《金融风险管理》课程PPT教学课件（Risk Management and Financial Institutions）Chapter 08 Interest Rate Risk

InterestRateRiskChapter 8RiskManagementandFinanciallnstitutions,3e,Chapter8,CopyrightJohnC.Hull2012

Interest Rate Risk Chapter 8 Risk Management and Financial Institutions, 3e, Chapter 8, Copyright © John C. Hull 2012 1

ManagementofNetInterestIncome(Table 8.1, page 159)Suppose that the market's best guess is that futureshort term rates will equal today's ratesWhat would happen if a bank posted the followingrates?Maturity (yrs)Deposit RateMortgageRate13%6%53%6%How can the bank manage its risks?2RiskManagementandFinancial Institutions,3e,Chapter8,CopyrightJohnC.Hull2012

Management of Net Interest Income (Table 8.1, page 159) ⚫ Suppose that the market’s best guess is that future short term rates will equal today’s rates ⚫ What would happen if a bank posted the following rates? ⚫ How can the bank manage its risks? Maturity (yrs) Deposit Rate Mortgage Rate 1 3% 6% 5 3% 6% Risk Management and Financial Institutions, 3e, Chapter 8, Copyright © John C. Hull 2012 2

Management of NetInterestIncomeMost banks have asset-liabilitymanagement groups to manage interestrate risk When long term loans are funded withshort term deposits interest rate swapscan be used to hedge the interest rate risk But this does not hedge the liquidity riskRiskManagementandFinancialInstitutions,3e,Chapter8,CopyrightJohnC.Hull20123

Management of Net Interest Income ⚫ Most banks have asset-liability management groups to manage interest rate risk ⚫ When long term loans are funded with short term deposits interest rate swaps can be used to hedge the interest rate risk ⚫ But this does not hedge the liquidity risk Risk Management and Financial Institutions, 3e, Chapter 8, Copyright © John C. Hull 2012 3

LIBORRates and Swap Rates LIBOR rates are 1-, 3-, 6-, and 12-monthborrowing rates for companies that have aAA-ratingSwap Rates are the fixed rates exchangedfor floating in an interest rate swapagreementRiskManagementandFinancialInstitutions,3e,Chapter8,CopyrightJohnC.Hull20124

LIBOR Rates and Swap Rates ⚫ LIBOR rates are 1-, 3-, 6-, and 12-month borrowing rates for companies that have a AA-rating ⚫ Swap Rates are the fixed rates exchanged for floating in an interest rate swap agreement Risk Management and Financial Institutions, 3e, Chapter 8, Copyright © John C. Hull 2012 4

Understanding Swap RatesA bank canLend to a series AA-rated borrowers for tensuccessive six month periodsSwap the LiBOR interest received for thefive-year swap rateThis shows that the swap rate has thecredit risk corresponding to a series ofshort-term loans to AA-rated borrowersRiskManagementandFinancialInstitutions,3e,Chapter8,CopyrightJohnC.Hull20125

Understanding Swap Rates ⚫ A bank can ⚫ Lend to a series AA-rated borrowers for ten successive six month periods ⚫ Swap the LIBOR interest received for the five-year swap rate ⚫ This shows that the swap rate has the credit risk corresponding to a series of short-term loans to AA-rated borrowers Risk Management and Financial Institutions, 3e, Chapter 8, Copyright © John C. Hull 2012 5

ExtendingtheLIBORCurveAlternative 1: Create a term structure of interest ratesshowing the rate of interest at which a AA-ratedcompany can borrow for 1, 2, 3 ... yearsAlternative 2: Use swap rates so that the termstructure represents future short term AA borrowingratesAlternative 2 is the usual approach. It creates theLIBOR/swap term structure of interest ratesRiskManagementandFinancialInstitutions,3e,Chapter8,CopyrightJohnC.Hull20126

Extending the LIBOR Curve ⚫ Alternative 1: Create a term structure of interest rates showing the rate of interest at which a AA-rated company can borrow for 1, 2, 3 . years ⚫ Alternative 2: Use swap rates so that the term structure represents future short term AA borrowing rates ⚫ Alternative 2 is the usual approach. It creates the LIBOR/swap term structure of interest rates Risk Management and Financial Institutions, 3e, Chapter 8, Copyright © John C. Hull 2012 6

Risk-FreeRate Traders has traditionally assumed that theLIBOR/swapzero curveis the risk-freezero curveThe Treasury curve is about 50 basispoints below the LIBOR/swap zero curveTreasury rates are considered to beartificially low for a variety of regulatoryandtaxreasonsRiskManagementandFinancialInstitutions,3e,Chapter8,CopyrightJohnC.Hull20127

Risk-Free Rate ⚫ Traders has traditionally assumed that the LIBOR/swap zero curve is the risk-free zero curve ⚫ The Treasury curve is about 50 basis points below the LIBOR/swap zero curve ⚫ Treasury rates are considered to be artificially low for a variety of regulatory and tax reasons Risk Management and Financial Institutions, 3e, Chapter 8, Copyright © John C. Hull 2012 7

OIS RateLIBOR/swap rates were clearly not “risk-free'during the crisisAs a result there has been a trend toward usingovernight indexed swap (OiS) rates as proxiesfor the risk-free rate instead of LIBOR and swapratesThe OiS rate is the rate swapped for thegeometric average of overnight borrowing rates(ln the U.S. the relevant overnight rate is the fedfunds rate)RiskManagementandFinancialInstitutions,3e,Chapter8,CopyrightJohnC.Hull20128

OIS Rate ⚫ LIBOR/swap rates were clearly not “risk-free” during the crisis ⚫ As a result there has been a trend toward using overnight indexed swap (OIS) rates as proxies for the risk-free rate instead of LIBOR and swap rates ⚫ The OIS rate is the rate swapped for the geometric average of overnight borrowing rates. (In the U.S. the relevant overnight rate is the fed funds rate) Risk Management and Financial Institutions, 3e, Chapter 8, Copyright © John C. Hull 2012 8

Duration (page164)Duration of a bond that provides cash flow c, at time t, isnVttBi=1where Bis itsprice and yis itsyield (continuouslycompounded)This leads to△B-D△YB9RiskManagementandFinancialInstitutions,3e,Chapter8,CopyrightJohnC.Hull2012

Duration (page 164) ⚫ Duration of a bond that provides cash flow ci at time t i is where B is its price and y is its yield (continuously compounded) ⚫ This leads to Risk Management and Financial Institutions, 3e, Chapter 8, Copyright © John C. Hull 2012 9         − =  B c e t yti i n i i 1 D y B B = −  

Calculation ofDuration for a3-year bondpayingacoupon10%.Bondyield=12%.(Table8.3,page166)PV ($)Time (yrs)CashFlowWeightTime X($)Weight50.54.7090.0500.02551.04.4350.0470.04751.54.1760.0440.06652.03.9330.0420.08352.53.7040.0390.0983.010573.2560.7782.333Total1301.00094.2132.65310RiskManagementandFinancialInstitutions,3e,Chapter8,CopyrightJohnC.Hull2012

Calculation of Duration for a 3-year bond paying a coupon 10%. Bond yield=12%. (Table 8.3, page 166) Risk Management and Financial Institutions, 3e, Chapter 8, Copyright © John C. Hull 2012 10 Time (yrs) Cash Flow ($) PV ($) Weight Time × Weight 0.5 5 4.709 0.050 0.025 1.0 5 4.435 0.047 0.047 1.5 5 4.176 0.044 0.066 2.0 5 3.933 0.042 0.083 2.5 5 3.704 0.039 0.098 3.0 105 73.256 0.778 2.333 Total 130 94.213 1.000 2.653