Bank Management, 6th edition. Timothy W. Koch and S. Scott MacDonald Copyright 2006 by South-Western, a division of Thomson Learning
|
|
- Easter Hunter
- 7 years ago
- Views:
Transcription
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. 1
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 2 equity.
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. 3
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 $1, $100 4
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 5
6 Duration versus Maturity Duration is an approximate measure of the price elasticity of demand Price Elasticity of Demand - % Change in Quantity Demanded % Change in Price 6
7 Duration versus Maturity The longer the duration, the larger the change in price for a given change in interest rates. Duration P - P P i (1 i) i - Duration P (1 i) 7
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 D = k t=1 k t=1 CF(t) t t (1+ r) CFt t (1+ r) n t=1 Price of CF(t) t t (1+ r) the Security 8
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 $ (1.12) D (1.12) 100 t (1.12) t= (1.12) (1.12) 1, (1.12) 2, = 2.73 years 9
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, D 100 *1 1 (1.05) * * (1.05) (1.05) ,000 * 3 3 (1.05) 3, , = 2.75 years 10
11 D 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 $ *1 1 (1.20) 100 * * (1.20) (1.20) ,000 * (1.20) 2, = 2.68 years 11
12 Measuring Duration Example What is the duration of a zero coupon bond with a $1,000 face value, 3 years to maturity but the YTM is 12%? D 1,000 * 3 3 (1.12) 1,000 3 (1.12) 2, = 3 years By definition, the duration of a zero coupon bond is equal to its maturity 12
13 Duration and Modified Duration The greater the duration, the greater the price sensitivity Modified Duration gives an estimate of price volatility: Modified Duration Macaulay' s Duration (1 i) P P - Modified Duration i 13
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. 14
15 Effective Duration Pi- - Pi Effective Duration - P (i - i 0 ) Where: P i- = Price if rates fall P i+ = Price if rates rise P 0 = Initial (current) price i + = Initial market rate plus the increase in rate i - = Initial market rate minus the decrease in rate 15
16 Effective Duration Example Consider a 3-year, 9.4 percent semiannual 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. 16
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 17
18 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 $10,000 - $9, Effective Duration $10,000( ) 18
19 Duration GAP Duration GAP Model Focuses on 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 19
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. 20
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 21
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 22
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 23
24 Reinvestment Rate Risk and Price Risk Reinvestment Rate Risk If interest 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). 24
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. 25
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. 26
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 offbalance sheet items. These estimates are used to calculate duration gap. Forecasts changes in the market value of stockholders equity across different interest rate environments. 27
28 Weighted Average Duration of Bank Assets Weighted Average Duration of Bank Assets (DA) DA Where n i w i Da i w i = Market value of asset i divided by the market value of all bank assets Da i = Macaulay s duration of asset i n = number of different bank assets 28
29 Weighted Average Duration of Bank Liabilities Weighted Average Duration of Bank Liabilities (DL) DL Where m j z j Dl j z j = Market value of liability j divided by the market value of all bank liabilities Dl j = Macaulay s duration of liability j m = number of different bank liabilities 29
30 Duration GAP and Economic Value of Equity Let MVA and MVL equal the market values of assets and liabilities, respectively. If: and Duration GAP DGAP DA - Then: ΔEVE ΔEVE ΔMVA ΔMVL (MVL/MVA)DL y - DGAP MVA (1 y) where y = the general level of interest rates 30
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: ΔEVE y - DGAP MVA (1 y) 31
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 $ % % $ yr Treasury bond $ % % $ Total Earning Assets $ % $ Non-cash earning (1.12) assets $ (1.12) - (1.12) (1.12) $ - Total assetsd $ 1, % $ 1, Liabilities Interest bearing liabs. 1-yr Time deposit $ % % $ yr Certificate of deposit $ % % $ Tot. Int Bearing Liabs. $ % $ 920 Tot. non-int. bearing $ - $ - Total liabilities $ % $ Total equity $ 80 $ 80 Total liabs & equity $ 1,000 $ 1,000 32
33 Calculating DGAP DA DL ($700/$1000)* ($200/$1000)*4.99 = 2.88 ($620/$920)* ($300/$920)*2.81 = 1.59 DGAP (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. 33
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 $ % % $ yr Treasury bond $ % % $ Total Earning Assets $ % $ Non-cash earning assets PV$ - $ - 3 Total assets $ 1,000 t 1 t 10.88% $ Liabilities Interest bearing liabs. 1-yr Time deposit $ % % $ yr Certificate of deposit $ % % $ Tot. Int Bearing Liabs. $ % $ 906 Tot. non-int. bearing $ - $ - Total liabilities $ % $ Total equity $ 80 $ 68 Total liabs & equity $ 1,000 $
35 Calculating DGAP DA DA ($683/$974)* ($191/$974)*4.97 = 2.86 ($614/$906)* ($292/$906)*2.80 = 1.58 DGAP ($906/$974) * 1.58 = 1.36 years What does 1.36 mean? The average duration of assets is greater than the average duration of liabilities, thus asset values change by more than liability values. 35
36 Change in the Market Value of Equity ΔEVE y - DGAP[ ]MVA (1 y) In this case: ΔEVE [ ]$ 1000, $
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). 37
38 DGAP Summary DGAP Summary Change in DGAP Interest Rates Assets Liabilities Equity 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 38
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 39
40 Immunized Portfolio 1 Par Years Market $1,000 % Coup Mat. YTM Value Dur. Assets Cash $ 100 $ 100 Earning assets 3-yr Commercial loan $ % % $ yr Treasury bond $ % % $ Total Earning Assets $ % $ 900 Non-cash earning asset $ - $ - Total assets $ 1, % $ 1, Liabilities Interest bearing liabs. 1-yr Time deposit $ % % $ yr Certificate of depos $ % % $ yr Zero-coupon CD* $ % % $ Tot. Int Bearing Liabs. $ 1, % $ 920 Tot. non-int. bearing $ - $ - Total liabilities $ 1, % $ Total equity $ 80 $ 80 DGAP = (3.11) 0 40
41 Immunized Portfolio with a 1% increase in rates 1 Par Years Market $1,000 % Coup Mat. YTM Value Dur. Assets Cash $ $ Earning assets 3-yr Commercial loan $ % % $ yr Treasury bond $ % % $ Total Earning Assets $ % $ Non-cash earning asset $ - $ - Total assets $ 1, % $ Liabilities Interest bearing liabs. 1-yr Time deposit $ % % $ yr Certificate of depos $ % % $ yr Zero-coupon CD* $ % % $ Tot. Int Bearing Liabs. $ 1, % $ Tot. non-int. bearing $ - $ - Total liabilities $ 1, % $ Total equity $ 80.0 $ 80.5
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. 42
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. 43
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. 44
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 45
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. 46
47 Assets First Savings Bank Economic Value of Equity Market Value/Duration Report as of 12/31/04 Most Likely Rate Scenario-Base Strategy Book Value Market Value Book Yield Duration* Loans Prime Based Ln $ 100,000 $ 102, % Equity Credit Lines $ 25,000 $ 25, % - Fixed Rate > I yr $ 170,000 $ 170, % 1.1 Var Rate Mtg 1 Yr $ 55,000 $ 54, % Year Mortgage $ 250,000 $ 245, % 6.0 Consumer Ln $ 100,000 $ 100, % 1.9 Credit Card $ 25,000 $ 25, % 1.0 Total Loans $ 725,000 $ 723, % 2.6 Loan Loss Reserve $ (15,000) $ 11, % 8.0 Net Loans $ 710,000 $ 712, % 2.5 Investments Eurodollars $ 80,000 $ 80, % 0.1 CMO Fix Rate $ 35,000 $ 34, % 2.0 US Treasury $ 75,000 $ 74, % 1.8 Total Investments $ 190,000 $ 189, % 1.1 Fed Funds Sold $ 25,000 $ 25, % - Cash & Due From $ 15,000 $ 15, % 6.5 Non-int Rel Assets $ 60,000 $ 60, % Total Assets $ 100,000 $ 100, % 2.6
48 Liabilities First Savings Bank Economic Value of Equity Market Value/Duration Report as of 12/31/04 Most Likely Rate Scenario-Base Strategy Book Value Market Value Book Yield Duration* Deposits MMDA $ 240,000 $ 232, % - Retail CDs $ 400,000 $ 400, % 1.1 Savings $ 35,000 $ 33, % 1.9 NOW $ 40,000 $ 38, % 1.9 DDA Personal $ 55,000 $ 52, Comm'l DDA $ 60,000 $ 58, Total Deposits $ 830,000 $ 815, TT&L $ 25,000 $ 25, % - L-T Notes Fixed $ 50,000 $ 50, % 5.9 Fed Funds Purch % - NIR Liabilities $ 30,000 $ 28, Total Liabilities $ 935,000 $ 919, Equity $ 65,000 $ 82, Total Liab & Equity $ 1,000,000 $ 1,001, Off Balance Sheet Notional lnt Rate Swaps - $ 1, % ,000 Adjusted Equity $ 65,000 $ 83,
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 49
50 Duration Gap for First Savings Bank EVE Duration Gap = 2.6 ($919,400/$1,001,963)*2.0 = years Example: A 1% increase in rates would reduce EVE by $7.2 million = (0.01 / ) * $1,001,963 Recall that the average rate on assets is 6.93% 50
51 Sensitivity of EVE versus Most Likely (Zero Shock) Interest Rate Scenario Change in EVE (millions of dollars) (10.0) (20.0) (30.0) (40.0) ALCO Guideline Board Limit (8.2) (20.4) (36.6) 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 51 in the market value of liabilities.
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 52
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. 53
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 Duration analysis takes a longer term view than static gap analysis 54
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 55 Duration measures are highly subjective
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 56
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 Two-Year Security One-Year Security & then another One-Year Security $60 $ $55? 57
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% 58
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% 59
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. 60
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 61
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. P e a k t ) n e r c e ( P s t e a C o n t r a c t i o n R t E x p a n s i o n s r e In contractionary t e I n they reach a trough stages rates fall until In expansionary S h o r t - T e r m R a t e s stages rates rise until they reach a peak as the Federal Reserve L o n g - T e r m R a t e s tightens credit availability. T i m e E x p a n s i o n T r o u g h The inverted yield curve has predicted the last five recessions DATE WHEN 1-YEAR RATE FIRST EXCEEDS 10-YEAR RATE LENGTH OF TIME UNTIL START OF NEXT RECESSION Apr months (Dec. 69) Mar months (Nov. 73) Sept months (Jan. 80) Sept months (July 81) Feb months (July 90) Dec months (March 01) when the U.S. economy falls into recession. 62
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. 63
Chapter Nine Selected Solutions
Chapter Nine Selected Solutions 1. What is the difference between book value accounting and market value accounting? How do interest rate changes affect the value of bank assets and liabilities under the
More informationASSET LIABILITY MANAGEMENT Significance and Basic Methods. Dr Philip Symes. Philip Symes, 2006
1 ASSET LIABILITY MANAGEMENT Significance and Basic Methods Dr Philip Symes Introduction 2 Asset liability management (ALM) is the management of financial assets by a company to make returns. ALM is necessary
More informationDuration Gap Analysis
appendix 1 to chapter 9 Duration Gap Analysis An alternative method for measuring interest-rate risk, called duration gap analysis, examines the sensitivity of the market value of the financial institution
More informationCHAPTER 16: MANAGING BOND PORTFOLIOS
CHAPTER 16: MANAGING BOND PORTFOLIOS PROBLEM SETS 1. While it is true that short-term rates are more volatile than long-term rates, the longer duration of the longer-term bonds makes their prices and their
More informationReview for Exam 1. Instructions: Please read carefully
Review for Exam 1 Instructions: Please read carefully The exam will have 20 multiple choice questions and 5 work problems. Questions in the multiple choice section will be either concept or calculation
More informationTrading the Yield Curve. Copyright 1999-2006 Investment Analytics
Trading the Yield Curve Copyright 1999-2006 Investment Analytics 1 Trading the Yield Curve Repos Riding the Curve Yield Spread Trades Coupon Rolls Yield Curve Steepeners & Flatteners Butterfly Trading
More informationI. Readings and Suggested Practice Problems. II. Risks Associated with Default-Free Bonds
Prof. Alex Shapiro Lecture Notes 13 Bond Portfolio Management I. Readings and Suggested Practice Problems II. Risks Associated with Default-Free Bonds III. Duration: Details and Examples IV. Immunization
More informationVALUATION OF DEBT CONTRACTS AND THEIR PRICE VOLATILITY CHARACTERISTICS QUESTIONS See answers below
VALUATION OF DEBT CONTRACTS AND THEIR PRICE VOLATILITY CHARACTERISTICS QUESTIONS See answers below 1. Determine the value of the following risk-free debt instrument, which promises to make the respective
More informationFixed Income Portfolio Management. Interest rate sensitivity, duration, and convexity
Fixed Income ortfolio Management Interest rate sensitivity, duration, and convexity assive bond portfolio management Active bond portfolio management Interest rate swaps 1 Interest rate sensitivity, duration,
More informationCHAPTER 6 ASSET-LIABILITY MANAGEMENT: DETERMINING AND MEASURING INTEREST RATES AND CONTROLLING INTEREST-SENSITIVE AND DURATION GAPS
CHAPTER 6 ASSET-LIABILITY MANAGEMENT: DETERMINING AND MEASURING INTEREST RATES AND CONTROLLING INTEREST-SENSITIVE AND DURATION GAPS Goals of This Chapter: The purpose of this chapter is to explore the
More informationInterest Rate Risk in The Banking Book (IRRBB) JOHN N.CHALOUHI Chief Risk Officer, FNB group
Interest Rate Risk in The Banking Book (IRRBB) JOHN N.CHALOUHI Chief Risk Officer, FNB group Table of Contents I. Interest Rate Risk in the Banking Book 1. Overview 2. Banking Book v/s Trading Book 3.
More informationChapter 12 Practice Problems
Chapter 12 Practice Problems 1. Bankers hold more liquid assets than most business firms. Why? The liabilities of business firms (money owed to others) is very rarely callable (meaning that it is required
More information2. Determine the appropriate discount rate based on the risk of the security
Fixed Income Instruments III Intro to the Valuation of Debt Securities LOS 64.a Explain the steps in the bond valuation process 1. Estimate the cash flows coupons and return of principal 2. Determine the
More informationInterest rate Derivatives
Interest rate Derivatives There is a wide variety of interest rate options available. The most widely offered are interest rate caps and floors. Increasingly we also see swaptions offered. This note will
More informationSSI 1 - INTRODUCTION TO CREDIT UNION FINANCIAL MANAGEMENT
Sponsored by Catalyst Corporate FCU 1 Sponsored by Catalyst Corporate FCU SSI 1 - INTRODUCTION TO CREDIT UNION FINANCIAL MANAGEMENT Reviews the basic financial components and variables that impact credit
More information1.2 Structured notes
1.2 Structured notes Structured notes are financial products that appear to be fixed income instruments, but contain embedded options and do not necessarily reflect the risk of the issuing credit. Used
More informationAlliance Consulting BOND YIELDS & DURATION ANALYSIS. Bond Yields & Duration Analysis Page 1
BOND YIELDS & DURATION ANALYSIS Bond Yields & Duration Analysis Page 1 COMPUTING BOND YIELDS Sources of returns on bond investments The returns from investment in bonds come from the following: 1. Periodic
More informationCanadian Life Insurance Company Asset/Liability Management Summary Report as at: 31-Jan-08 interest rates as of: 29-Feb-08 Run: 2-Apr-08 20:07 Book
Canadian Life Insurance Company Asset/Liability Management Summary Report as at: 31Jan08 interest rates as of: 29Feb08 Run: 2Apr08 20:07 Book Book Present Modified Effective Projected change in net present
More informationLiquidity Measurement and Management
Liquidity Measurement and Management by: George K. Darling Chief Executive Officer Introduction An important area of balance sheet management that does not receive enough attention in many banks is the
More informationYIELD CURVE GENERATION
1 YIELD CURVE GENERATION Dr Philip Symes Agenda 2 I. INTRODUCTION II. YIELD CURVES III. TYPES OF YIELD CURVES IV. USES OF YIELD CURVES V. YIELD TO MATURITY VI. BOND PRICING & VALUATION Introduction 3 A
More informationManaging the Investment Portfolio
Managing the Investment Portfolio GSBC Executive Development Institute April 26, 2015 Portfolio Purpose & Objectives Tale of Two Balance Sheets o Components of Core Balance Sheet Originated loans Retail
More informationMoney Market and Debt Instruments
Prof. Alex Shapiro Lecture Notes 3 Money Market and Debt Instruments I. Readings and Suggested Practice Problems II. Bid and Ask III. Money Market IV. Long Term Credit Markets V. Additional Readings Buzz
More informationFIN 683 Financial Institutions Management Interest-Rate Risk
FIN 683 Financial Institutions Management Interest-Rate Risk Professor Robert B.H. Hauswald Kogod School of Business, AU Interest Rate Risk FIs (financial institutions or intermediaries) face two core
More informationDuration and convexity
Duration and convexity Prepared by Pamela Peterson Drake, Ph.D., CFA Contents 1. Overview... 1 A. Calculating the yield on a bond... 4 B. The yield curve... 6 C. Option-like features... 8 D. Bond ratings...
More informationPractice Questions for Midterm II
Finance 333 Investments Practice Questions for Midterm II Winter 2004 Professor Yan 1. The market portfolio has a beta of a. 0. *b. 1. c. -1. d. 0.5. By definition, the beta of the market portfolio is
More informationInterest Rate Swaps. Key Concepts and Buzzwords. Readings Tuckman, Chapter 18. Swaps Swap Spreads Credit Risk of Swaps Uses of Swaps
Interest Rate Swaps Key Concepts and Buzzwords Swaps Swap Spreads Credit Risk of Swaps Uses of Swaps Readings Tuckman, Chapter 18. Counterparty, Notional amount, Plain vanilla swap, Swap rate Interest
More informationProblems and Solutions
Problems and Solutions CHAPTER Problems. Problems on onds Exercise. On /04/0, consider a fixed-coupon bond whose features are the following: face value: $,000 coupon rate: 8% coupon frequency: semiannual
More informationInvestments Analysis
Investments Analysis Last 2 Lectures: Fixed Income Securities Bond Prices and Yields Term Structure of Interest Rates This Lecture (#7): Fixed Income Securities Term Structure of Interest Rates Interest
More informationFinancial-Institutions Management. Solutions 1. 6. A financial institution has the following market value balance sheet structure:
FIN 683 Professor Robert Hauswald Financial-Institutions Management Kogod School of Business, AU Solutions 1 Chapter 7: Bank Risks - Interest Rate Risks 6. A financial institution has the following market
More informationOptions on 10-Year U.S. Treasury Note & Euro Bund Futures in Fixed Income Portfolio Analysis
White Paper Whitepaper Options on 10-Year U.S. Treasury Note & Euro Bund Futures in Fixed Income Portfolio Analysis Copyright 2015 FactSet Research Systems Inc. All rights reserved. Options on 10-Year
More informationReview for Exam 1. Instructions: Please read carefully
Review for Exam 1 Instructions: Please read carefully The exam will have 25 multiple choice questions and 5 work problems covering chapter 1, 2, 3, 4, 14, 16. Questions in the multiple choice section will
More informationFloating-Rate Securities
Floating-Rate Securities A floating-rate security, or floater, is a debt security whose coupon rate is reset at designated dates and is based on the value of a designated reference rate. - Handbook of
More informationFixed Income 2015 Update. Kathy Jones, Senior Vice President Chief Fixed Income Strategist, Schwab Center for Financial Research
Fixed Income 2015 Update Kathy Jones, Senior Vice President Chief Fixed Income Strategist, Schwab Center for Financial Research 1 Fed: Slow and Low 2015 Fixed Income Outlook 2 Yield Curve Flattening 3
More informationAmerican Options and Callable Bonds
American Options and Callable Bonds American Options Valuing an American Call on a Coupon Bond Valuing a Callable Bond Concepts and Buzzwords Interest Rate Sensitivity of a Callable Bond exercise policy
More informationCHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES 1. Expectations hypothesis. The yields on long-term bonds are geometric averages of present and expected future short rates. An upward sloping curve is
More informationChapter. Bond Prices and Yields. McGraw-Hill/Irwin. Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter Bond Prices and Yields McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Bond Prices and Yields Our goal in this chapter is to understand the relationship
More informationBest Practices in Asset Liability Management
Best Practices in Asset Liability Management Frank Wilary Principal Wilary Winn LLC September 22, 2014 1 Topics Covered Best practices related to ALM modeling Best practices related to managing the ALM
More informationDistinguishing duration from convexity
Distinguishing duration from convexity Vanguard research May 010 Executive summary. For equity investors, the perception of risk is generally straightforward: Market risk the possibility that prices may
More informationPricing and Strategy for Muni BMA Swaps
J.P. Morgan Management Municipal Strategy Note BMA Basis Swaps: Can be used to trade the relative value of Libor against short maturity tax exempt bonds. Imply future tax rates and can be used to take
More informationActive Fixed Income: A Primer
Active Fixed Income: A Primer www.madisonadv.com Active Fixed Income: A Primer Most investors have a basic understanding of equity securities and may even spend a good deal of leisure time reading about
More informationInterest Rate and Credit Risk Derivatives
Interest Rate and Credit Risk Derivatives Interest Rate and Credit Risk Derivatives Peter Ritchken Kenneth Walter Haber Professor of Finance Weatherhead School of Management Case Western Reserve University
More informationBonds and the Term Structure of Interest Rates: Pricing, Yields, and (No) Arbitrage
Prof. Alex Shapiro Lecture Notes 12 Bonds and the Term Structure of Interest Rates: Pricing, Yields, and (No) Arbitrage I. Readings and Suggested Practice Problems II. Bonds Prices and Yields (Revisited)
More informationInterest Rate Futures. Chapter 6
Interest Rate Futures Chapter 6 1 Day Count Convention The day count convention defines: The period of time to which the interest rate applies. The period of time used to calculate accrued interest (relevant
More informationVALUATION OF FIXED INCOME SECURITIES. Presented By Sade Odunaiya Partner, Risk Management Alliance Consulting
VALUATION OF FIXED INCOME SECURITIES Presented By Sade Odunaiya Partner, Risk Management Alliance Consulting OUTLINE Introduction Valuation Principles Day Count Conventions Duration Covexity Exercises
More informationExamination II. Fixed income valuation and analysis. Economics
Examination II Fixed income valuation and analysis Economics Questions Foundation examination March 2008 FIRST PART: Multiple Choice Questions (48 points) Hereafter you must answer all 12 multiple choice
More informationStudy Questions for Actuarial Exam 2/FM By: Aaron Hardiek June 2010
P a g e 1 Study Questions for Actuarial Exam 2/FM By: Aaron Hardiek June 2010 P a g e 2 Background The purpose of my senior project is to prepare myself, as well as other students who may read my senior
More informationHow To Invest In Stocks And Bonds
Review for Exam 1 Instructions: Please read carefully The exam will have 21 multiple choice questions and 5 work problems. Questions in the multiple choice section will be either concept or calculation
More informationINTEREST RATE RISK IN THE BANKING BOOK
INTEREST RATE RISK IN THE BANKING BOOK FREQUENTLY ASKED QUESTIONS JANUARY 2015 PUBLISHED BY: European Banking Federation aisbl Avenue des Arts 56 B-1000 Brussels www.ebf-fbe.eu +32 (0)2 508 3711 info@ebf-fbe.eu
More informationChapter Two. Determinants of Interest Rates. McGraw-Hill /Irwin. Copyright 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter Two Determinants of Interest Rates Interest Rate Fundamentals Nominal interest rates - the interest rate actually observed in financial markets directly affect the value (price) of most securities
More informationReview Solutions FV = 4000*(1+.08/4) 5 = $4416.32
Review Solutions 1. Planning to use the money to finish your last year in school, you deposit $4,000 into a savings account with a quoted annual interest rate (APR) of 8% and quarterly compounding. Fifteen
More informationChapter 6. Commodity Forwards and Futures. Question 6.1. Question 6.2
Chapter 6 Commodity Forwards and Futures Question 6.1 The spot price of a widget is $70.00. With a continuously compounded annual risk-free rate of 5%, we can calculate the annualized lease rates according
More informationShares Mutual funds Structured bonds Bonds Cash money, deposits
FINANCIAL INSTRUMENTS AND RELATED RISKS This description of investment risks is intended for you. The professionals of AB bank Finasta have strived to understandably introduce you the main financial instruments
More informationLOCKING IN TREASURY RATES WITH TREASURY LOCKS
LOCKING IN TREASURY RATES WITH TREASURY LOCKS Interest-rate sensitive financial decisions often involve a waiting period before they can be implemen-ted. This delay exposes institutions to the risk that
More informationWhat are Swaps? Spring 2014. Stephen Sapp
What are Swaps? Spring 2014 Stephen Sapp Basic Idea of Swaps I have signed up for the Wine of the Month Club and you have signed up for the Beer of the Month Club. As winter approaches, I would like to
More informationCHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
Chapter - The Term Structure of Interest Rates CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future
More informationCIS September 2012 Exam Diet. Examination Paper 2.2: Corporate Finance Equity Valuation and Analysis Fixed Income Valuation and Analysis
CIS September 2012 Exam Diet Examination Paper 2.2: Corporate Finance Equity Valuation and Analysis Fixed Income Valuation and Analysis Corporate Finance (1 13) 1. Assume a firm issues N1 billion in debt
More informationCHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
CHAPTER : THE TERM STRUCTURE OF INTEREST RATES CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future
More informationAssumptions: No transaction cost, same rate for borrowing/lending, no default/counterparty risk
Derivatives Why? Allow easier methods to short sell a stock without a broker lending it. Facilitates hedging easily Allows the ability to take long/short position on less available commodities (Rice, Cotton,
More informationDirect Transfer. Investment Banking. Investment Banking. Basic Concepts. Economics of Money and Banking. Basic Concepts
Basic Concepts Economics of Money and Banking 2014 South Carolina Bankers School Ron Best University of West Georgia rbest@westga.edu Risk and return: investors will only take on additional risk if they
More informationThe International Certificate in Banking Risk and Regulation (ICBRR)
The International Certificate in Banking Risk and Regulation (ICBRR) The ICBRR fosters financial risk awareness through thought leadership. To develop best practices in financial Risk Management, the authors
More informationUS TREASURY SECURITIES - Issued by the U.S. Treasury Department and guaranteed by the full faith and credit of the United States Government.
Member NASD/SIPC Bond Basics TYPES OF ISSUERS There are essentially five entities that issue bonds: US TREASURY SECURITIES - Issued by the U.S. Treasury Department and guaranteed by the full faith and
More information1Q 2014 Stockholder Supplement. May 7, 2014
1Q 2014 Stockholder Supplement May 7, 2014 Safe Harbor Notice This presentation, other written or oral communications and our public documents to which we refer contain or incorporate by reference certain
More informationMANAGING INTEREST RATE RISK IN A FIXED INCOME PORTFOLIO
CALIFORNIA DEBT & INVESTMENT ADVISORY COMMISSION MANAGING INTEREST RATE RISK IN A FIXED INCOME PORTFOLIO SEPTEMBER 2008 CDIAC #08-11 INTRODUCTION California statute requires the governing body of local
More informationJanuary 1, Year 1 Equipment... 100,000 Note Payable... 100,000
Illustrations of Accounting for Derivatives Extension of Chapter 11 Web This reading illustrates the accounting for the interest rate swaps in Examples 13 and 14 in Chapter 11. Web problem DERIVATIVE 1
More informationFNCE 301, Financial Management H Guy Williams, 2006
REVIEW We ve used the DCF method to find present value. We also know shortcut methods to solve these problems such as perpetuity present value = C/r. These tools allow us to value any cash flow including
More informationUnderstanding Fixed Income
Understanding Fixed Income 2014 AMP Capital Investors Limited ABN 59 001 777 591 AFSL 232497 Understanding Fixed Income About fixed income at AMP Capital Our global presence helps us deliver outstanding
More informationCHAPTER 11 INTRODUCTION TO SECURITY VALUATION TRUE/FALSE QUESTIONS
1 CHAPTER 11 INTRODUCTION TO SECURITY VALUATION TRUE/FALSE QUESTIONS (f) 1 The three step valuation process consists of 1) analysis of alternative economies and markets, 2) analysis of alternative industries
More informationTopics in Chapter. Key features of bonds Bond valuation Measuring yield Assessing risk
Bond Valuation 1 Topics in Chapter Key features of bonds Bond valuation Measuring yield Assessing risk 2 Determinants of Intrinsic Value: The Cost of Debt Net operating profit after taxes Free cash flow
More informationClick Here to Buy the Tutorial
FIN 534 Week 4 Quiz 3 (Str) Click Here to Buy the Tutorial http://www.tutorialoutlet.com/fin-534/fin-534-week-4-quiz-3- str/ For more course tutorials visit www.tutorialoutlet.com Which of the following
More informationIntroduction to Risk, Return and the Historical Record
Introduction to Risk, Return and the Historical Record Rates of return Investors pay attention to the rate at which their fund have grown during the period The holding period returns (HDR) measure the
More informationSwaps: complex structures
Swaps: complex structures Complex swap structures refer to non-standard swaps whose coupons, notional, accrual and calendar used for coupon determination and payments are tailored made to serve client
More informationBond Valuation. What is a bond?
Lecture: III 1 What is a bond? Bond Valuation When a corporation wishes to borrow money from the public on a long-term basis, it usually does so by issuing or selling debt securities called bonds. A bond
More informationChapter 11. Bond Pricing - 1. Bond Valuation: Part I. Several Assumptions: To simplify the analysis, we make the following assumptions.
Bond Pricing - 1 Chapter 11 Several Assumptions: To simplify the analysis, we make the following assumptions. 1. The coupon payments are made every six months. 2. The next coupon payment for the bond is
More informationEurodollar Futures, and Forwards
5 Eurodollar Futures, and Forwards In this chapter we will learn about Eurodollar Deposits Eurodollar Futures Contracts, Hedging strategies using ED Futures, Forward Rate Agreements, Pricing FRAs. Hedging
More informationCHAPTER 7: FIXED-INCOME SECURITIES: PRICING AND TRADING
CHAPTER 7: FIXED-INCOME SECURITIES: PRICING AND TRADING Topic One: Bond Pricing Principles 1. Present Value. A. The present-value calculation is used to estimate how much an investor should pay for a bond;
More informationPhantom Income Thomas B. Lupo, Ph.D.
Phantom Income Thomas B. Lupo, Ph.D. A. Introduction 2 B. Illustration of Phantom Income 3 C. Phantom Income and the Yield Curve 4 1. Dynamic Yie ld 7 2. Economic Income 8 3. Phantom Income 9 D. Quantifying
More informationFinance 350: Problem Set 6 Alternative Solutions
Finance 350: Problem Set 6 Alternative Solutions Note: Where appropriate, the final answer for each problem is given in bold italics for those not interested in the discussion of the solution. I. Formulas
More informationThe Money Market and the Interest Rate. 2003 South-Western/Thomson Learning
The Money Market and the Interest Rate 2003 South-Western/Thomson Learning Individuals Demand for Money An individual s quantity of money demanded is the amount of wealth that the individual chooses to
More informationInvestment insight. Fixed income the what, when, where, why and how TABLE 1: DIFFERENT TYPES OF FIXED INCOME SECURITIES. What is fixed income?
Fixed income investments make up a large proportion of the investment universe and can form a significant part of a diversified portfolio but investors are often much less familiar with how fixed income
More information1. a. (iv) b. (ii) [6.75/(1.34) = 10.2] c. (i) Writing a call entails unlimited potential losses as the stock price rises.
1. Solutions to PS 1: 1. a. (iv) b. (ii) [6.75/(1.34) = 10.2] c. (i) Writing a call entails unlimited potential losses as the stock price rises. 7. The bill has a maturity of one-half year, and an annualized
More informationCHAPTER 14: BOND PRICES AND YIELDS
CHAPTER 14: BOND PRICES AND YIELDS PROBLEM SETS 1. The bond callable at 105 should sell at a lower price because the call provision is more valuable to the firm. Therefore, its yield to maturity should
More informationRate of Return. Reading: Veronesi, Chapter 7. Investment over a Holding Period
Rate of Return Reading: Veronesi, Chapter 7 Investment over a Holding Period Consider an investment in any asset over a holding period from time 0 to time T. Suppose the amount invested at time 0 is P
More informationEstimating Risk free Rates. Aswath Damodaran. Stern School of Business. 44 West Fourth Street. New York, NY 10012. Adamodar@stern.nyu.
Estimating Risk free Rates Aswath Damodaran Stern School of Business 44 West Fourth Street New York, NY 10012 Adamodar@stern.nyu.edu Estimating Risk free Rates Models of risk and return in finance start
More informationUnderstanding duration and convexity of fixed income securities. Vinod Kothari
Understanding duration and convexity of fixed income securities Vinod Kothari Notation y : yield p: price of the bond T: total maturity of the bond t: any given time during T C t : D m : Cashflow from
More informationChapter 5 Financial Forwards and Futures
Chapter 5 Financial Forwards and Futures Question 5.1. Four different ways to sell a share of stock that has a price S(0) at time 0. Question 5.2. Description Get Paid at Lose Ownership of Receive Payment
More informationAPPENDIX 3 TIME VALUE OF MONEY. Time Lines and Notation. The Intuitive Basis for Present Value
1 2 TIME VALUE OF MONEY APPENDIX 3 The simplest tools in finance are often the most powerful. Present value is a concept that is intuitively appealing, simple to compute, and has a wide range of applications.
More informationExit Strategies for Fixed Rate Financing. Comparing Yield Maintenance and Defeasance Alternatives. by Regan Campbell and Jehane Walsh
Defeasance Vs. Yield Maintenance Exit Strategies for Fixed Rate Financing Comparing Yield Maintenance and Defeasance Alternatives by Regan Campbell and Jehane Walsh When looking to refinance or sell a
More informationChapter 1 THE MONEY MARKET
Page 1 The information in this chapter was last updated in 1993. Since the money market evolves very rapidly, recent developments may have superseded some of the content of this chapter. Chapter 1 THE
More informationThe Bank Balance Sheet
Chapter 9 THE BANKING FIRM AND THE MANAGEMENT OF FINANCIAL INSTITUTIONS The Bank Balance Sheet T-account Analysis: Bank Operation Deposit of $100 cash into First National Bank Vault Cash + $100 Checkable
More informationHow To Calculate Bond Price And Yield To Maturity
CHAPTER 10 Bond Prices and Yields Interest rates go up and bond prices go down. But which bonds go up the most and which go up the least? Interest rates go down and bond prices go up. But which bonds go
More informationFin 5413 CHAPTER FOUR
Slide 1 Interest Due Slide 2 Fin 5413 CHAPTER FOUR FIXED RATE MORTGAGE LOANS Interest Due is the mirror image of interest earned In previous finance course you learned that interest earned is: Interest
More informationHow To Sell A Callable Bond
1.1 Callable bonds A callable bond is a fixed rate bond where the issuer has the right but not the obligation to repay the face value of the security at a pre-agreed value prior to the final original maturity
More informationChapter Review Problems
Chapter Review Problems State all stock and bond prices in dollars and cents. Unit 14.1 Stocks 1. When a corporation earns a profit, the board of directors is obligated by law to immediately distribute
More informationDerivatives Interest Rate Futures. Professor André Farber Solvay Brussels School of Economics and Management Université Libre de Bruxelles
Derivatives Interest Rate Futures Professor André Farber Solvay Brussels School of Economics and Management Université Libre de Bruxelles Interest Rate Derivatives Forward rate agreement (FRA): OTC contract
More informationCHAPTER 8 INTEREST RATES AND BOND VALUATION
CHAPTER 8 INTEREST RATES AND BOND VALUATION Solutions to Questions and Problems 1. The price of a pure discount (zero coupon) bond is the present value of the par value. Remember, even though there are
More informationIntroduction to Fixed Income (IFI) Course Syllabus
Introduction to Fixed Income (IFI) Course Syllabus 1. Fixed income markets 1.1 Understand the function of fixed income markets 1.2 Know the main fixed income market products: Loans Bonds Money market instruments
More information5.5 The Opportunity Cost of Capital
Problems 161 The correct discount rate for a cash flow is the expected return available in the market on other investments of comparable risk and term. If the interest on an investment is taxed at rate
More informationChapter 6 Interest rates and Bond Valuation. 2012 Pearson Prentice Hall. All rights reserved. 4-1
Chapter 6 Interest rates and Bond Valuation 2012 Pearson Prentice Hall. All rights reserved. 4-1 Interest Rates and Required Returns: Interest Rate Fundamentals The interest rate is usually applied to
More informationMath of Finance. Texas Association of Counties January 2014
Math of Finance Texas Association of Counties January 2014 Money Market Securities Sample Treasury Bill Quote*: N Bid Ask Ask Yld 126 4.86 4.85 5.00 *(Yields do not reflect current market conditions) Bank
More information