Effective Duration

                           Pi- - Pi
     Effective Duration           -
                          P...
Effective Duration

 Example
   Consider   a 3-year, 9.4 percent semi-
    annual coupon bond selling for $10,000
    pa...
Effective Duration

 Example
   Assume,  instead, that the bond is
   callable at par in the near-term .
     If rates ...
Effective Duration

 Example
    If  rates rise 30 basis points to 5%
      semiannually, the price will fall to
      $...
Duration GAP

 Duration GAP Model
   Focuseson either managing the
   market value of stockholders’ equity
       The b...
Duration GAP

 Duration GAP Analysis
   Compares    the duration of a bank’s
   assets with the duration of the bank’s
 ...
Two Types of Interest Rate Risk

 Reinvestment Rate Risk
   Changes in interest rates will change
   the bank’s cost of ...
Reinvestment Rate Risk

 If interest rates change, the bank will
 have to reinvest the cash flows from
 assets or refinan...
Price Risk

 If interest rates change, the value of
 assets and liabilities also change.
   The  longer the duration, th...
Reinvestment Rate Risk and Price Risk

 Reinvestment Rate Risk
   Ifinterest rates rise (fall), the yield from
    the r...
Reinvestment Rate Risk and Price Risk

 Increases in interest rates will increase
  the HPR from a higher reinvestment
  ...
Reinvestment Rate Risk and Price Risk

 An immunized security or portfolio is
  one in which the gain from the higher
  r...
Steps in Duration GAP Analysis

 Forecast interest rates.
 Estimate the market values of bank assets,
  liabilities and ...
Weighted Average Duration of Bank Assets

 Weighted Average Duration of Bank
 Assets (DA)
            n
    DA   w iDai...
Weighted Average Duration of Bank Liabilities

 Weighted Average Duration of Bank
  Liabilities (DL)
               m
   ...
Duration GAP and Economic Value of Equity

 Let MVA and MVL equal the market values
  of assets and liabilities, respecti...
Duration GAP and Economic Value of Equity

 To protect the economic value of
 equity against any change when rates
 chang...
Hypothetical Bank Balance Sheet
1                                       Par          Years              Market
           ...
Calculating DGAP

 DA
     ($700/$1000)*2.69 + ($200/$1000)*4.99 = 2.88
 DL
     ($620/$920)*1.00 + ($300/$920)*2.81 =...
1 percent increase in all rates.
1                                      Par           Years         Market
               ...
Calculating DGAP

 DA
     ($683/$974)*2.68 + ($191/$974)*4.97 = 2.86
 DA
     ($614/$906)*1.00 + ($292/$906)*2.80 = 1...
Change in the Market Value of Equity

                      y
     ΔEVE  - DGAP[         ]MVA
                    (1  y...
Positive and Negative Duration GAPs

 Positive DGAP
     Indicates that assets are more price sensitive
      than liabi...
DGAP Summary

                       DGAP Summary
           Change in
DGAP        Interest
                         Asset...
An Immunized Portfolio

 To immunize the EVE from rate
 changes in the example, the bank
 would need to:
   decrease   t...
Immunized Portfolio
1                                  Par       Years             Market
                               $...
Immunized Portfolio with a 1% increase in rates

1                                Par              Years            Market...
Immunized Portfolio with a 1% increase in rates

 EVE changed by only $0.5 with the
  immunized portfolio versus $25.0
  ...
Stabilizing the Book Value of Net Interest Income

 This can be done for a 1-year time horizon,
  with the appropriate du...
Stabilizing the Book Value of Net Interest Income

 If DGAP* is positive, the bank’s net interest
  income will decrease ...
Economic Value of Equity Sensitivity Analysis

 Effectively involves the same steps as
  earnings sensitivity analysis.
...
Embedded Options

 Embedded options sharply influence the
 estimated volatility in EVE
   Prepayments   that exceed (fal...
First Savings Bank Economic Value of Equity
         Market Value/Duration Report as of 12/31/04
         Most Likely Rate...
First Savings Bank Economic Value of Equity
              Market Value/Duration Report as of 12/31/04
              Most L...
Duration Gap for First Savings Bank EVE

 Market Value of Assets
   $1,001,963

 Duration of Assets
   2.6   years
 M...
Duration Gap for First Savings Bank EVE

 Duration Gap
  =  2.6 – ($919,400/$1,001,963)*2.0
    = 0.765 years
 Example:...
Sensitivity of EVE versus Most Likely (Zero Shock)
                              Interest Rate Scenario

                 ...
Effective “Duration” of Equity

 By definition, duration measures the
 percentage change in market value for
 a given cha...
Asset/Liability Sensitivity and DGAP
 Funding GAP and Duration GAP are NOT
 directly comparable
   Funding  GAP examines...
Strengths and Weaknesses: DGAP and EVE-
Sensitivity Analysis
 Strengths
   Duration analysis provides a
    comprehensiv...
Strengths and Weaknesses: DGAP and EVE-
Sensitivity Analysis
 Weaknesses
  It is difficult to compute duration
   accura...
Speculating on Duration GAP

 It is difficult to actively vary GAP or
 DGAP and consistently win
   Interest   rates for...
Gap and DGAP Management Strategies
Example
 Cash flows from investing $1,000 either
 in a 2-year security yielding 6 perc...
Gap and DGAP Management Strategies
Example
 It is not known today what a 1-year
  security will yield in one year.
 For ...
Gap and DGAP Management Strategies
Example
 By investing in the 1-year security, a
  depositor is betting that the 1-year...
Yield Curve Strategy

 When the U.S. economy hits its peak,
 the yield curve typically inverts, with
 short-term rates ex...
Yield Curve Strategy

 To take advantage of this trend, when
 the yield curve inverts, banks could:
   Buy   long-term n...
Interest Rates and the Business Cycle
   The general level of interest rates and the shape of the yield curve
   appear to...
Bank Management, 6th edition.
           Timothy W. Koch and S. Scott MacDonald
           Copyright © 2006 by South-Weste...
Upcoming SlideShare
Loading in...5
×

Session8 Koch6

2,468

Published on

0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
2,468
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
68
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Transcript of "Session8 Koch6"

  1. 1. Bank Management, 6th edition. Timothy W. Koch and S. Scott MacDonald Copyright © 2006 by South-Western, a division of Thomson Learning Managing Interest Rate Risk: Duration GAP and Economic Value of Equity Chapter 6 William Chittenden edited and updated the PowerPoint slides for this edition.
  2. 2. Measuring Interest Rate Risk with Duration GAP  Economic Value of Equity Analysis  Focuses on changes in stockholders’ equity given potential changes in interest rates  Duration GAP Analysis  Compares the price sensitivity of a bank’s total assets with the price sensitivity of its total liabilities to assess the impact of potential changes in interest rates on stockholders’ equity.
  3. 3. Recall from Chapter 4  Duration is a measure of the effective maturity of a security.  Duration incorporates the timing and size of a security’s cash flows.  Duration measures how price sensitive a security is to changes in interest rates.  The greater (shorter) the duration, the greater (lesser) the price sensitivity.
  4. 4. Duration and Price Volatility  Duration as an Elasticity Measure  Duration versus Maturity  Consider the cash flows for these two securities over the following time line 0 5 10 15 20 $1,000 01 5 10 15 20 900 $100
  5. 5. Duration versus Maturity  The maturity of both is 20 years  Maturity does not account for the differences in timing of the cash flows  What is the effective maturity of both?  The effective maturity of the first security is:  (1,000/1,000) x 1 = 20 years  The effective maturity of the second security is:  [(900/1,000) x 1]+[(100/1,000) x 20] = 2.9 years  Duration is similar, however, it uses a weighted average of the present values of the cash flows
  6. 6. Duration versus Maturity Duration is an approximate measure of the price elasticity of demand % Change in Quantity Demanded Price Elasticity of Demand  - % Change in Price
  7. 7. Duration versus Maturity  The longer the duration, the larger the change in price for a given change in interest rates. P Duration  - P i (1  i)  i  P  - Duration  P  (1  i) 
  8. 8. Measuring Duration  Duration is a weighted average of the time until the expected cash flows from a security will be received, relative to the security’s price  Macaulay’s Duration k n CFt (t) CFt (t)  (1+ r)t  (1+ r)t D = t=1 k  t =1 CFt Price of the Security  (1+ r)t t =1
  9. 9. Measuring Duration  Example  What is the duration of a bond with a $1,000 face value, 10% annual coupon payments, 3 years to maturity and a 12% YTM? The bond’s price is $951.96. 100  1 100  2 100  3 1,000  3 1 + 2 + 3 + (1.12) (1.12) (1.12) (1.12) 3 2,597.6 D 3  = 2.73 years 100 1000 951.96  (1.12) t (1.12) 3 t =1 +
  10. 10. Measuring Duration  Example  What is the duration of a bond with a $1,000 face value, 10% coupon, 3 years to maturity but the YTM is 5%?The bond’s price is $1,136.16. 100 * 1 100 * 2 100 * 3 1,000 * 3 1 + 2 + 3 + (1.05) (1.05) (1.05) (1.05) 3 3,127.31 D  = 2.75 years 1136.16 1,136.16
  11. 11. Measuring Duration  Example  What is the duration of a bond with a $1,000 face value, 10% coupon, 3 years to maturity but the YTM is 20%?The bond’s price is $789.35. 100 * 1 100 * 2 100 * 3 1,000 * 3 1 + 2 + 3 + (1.20) (1.20) (1.20) (1.20) 3 2,131.95 D  = 2.68 years 789.35 789.35
  12. 12. Measuring Duration  Example  Whatis the duration of a zero coupon bond with a $1,000 face value, 3 years to maturity but the YTM is 12%? 1,000 * 3 (1.12) 3 2,135.34 D  = 3 years 1,000 711.78 (1.12) 3  By definition, the duration of a zero coupon bond is equal to its maturity
  13. 13. Duration and Modified Duration  The greater the duration, the greater the price sensitivity  Modified Duration gives an estimate of price volatility: Macaulay' s Duration Modified Duration  (1  i) P  - Modified Duration  i P
  14. 14. Effective Duration  Effective Duration  Used to estimate a security’s price sensitivity when the security contains embedded options.  Compares a security’s estimated price in a falling and rising rate environment.
  15. 15. Effective Duration Pi- - Pi Effective Duration   - P0 (i - i )  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
  16. 16. Effective Duration  Example  Consider a 3-year, 9.4 percent semi- annual coupon bond selling for $10,000 par to yield 9.4 percent to maturity.  Macaulay’s Duration for the option-free version of this bond is 5.36 semiannual periods, or 2.68 years.  The Modified Duration of this bond is 5.12 semiannual periods or 2.56 years.
  17. 17. Effective Duration  Example  Assume, instead, that the bond is callable at par in the near-term .  If rates fall, the price will not rise much above the par value since it will likely be called  If rates rise, the bond is unlikely to be called and the price will fall
  18. 18. Effective Duration  Example  If rates rise 30 basis points to 5% semiannually, the price will fall to $9,847.72.  If rates fall 30 basis points to 4.4% semiannually, the price will remain at par $10,000 - $9,847.72 Effective Duration   2.54 $10,000( 0.05 - 0.044)
  19. 19. Duration GAP  Duration GAP Model  Focuseson either managing the market value of stockholders’ equity  The bank can protect EITHER the market value of equity or net interest income, but not both  Duration GAP analysis emphasizes the impact on equity
  20. 20. Duration GAP  Duration GAP Analysis  Compares the duration of a bank’s assets with the duration of the bank’s liabilities and examines how the economic value stockholders’ equity will change when interest rates change.
  21. 21. Two Types of Interest Rate Risk  Reinvestment Rate Risk  Changes in interest rates will change the bank’s cost of funds as well as the return on invested assets  Price Risk  Changes in interest rates will change the market values of the bank’s assets and liabilities
  22. 22. Reinvestment Rate Risk  If interest rates change, the bank will have to reinvest the cash flows from assets or refinance rolled-over liabilities at a different interest rate in the future  An increase in rates increases a bank’s return on assets but also increases the bank’s cost of funds
  23. 23. Price Risk  If interest rates change, the value of assets and liabilities also change.  The longer the duration, the larger the change in value for a given change in interest rates  Duration GAP considers the impact of changing rates on the market value of equity
  24. 24. Reinvestment Rate Risk and Price Risk  Reinvestment Rate Risk  Ifinterest rates rise (fall), the yield from the reinvestment of the cash flows rises (falls) and the holding period return (HPR) increases (decreases).  Price risk  If interest rates rise (fall), the price falls (rises). Thus, if you sell the security prior to maturity, the HPR falls (rises).
  25. 25. Reinvestment Rate Risk and Price Risk  Increases in interest rates will increase the HPR from a higher reinvestment rate but reduce the HPR from capital losses if the security is sold prior to maturity.  Decreases in interest rates will decrease the HPR from a lower reinvestment rate but increase the HPR from capital gains if the security is sold prior to maturity.
  26. 26. Reinvestment Rate Risk and Price Risk  An immunized security or portfolio is one in which the gain from the higher reinvestment rate is just offset by the capital loss.  For an individual security, immunization occurs when an investor’s holding period equals the duration of the security.
  27. 27. Steps in Duration GAP Analysis  Forecast interest rates.  Estimate the market values of bank assets, liabilities and stockholders’ equity.  Estimate the weighted average duration of assets and the weighted average duration of liabilities.  Incorporate the effects of both on- and off- balance sheet items. These estimates are used to calculate duration gap.  Forecasts changes in the market value of stockholders’ equity across different interest rate environments.
  28. 28. Weighted Average Duration of Bank Assets  Weighted Average Duration of Bank Assets (DA) n DA   w iDai i  Where  wi = Market value of asset i divided by the market value of all bank assets  Dai = Macaulay’s duration of asset i  n = number of different bank assets
  29. 29. Weighted Average Duration of Bank Liabilities  Weighted Average Duration of Bank Liabilities (DL) m DL   z jDlj j  Where  zj = Market value of liability j divided by the market value of all bank liabilities  Dlj= Macaulay’s duration of liability j  m = number of different bank liabilities
  30. 30. Duration GAP and Economic Value of Equity  Let MVA and MVL equal the market values of assets and liabilities, respectively.  If: ΔEVE  ΔMVA  ΔMVL and Duration GAP DGAP  DA - (MVL/MVA)DL  Then:  y  ΔEVE  - DGAP  MVA  (1  y)   where y = the general level of interest rates
  31. 31. Duration GAP and Economic Value of Equity  To protect the economic value of equity against any change when rates change , the bank could set the duration gap to zero:  y  ΔEVE  - DGAP  MVA  (1  y) 
  32. 32. Hypothetical Bank Balance Sheet 1 Par Years Market $1,000 % Coup Mat. YTM Value Dur. Assets Cash $100 $ 100 Earning assets 3-yr Commercial loan $ 700 12.00% 3 12.00% $ 700 2.69 6-yr Treasury bond 84 1 84  2 8.00%  3 $ 200 84 6 700  3 $ 200 8.00% 4.99 Total Earning Assets  900 2  $  11.11% $ 900 (assets1 Non-cash earning 1.12) $ (1- 12) . (1.12)3 (1.12)3 $ - Total assets D  $ 1,000 10.00% $ 1,000 2.88 700 Liabilities Interest bearing liabs. 1-yr Time deposit $ 620 5.00% 1 5.00% $ 620 1.00 3-yr Certificate of deposit $ 300 7.00% 3 7.00% $ 300 2.81 Tot. Int Bearing Liabs. $ 920 5.65% $ 920 Tot. non-int. bearing $ - $ - Total liabilities $ 920 5.65% $ 920 1.59 Total equity $ 80 $ 80 Total liabs & equity $ 1,000 $ 1,000
  33. 33. Calculating DGAP  DA  ($700/$1000)*2.69 + ($200/$1000)*4.99 = 2.88  DL  ($620/$920)*1.00 + ($300/$920)*2.81 = 1.59  DGAP  2.88 - (920/1000)*1.59 = 1.42 years  What does this tell us?  The average duration of assets is greater than the average duration of liabilities; thus asset values change by more than liability values.
  34. 34. 1 percent increase in all rates. 1 Par Years Market $1,000 % Coup Mat. YTM Value Dur. Assets Cash $ 100 $ 100 Earning assets 3-yr Commercial loan $ 700 12.00% 3 13.00% $ 683 2.69 6-yr Treasury bond $ 200 8.00% 6 9.00% $ 191 4.97 Total Earning Assets $ 900 12.13% $ 875 84 700 $  3 Non-cash earning assets $ - PV  - t 1 t Total assets $ 1,000 1.13 1.133 $ 10.88% 975 2.86 Liabilities Interest bearing liabs. 1-yr Time deposit $ 620 5.00% 1 6.00% $ 614 1.00 3-yr Certificate of deposit $ 300 7.00% 3 8.00% $ 292 2.81 Tot. Int Bearing Liabs. $ 920 6.64% $ 906 Tot. non-int. bearing $ - $ - Total liabilities $ 920 6.64% $ 906 1.58 Total equity $ 80 $ 68 Total liabs & equity $ 1,000 $ 975
  35. 35. Calculating DGAP  DA  ($683/$974)*2.68 + ($191/$974)*4.97 = 2.86  DA  ($614/$906)*1.00 + ($292/$906)*2.80 = 1.58  DGAP  2.86 - ($906/$974) * 1.58 = 1.36 years  What does 1.36 mean?  The average duration of assets is greater than the average duration of liabilities, thus asset values change by more than liability values.
  36. 36. Change in the Market Value of Equity y ΔEVE  - DGAP[ ]MVA (1  y)  In this case: .01 ΔEVE  - 1.42[ ]$1,000  $12.91 1.10
  37. 37. Positive and Negative Duration GAPs  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 EVE will fall (rise) accordingly.  Negative DGAP  Indicates that weighted liabilities are more price sensitive than weighted assets.  Thus, when interest rates rise (fall), assets will fall proportionately less (more) in value that liabilities and the EVE will rise (fall).
  38. 38. DGAP Summary DGAP Summary Change in DGAP Interest Assets Liabilities Equity Rates Positive Increase Decrease > Decrease → Decrease Positive Decrease Increase > Increase → Increase Negative Increase Decrease < Decrease → Increase Negative Decrease Increase < Increase → Decrease Zero Increase Decrease = Decrease → None Zero Decrease Increase = Increase → None
  39. 39. An Immunized Portfolio  To immunize the EVE from rate changes in the example, the bank would need to:  decrease the asset duration by 1.42 years or  increase the duration of liabilities by 1.54 years  DA / ( MVA/MVL) = 1.42 / ($920 / $1,000) = 1.54 years
  40. 40. Immunized Portfolio 1 Par Years Market $1,000 % Coup Mat. YTM Value Dur. Assets Cash $ 100 $ 100 Earning assets 3-yr Commercial loan $ 700 12.00% 3 12.00% $ 700 2.69 6-yr Treasury bond $ 200 8.00% 6 8.00% $ 200 4.99 Total Earning Assets $ 900 11.11% $ 900 Non-cash earning assets - $ $ - Total assets $ 1,000 10.00% $ 1,000 2.88 Liabilities Interest bearing liabs. 1-yr Time deposit $ 340 5.00% 1 5.00% $ 340 1.00 3-yr Certificate of deposit 300 $ 7.00% 3 7.00% $ 300 2.81 6-yr Zero-coupon CD* $ 444 0.00% 6 8.00% $ 280 6.00 Tot. Int Bearing Liabs. $ 1,084 6.57% $ 920 Tot. non-int. bearing $ - $ - Total liabilities $ 1,084 6.57% $ 920 3.11 Total equity $ 80 $ 80 DGAP = 2.88 – 0.92 (3.11) ≈ 0
  41. 41. Immunized Portfolio with a 1% increase in rates 1 Par Years Market $1,000 % Coup Mat. YTM Value Dur. Assets Cash $ 100.0 $ 100.0 Earning assets 3-yr Commercial loan $ 700.0 12.00% 3 13.00% $ 683.5 2.69 6-yr Treasury bond $ 200.0 8.00% 6 9.00% $ 191.0 4.97 Total Earning Assets $ 900.0 12.13% $ 874.5 Non-cash earning assets$ - $ - Total assets $ 1,000.0 10.88% $ 974.5 2.86 Liabilities Interest bearing liabs. 1-yr Time deposit $ 340.0 5.00% 1 6.00% $ 336.8 1.00 3-yr Certificate of deposit 300.0 $ 7.00% 3 8.00% $ 292.3 2.81 6-yr Zero-coupon CD* $ 444.3 0.00% 6 9.00% $ 264.9 6.00 Tot. Int Bearing Liabs. $ 1,084.3 7.54% $ 894.0 Tot. non-int. bearing $ - $ - Total liabilities $ 1,084.3 7.54% $ 894.0 3.07 Total equity $ 80.0 $ 80.5
  42. 42. Immunized Portfolio with a 1% increase in rates  EVE changed by only $0.5 with the immunized portfolio versus $25.0 when the portfolio was not immunized.
  43. 43. Stabilizing the Book Value of Net Interest Income  This can be done for a 1-year time horizon, with the appropriate duration gap measure  DGAP* MVRSA(1- DRSA) - MVRSL(1- DRSL) where:  MVRSA = cumulative market value of RSAs  MVRSL = cumulative market value of RSLs  DRSA = composite duration of RSAs for the given time horizon  Equal to the sum of the products of each asset’s duration with the relative share of its total asset market value  DRSL = composite duration of RSLs for the given time horizon  Equal to the sum of the products of each liability’s duration with the relative share of its total liability market value.
  44. 44. Stabilizing the Book Value of Net Interest Income  If DGAP* is positive, the bank’s net interest income will decrease when interest rates decrease, and increase when rates increase.  If DGAP* is negative, the relationship is reversed.  Only when DGAP* equals zero is interest rate risk eliminated.  Banks can use duration analysis to stabilize a number of different variables reflecting bank performance.
  45. 45. Economic Value of Equity Sensitivity Analysis  Effectively involves the same steps as earnings sensitivity analysis.  In EVE analysis, however, the bank focuses on:  The relative durations of assets and liabilities  How much the durations change in different interest rate environments  What happens to the economic value of equity across different rate environments
  46. 46. Embedded Options  Embedded options sharply influence the estimated volatility in EVE  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.
  47. 47. First Savings Bank Economic Value of Equity Market Value/Duration Report as of 12/31/04 Most Likely Rate Scenario-Base Strategy Assets Book Value Market Value Book Yield Duration* Loans Prime Based Ln $ 100,000 $ 102,000 9.00% Equity Credit Lines $ 25,000 $ 25,500 8.75% - Fixed Rate > I yr $ 170,000 $ 170,850 7.50% 1.1 Var Rate Mtg 1 Yr $ 55,000 $ 54,725 6.90% 0.5 30-Year Mortgage $ 250,000 $ 245,000 7.60% 6.0 Consumer Ln $ 100,000 $ 100,500 8.00% 1.9 Credit Card $ 25,000 $ 25,000 14.00% 1.0 Total Loans $ 725,000 $ 723,575 8.03% 2.6 Loan Loss Reserve $ (15,000) $ 11,250 0.00% 8.0 Net Loans $ 710,000 $ 712,325 8.03% 2.5 Investments Eurodollars $ 80,000 $ 80,000 5.50% 0.1 CMO Fix Rate $ 35,000 $ 34,825 6.25% 2.0 US Treasury $ 75,000 $ 74,813 5.80% 1.8 Total Investments $ 190,000 $ 189,638 5.76% 1.1 Fed Funds Sold $ 25,000 $ 25,000 5.25% - Cash & Due From $ 15,000 $ 15,000 0.00% 6.5 Non-int Rel Assets $ 60,000 $ 60,000 0.00% 8.0 Total Assets $ 100,000 $ 100,000 6.93% 2.6
  48. 48. First Savings Bank Economic Value of Equity Market Value/Duration Report as of 12/31/04 Most Likely Rate Scenario-Base Strategy Liabilities Book Value Market Value Book Yield Duration* Deposits MMDA $ 240,000 $ 232,800 2.25% - Retail CDs $ 400,000 $ 400,000 5.40% 1.1 Savings $ 35,000 $ 33,600 4.00% 1.9 NOW $ 40,000 $ 38,800 2.00% 1.9 DDA Personal $ 55,000 $ 52,250 8.0 Comm'l DDA $ 60,000 $ 58,200 4.8 Total Deposits $ 830,000 $ 815,650 1.6 TT&L $ 25,000 $ 25,000 5.00% - L-T Notes Fixed $ 50,000 $ 50,250 8.00% 5.9 Fed Funds Purch - - 5.25% - NIR Liabilities $ 30,000 $ 28,500 8.0 Total Liabilities $ 935,000 $ 919,400 2.0 Equity $ 65,000 $ 82,563 9.9 Total Liab & Equity $ 1,000,000 $ 1,001,963 2.6 Off Balance Sheet Notional lnt Rate Swaps - $ 1,250 6.00% 2.8 50,000 Adjusted Equity $ 65,000 $ 83,813 7.9
  49. 49. Duration Gap for First Savings Bank EVE  Market Value of Assets  $1,001,963  Duration of Assets  2.6 years  Market Value of Liabilities  $919,400  Duration of Liabilities  2.0 years
  50. 50. Duration Gap for First Savings Bank EVE  Duration Gap = 2.6 – ($919,400/$1,001,963)*2.0 = 0.765 years  Example: A 1% increase in rates would reduce EVE by $7.2 million = 0.765 (0.01 / 1.0693) * $1,001,963  Recall that the average rate on assets is 6.93%
  51. 51. Sensitivity of EVE versus Most Likely (Zero Shock) Interest Rate Scenario 20.0 Change in EVE (millions of dollars) 13.6 8.8 8.2 10.0 2 (10.0) ALCO Guideline (8.2) Board Limit (20.0) (20.4) (30.0) (36.6) (40.0) -300 -200 -100 0 +100 +200 +300 Shocks to Current Rates Sensitivity of Economic Value of Equity measures the change in the economic value of the corporation’s 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.
  52. 52. Effective “Duration” of Equity  By definition, duration measures the percentage change in market value for a given change in interest rates  Thus,a bank’s duration of equity measures the percentage change in EVE that will occur with a 1 percent change in rates:  Effective duration of equity 9.9 yrs. = $8,200 / $82,563
  53. 53. Asset/Liability Sensitivity and DGAP  Funding GAP and Duration GAP are NOT directly comparable  Funding GAP examines various “time buckets” while Duration GAP 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.
  54. 54. Strengths and Weaknesses: DGAP and EVE- Sensitivity Analysis  Strengths  Duration analysis provides a comprehensive measure of interest rate risk  Duration measures are additive  This allows for the matching of total assets with total liabilities rather than the matching of individual accounts  Durationanalysis takes a longer term view than static gap analysis
  55. 55. Strengths and Weaknesses: DGAP and EVE- Sensitivity Analysis  Weaknesses  It is difficult to compute duration accurately  “Correct” duration analysis requires that each future cash flow be discounted by a distinct discount rate  A bank must continuously monitor and adjust the duration of its portfolio  It is difficult to estimate the duration on assets and liabilities that do not earn or pay interest  Duration measures are highly subjective
  56. 56. Speculating on Duration GAP  It is difficult to actively vary GAP or DGAP and consistently win  Interest rates forecasts are frequently wrong  Even if rates change as predicted, banks have limited flexibility in vary GAP and DGAP and must often sacrifice yield to do so
  57. 57. Gap and DGAP Management Strategies Example  Cash flows from investing $1,000 either in a 2-year security yielding 6 percent or two consecutive 1-year securities, with the current 1-year yield equal to 5.5 percent. 0 1 2 Two-Year Security $60 $60 0 1 2 One-Year Security & then another One-Year Security $55 ?
  58. 58. Gap and DGAP Management Strategies Example  It is not known today what a 1-year security will yield in one year.  For the two consecutive 1-year securities to generate the same $120 in interest, ignoring compounding, the 1-year security must yield 6.5% one year from the present.  This break-even rate is a 1-year forward rate, one year from the present:  6% + 6% = 5.5% + x so x must = 6.5%
  59. 59. Gap and DGAP Management Strategies Example  By investing in the 1-year security, a depositor is betting that the 1-year interest rate in one year will be greater than 6.5%  By issuing the 2-year security, the bank is betting that the 1-year interest rate in one year will be greater than 6.5%
  60. 60. Yield Curve Strategy  When the U.S. economy hits its peak, the yield curve typically inverts, with short-term rates exceeding long-term rates.  Only twice since WWII has a recession not followed an inverted yield curve  As the economy contracts, the Federal Reserve typically increases the money supply, which causes the rates to fall and the yield curve to return to its “normal” shape.
  61. 61. Yield Curve Strategy  To take advantage of this trend, when the yield curve inverts, banks could:  Buy long-term non-callable securities  Prices will rise as rates fall  Make fixed-rate non-callable loans  Borrowers are locked into higher rates  Price deposits on a floating-rate basis  Lengthen the duration of assets relative to the duration of liabilities
  62. 62. Interest Rates and the Business Cycle The general level of interest rates and the shape of the yield curve appear to follow the U.S. business cycle. Peak In expansionary Short-TermRates stages rates rise until they reach a peak as ) t the Federal Reserve Long-TermRates n tightens credit e c r availability. e P ( Expansion The inverted yield curve has predicted the last s five recessions e t a Contraction DATE WHEN 1-YEAR RATE LENGTH OF TIME UNTIL R FIRST EXCEEDS 10-YEAR RATE START OF NEXT RECESSION t Expansion Apr. ’68 20 months (Dec. ’69) s Mar. ’73 8 months (Nov. ’73) e contractionary In rstages rates fall until Sept. ’78 16 months (Jan. ’80) e tthey reach a trough Sept. ’80 10 months (July ’81) n Trough Feb. ’89 17 months (July ’90) Iwhen the U.S. Dec. ’00 15 months (March ’01) economy falls into recession. Time
  63. 63. Bank Management, 6th edition. Timothy W. Koch and S. Scott MacDonald Copyright © 2006 by South-Western, a division of Thomson Learning Managing Interest Rate Risk: Duration GAP and Economic Value of Equity Chapter 6 William Chittenden edited and updated the PowerPoint slides for this edition.
  1. A particular slide catching your eye?

    Clipping is a handy way to collect important slides you want to go back to later.

×