Managing Interest Rate Risk: Economic Value of Equity

Managing Interest Rate Risk: Economic Value of Equity
Chapter 8 Managing Interest Rate Risk: Economic Value of Equity

Economic Value of Equity (EVE) 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

GAP and Earnings Sensitivity versus Duration GAP and EVE Sensitivity

What is duration? 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

Market Value Accounting Issues EVE sensitivity analysis is linked with the debate concerning whether market value accounting is appropriate for financial institutions Recently many large commercial and investment banks reported large write-downs of mortgage-related assets, which depleted their capital 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

Measuring Interest Rate Risk with Duration GAP
Duration GAP Analysis Compares the price sensitivity of a bank’s total assets with the price sensitivity of its total liabilities to assess whether the market value of assets or liabilities changes more when rates change

Duration, Modified Duration, and Effective Duration Macaulay’s Duration (D) where P* is the initial price, i is the market interest rate, and t is equal to the time until the cash payment is made

Duration, Modified Duration, and Effective Duration Macaulay’s Duration (D) Macaulay’s duration is a measure of price sensitivity where P refers to the price of the underlying security:

Duration, Modified Duration, and Effective Duration Modified 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)

Duration, Modified Duration, and Effective Duration 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%. What is the expected change in the bond’s price if interest rates fall by 25 basis points?

Duration, Modified Duration, and Effective Duration Example Since the bond is a zero-coupon bond, Macaulay’s Duration equals the time to maturity, 10 years. With a market rate of interest, the Modified Duration is 10/(1.05) = years. If rates change by 0.25% (.0025), the bond’s price will change by approximately × × $7, = $186.56

Duration, Modified Duration, and 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

Duration, Modified Duration, and Effective Duration Effective Duration where: Pi- = Price if rates fall Pi+ = Price if rates rise P0 = Initial (current) price i+ = Initial market rate plus the increase in the rate i- = Initial market rate minus the decrease in the rate

Duration, Modified Duration, and Effective Duration 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

Duration, Modified Duration, and Effective Duration Effective Duration Example Assume 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

Duration, Modified Duration, and Effective Duration Effective Duration Example If rates rise 30 basis points to 5% semiannually, the price will fall to $9, If rates fall 30 basis points to 4.4% semiannually, the price will remain at par

Duration, Modified Duration, and Effective Duration Effective Duration Example

Duration GAP Model Focuses on 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 and focuses on price sensitivity

Duration GAP Model 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

Duration GAP Model Weighted Average Duration of Bank Assets (DA): 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

Duration GAP Model Weighted Average Duration of Bank Liabilities (DL): 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

Duration GAP Model 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 ΔEVE = -DGAP[Δy/(1+y)]MVA where y is the interest rate

Duration GAP Model To protect the economic value of equity against any change when rates change , the bank could set the duration gap to zero:

Duration GAP Model DGAP as a Measure of Risk 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 If DGAP is positive, an increase in rates will lower EVE, while a decrease in rates will increase EVE If DGAP is negative, an increase in rates will increase EVE, while a decrease in rates will lower EVE The closer DGAP is to zero, the smaller is the potential change in EVE for any change in rates

A Duration Application for Banks

A Duration Application for Banks 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 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 In this example, an increase in rates will cause a decrease in EVE, while a decrease in rates will cause an increase in EVE

A Duration Application for Banks Implications of DGAP > 0 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. Implications of DGAP < 0 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)

A Duration Application for Banks Duration GAP Summary

A Duration Application for Banks DGAP As a Measure of Risk DGAP measures can be used to approximate the expected change in economic value of equity for a given change in interest rates

A Duration Application for Banks DGAP As a Measure of Risk In this case: The actual decrease, as shown in Exhibit 8.3, was $12

A Duration Application for Banks 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 a combination of both

A Duration Application for Banks An Immunized Portfolio With a 1% increase in rates, the EVE did not change with the immunized portfolio versus $12.0 when the portfolio was not immunized

A Duration Application for Banks An Immunized Portfolio If DGAP > 0, reduce interest rate risk by: shortening asset durations Buy short-term securities and sell long-term 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

A Duration Application for Banks An Immunized Portfolio 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

A Duration Application for Banks Banks may choose to target variables other than the market value of equity in managing interest rate risk Many banks are interested in stabilizing the book value of net interest income This can be done for a one-year time horizon, with the appropriate duration gap measure

A Duration Application for Banks DGAP* = MVRSA(1 − DRSA) − MVRSL(1 − DRSL) where MVRSA = cumulative market value of rate-sensitive assets (RSAs) MVRSL = cumulative market value of rate-sensitive liabilities (RSLs) DRSA = composite duration of RSAs for the given time horizon DRSL = composite duration of RSLs for the given time horizon

A Duration Application for Banks DGAP* > 0 Net interest income will decrease (increase) when interest rates decrease (increase) DGAP* < 0 Net interest income will decrease (increase) when interest rates increase (decrease) DGAP* = 0 Interest rate risk eliminated A major point is that duration analysis can be used to stabilize a number of different variables reflecting bank performance

Economic Value of Equity Sensitivity Analysis
Involves the comparison of changes in the Economic Value of Equity (EVE) across different interest rate environments 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

Estimating the timing of cash flows and subsequent durations of assets and liabilities is complicated by: Prepayments that exceed (fall short of) those expected A bond being A deposit that is withdrawn early or a deposit that is not withdrawn as expected

EVE Sensitivity Analysis: An Example First Savings Bank Average duration of assets equals 2.6 years Market value of assets equals $1,001,963,000 Average duration of liabilities equals 2 years Market value of liabilities equals $919,400,000

EVE Sensitivity Analysis: An Example First Savings Bank Duration Gap 2.6 – ($919,400,000/$1,001,963,000) × 2.0 = years Example: A 1% increase in rates would reduce EVE by $7.2 million ΔMVE = -DGAP[Δy/(1+y)]MVA ΔMVE = (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

EVE Sensitivity Analysis: An Example

EVE Sensitivity Analysis: An Example First Savings Bank 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

EVE Sensitivity Analysis: An Example First Savings Bank 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

Earnings Sensitivity Analysis versus EVE Sensitivity Analysis
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 Duration analysis takes a longer term view than static gap analysis

Earnings Sensitivity Analysis versus EVE Sensitivity Analysis
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

A Critique of Strategies for Managing Earnings and EVE Sensitivity
GAP and DGAP Management Strategies 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 changing GAP and DGAP

Interest Rate Risk: An Example Consider the case where a bank has two alternatives for funding $1,000 for two years A 2-year security yielding 6 percent Two consecutive 1-year securities, with the current 1-year yield equal to 5.5 percent It is not known today what a 1-year security will yield in one year

Interest Rate Risk: An Example Consider the case where a bank has two alternative for funding $1,000 for two years

Interest Rate Risk: An Example Consider the case where a bank has two alternative for funding $1,000 for two years 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 of : 6% + 6% = 5.5% + x so x must = 6.5%

Interest Rate Risk: An Example Consider the case where a bank has two alternative for investing $1,000 for two years 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% By choosing one or the other, the depositor and the bank “place a bet” that the actual rate in one year will differ from the forward rate of 6.5 percent

Yield Curve Strategies
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 rates to fall and the yield curve to return to its “normal” shape.

Yield Curve Strategies
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 Follow strategies to become more liability sensitive and/or lengthen the duration of assets versus the duration of liabilities

Chapter 8 Managing Interest Rate Risk: Economic Value of Equity

Managing Interest Rate Risk: Economic Value of Equity

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Managing Interest Rate Risk: Economic Value of Equity

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