Chapter 8 Managing Interest Rate Risk Economic Value

Chapter 8 Managing Interest Rate Risk: Economic Value of Equity © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.

Managing Interest Rate Risk: Economic Value of Equity n Economic Value of Equity (EVE) Analysis n Focuses on changes in stockholders’ equity given potential changes in interest rates © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 2

Managing Interest Rate Risk: Economic Value of Equity n Duration GAP Analysis n 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 © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 3

Managing Interest Rate Risk: Economic Value of Equity n GAP and Earnings Sensitivity versus Duration GAP and EVE Sensitivity © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 4

Managing Interest Rate Risk: Economic Value of Equity What is duration? n Duration is a measure of the effective maturity of a security Duration incorporates the timing and size of a security’s cash flows n Duration measures how price sensitive a security is to changes in interest rates n § The greater (shorter) the duration, the greater (lesser) the price sensitivity © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 5

Managing Interest Rate Risk: Economic Value of Equity n Market Value Accounting Issues n EVE sensitivity analysis is linked with the debate concerning whether market value accounting is appropriate for financial institutions n Recently many large commercial and investment banks reported large write-downs of mortgage-related assets, which depleted their capital n Some managers argued that the write-downs far exceeded the true decline in value of the assets and because banks did not need to sell the assets they should not be forced to recognize the “paper” losses © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 6

Measuring Interest Rate Risk with Duration GAP n Duration GAP Analysis n Compares the price sensitivity of a bank’s total assets with the price sensitivity of its total liabilities to assess n whether the market value of assets or liabilities changes more when rates change © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 7

Measuring Interest Rate Risk with Duration GAP n Duration, Modified Duration, and Effective Duration n Macaulay’s n n n Duration (D) where P* is the initial price, i is the market interest rate, t is time until the cash payment is made © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 8

Measuring Interest Rate Risk with Duration GAP n Duration, Modified Duration, and Effective Duration n Macaulay’s Duration (D) Macaulay’s duration is a measure of price sensitivity n where P refers to the price of the underlying security: n © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 9

Measuring Interest Rate Risk with Duration GAP n Duration, Modified Duration, and Effective Duration n Modified n Duration Indicates how much the price of a security will change in percentage terms for a given change in interest rates Modified Duration = D/(1+i) © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 10

Measuring Interest Rate Risk with Duration GAP n Duration, Modified Duration, and Effective Duration n Example Assume that a ten-year zero coupon bond has a par value of $10, 000, current price of $7, 835. 26, and a market rate of interest of 5%. n What is the expected change in the bond’s price if interest rates fall by 25 basis points? n © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 11

Measuring Interest Rate Risk with Duration GAP n Duration, Modified Duration, and Effective Duration n Example n Since the bond is a zero-coupon bond, Macaulay’s Duration equals the time to maturity, 10 years. the Modified Duration is 10/(1. 05) = 9. 524 years. n If rates change by 0. 25% (. 0025), the bond’s price will change by n 9. 524 ×. 0025 × $7, 835. 26 = $186. 56 n © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 12

Measuring Interest Rate Risk with Duration GAP n Duration, Modified Duration, and Effective Duration n Effective Duration Used to estimate a security’s price sensitivity when the security contains embedded options n Compares a security’s estimated price in a falling and rising rate environment n © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 13

Measuring Interest Rate Risk with Duration GAP n Duration, Modified Duration, and Effective Duration n Effective Duration where: Pi- = Price if rates fall Pi+ = Price if rates rise P 0 = Initial (current) price i+ = Initial market rate plus the increase in the rate i- = Initial market rate minus the decrease in the rate © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 14

Measuring Interest Rate Risk with Duration GAP n Effective Duration n 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 © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 15

Measuring Interest Rate Risk with Duration GAP n Effective Duration n Example § Assume that the bond is callable at par in the nearterm. § 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 © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 16

Measuring Interest Rate Risk with Duration GAP n Effective Duration n 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 © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 17

Measuring Interest Rate Risk with Duration GAP n Duration GAP Model n Focuses on managing the market value of stockholders’ equity n The bank can protect EITHER the market value of equity or net interest income (NII), but not both n Duration GAP analysis emphasizes the impact on equity and focuses on price sensitivity © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 18

Measuring Interest Rate Risk with Duration GAP n Duration GAP Model n Steps in Duration GAP Analysis n Forecast interest rates n Estimate the market values of bank assets, liabilities and stockholders’ equity n 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 n Forecasts changes in the market value of stockholders’ equity across different interest rate environments © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 19

Measuring Interest Rate Risk with Duration GAP n Duration GAP Model n Weighted Average Duration of Bank Assets (DA): where wi = Market value of asset i divided by the market value of all bank assets n Dai = Macaulay’s duration of asset i n n = number of different bank assets n © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 20

Measuring Interest Rate Risk with Duration GAP n Duration GAP Model n Weighted Average Duration of Bank Liabilities (DL): where zj = Market value of liability j divided by the market value of all bank liabilities n Dlj= Macaulay’s duration of liability j n m = number of different bank liabilities n © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 21

Measuring Interest Rate Risk with Duration GAP n Duration GAP Model n Let MVA and MVL equal the market values of assets and liabilities, respectively n ΔEVE = ΔMVA – ΔMVL n Duration GAP ( DGAP ) = DA – (MVL/MVA)DL then n ΔEVE = -DGAP[Δy/(1+y)]MVA where y is the interest rate © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 22

Measuring Interest Rate Risk with Duration GAP n Duration GAP Model n To protect the economic value of equity against any change when rates change , the bank could set the duration gap to zero: © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 23

Measuring Interest Rate Risk with Duration GAP n Duration GAP Model n DGAP as a Measure of Risk n The sign and size of DGAP provide information about whether rising or falling rates are beneficial or harmful and how much risk the bank is taking © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 24

Measuring Interest Rate Risk with Duration GAP n If DGAP is positive, an increase in rates will lower EVE, while a decrease in rates will increase EVE n If DGAP is negative, an increase in rates will increase EVE, while a decrease in rates will lower EVE n The closer DGAP is to zero, the smaller is the potential change in EVE for any change in rates © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 25

Measuring Interest Rate Risk with Duration GAP n A Duration Application for Banks © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 26

Measuring Interest Rate Risk with Duration GAP n A Duration Application for Banks n Implications of DGAP The value of DGAP at 1. 42 years indicates that the bank has a substantial mismatch in average durations of assets and liabilities n Since the DGAP is positive, the market value of assets will change more than the market value of liabilities if all rates change by comparable amounts n § In this example, an increase in rates will cause a decrease in EVE, while a decrease in rates will cause an increase in EVE © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 27

Measuring Interest Rate Risk with Duration GAP n A Duration Application for Banks n Implications of DGAP > 0 n A positive DGAP indicates that assets are more price sensitive than liabilities § When interest rates rise (fall), assets will fall proportionately more (less) in value than liabilities and EVE will fall (rise) accordingly. n Implications of DGAP < 0 n A negative DGAP indicates that liabilities are more price sensitive than assets § When interest rates rise (fall), assets will fall proportionately less (more) in value that liabilities and the EVE will rise (fall) © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 28

Measuring Interest Rate Risk with Duration GAP n A Duration Application for Banks © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 29

Measuring Interest Rate Risk with Duration GAP n A Duration Application for Banks n Duration GAP Summary © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 30

Measuring Interest Rate Risk with Duration GAP n A Duration Application for Banks n DGAP As a Measure of Risk n DGAP measures can be used to approximate the expected change in economic value of equity for a given change in interest rates © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 31

Measuring Interest Rate Risk with Duration GAP n A Duration Application for Banks n DGAP As a Measure of Risk n In this case: The actual decrease, as shown in Exhibit 8. 3, was $12 n Y is average interest rate of assets n © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 32

Measuring Interest Rate Risk with Duration GAP n A Duration Application for Banks n An Immunized Portfolio n 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 or § a combination of both © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 33

Measuring Interest Rate Risk with Duration GAP n A Duration Application for Banks © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 34

Measuring Interest Rate Risk with Duration GAP n A Duration Application for Banks n An Immunized Portfolio n With a 1% increase in rates, the EVE did not change with the immunized portfolio versus $12. 0 when the portfolio was not immunized © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 35

Measuring Interest Rate Risk with Duration GAP n A Duration Application for Banks n An Immunized Portfolio n If DGAP > 0, reduce interest rate risk by: § shortening asset durations § Buy short-term securities and sell longterm securities § Make floating-rate loans and sell fixed-rate loans § lengthening liability durations § Issue longer-term CDs § Borrow via longer-term FHLB advances § Obtain more core transactions accounts from stable sources © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 36

Measuring Interest Rate Risk with Duration GAP n A Duration Application for Banks n An Immunized Portfolio n If DGAP < 0, reduce interest rate risk by: § lengthening asset durations § Sell short-term securities and buy long-term securities § Sell floating-rate loans and make fixed-rate loans § Buy securities without call options § shortening liability durations § Issue shorter-term CDs § Borrow via shorter-term FHLB advances § Use short-term purchased liability funding from federal funds and repurchase agreements © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 37

Measuring Interest Rate Risk with Duration GAP n A Duration Application for Banks n Banks may choose to target variables other than the market value of equity in managing interest rate risk n Many banks are interested in stabilizing the book value of net interest income n This can be done for a one-year time horizon, with the appropriate duration gap measure © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 38

Measuring Interest Rate Risk with Duration GAP n A Duration Application for Banks n DGAP* = MVRSA(1 − DRSA) − MVRSL(1 − DRSL) n where MVRSA = cumulative market value of ratesensitive assets (RSAs) n MVRSL = cumulative market value of ratesensitive liabilities (RSLs) n DRSA = composite duration of RSAs for the given time horizon n DRSL = composite duration of RSLs for the given time horizon n © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 39

Measuring Interest Rate Risk with Duration GAP n A Duration Application for Banks n DGAP* > 0 n Net interest income will decrease (increase) when interest rates decrease (increase) n DGAP* < 0 n Net interest income will decrease (increase) when interest rates increase (decrease) n DGAP* = 0 n Interest rate risk eliminated § A major point is that duration analysis can be used to stabilize a number of different variables reflecting bank performance © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 40

Economic Value of Equity Sensitivity Analysis n An important component of EVE sensitivity analysis is allowing different rates to change by different amounts and incorporating projections of when embedded customer options will be exercised and what their values will be © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 41

Economic Value of Equity Sensitivity Analysis n Estimating the timing of cash flows and subsequent durations of assets and liabilities is complicated by: n Prepayments that exceed (fall short of) those expected duration n A bond being called n A deposit that is withdrawn early or a deposit that is not withdrawn as expected © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 42

Economic Value of Equity Sensitivity Analysis n EVE Sensitivity Analysis: An Example n First Savings Bank n Average duration of assets equals 2. 6 years n Market value of assets equals $1, 001, 963, 000 n Average duration of liabilities equals 2 years n Market value of liabilities equals $919, 400, 000 © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 43

© 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 44

Economic Value of Equity Sensitivity Analysis n EVE Sensitivity Analysis: An Example n First Savings Bank n Duration Gap § 2. 6 – ($919, 400, 000/$1, 001, 963, 000) × 2. 0 = 0. 765 years n Example: § A 1% increase in rates would reduce EVE by $7. 2 million § ΔMVE = -DGAP[Δy/(1+y)]MVA § ΔMVE = -0. 765 (0. 01/1. 0693) × $1, 001, 963, 000 = -$7, 168, 257 § Recall that the average rate on assets is 6. 93% § The estimate of -$7, 168, 257 ignores the impact of interest rates on embedded options and the effective duration of assets and liabilities © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 45

Economic Value of Equity Sensitivity Analysis n EVE Sensitivity Analysis: An Example © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 46

Economic Value of Equity Sensitivity Analysis n EVE Sensitivity Analysis: An Example n First Savings Bank n The previous slide shows that FSB’s EVE will fall by $8. 2 million if rates are rise by 1% § This differs from the estimate of -$7, 168, 257 because this sensitivity analysis takes into account the embedded options on loans and deposits § For example, with an increase in interest rates, depositors may withdraw a CD before maturity to reinvest the funds at a higher interest rate © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 47

Economic Value of Equity Sensitivity Analysis n EVE Sensitivity Analysis: An Example n First Savings Bank n Effective “Duration” of Equity § Recall, duration measures the percentage change in market value for a given change in interest rates § 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 = $8, 200 / $82, 563 = 9. 9 years © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 48

Earnings Sensitivity Analysis versus EVE Sensitivity Analysis n Strengths and Weaknesses: DGAP and EVE-Sensitivity Analysis n Strengths Duration analysis provides a comprehensive measure of interest rate risk n Duration measures are additive n § This allows for the matching of total assets with total liabilities rather than the matching of individual accounts n Duration analysis takes a longer term view than static gap analysis © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 49

Earnings Sensitivity Analysis versus EVE Sensitivity Analysis n Strengths and Weaknesses: DGAP and EVE- Sensitivity Analysis n Weaknesses n n n 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 © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part. 50

Chapter 8 Managing Interest Rate Risk: Economic Value of Equity © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.