Interest Rate Risk Chapter 8 Risk Management and Financial Institutions 3e Chapter 8 Copyright John C Hull 2012 1 Management of Net Interest Income Table 8 1 page 159 lSuppose that the market s best guess is that future short term rates will equal today s rates lWhat would happen if a bank posted the following rates lHow can the bank manage its risks Maturity yrs Deposit RateMortgage Rate 13 6 53 6 Risk Management and Financial Institutions 3e Chapter 8 Copyright John C Hull 2012 2 Management of Net Interest Income lMost banks have asset liability management groups to manage interest rate risk lWhen long term loans are funded with short term deposits interest rate swaps can be used to hedge the interest rate risk lBut this does not hedge the liquidity risk Risk Management and Financial Institutions 3e Chapter 8 Copyright John C Hull 2012 3 LIBOR Rates and Swap Rates lLIBOR rates are 1 3 6 and 12 month borrowing rates for companies that have a AA rating lSwap 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 Rates lA bank can lLend to a series AA rated borrowers for ten successive six month periods lSwap the LIBOR interest received for the five year swap rate lThis 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 Extending the LIBOR Curve lAlternative 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 lAlternative 2 Use swap rates so that the term structure represents future short term AA borrowing rates lAlternative 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 Free Rate lTraders has traditionally assumed that the LIBOR swap zero curve is the risk free zero curve lThe Treasury curve is about 50 basis points below the LIBOR swap zero curve lTreasury 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 Rate lLIBOR swap rates were clearly not risk free during the crisis lAs 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 lThe 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 page 164 lDuration of a bond that provides cash flow ci at time ti is where B is its price and y is its yield continuously compounded lThis leads to Risk Management and Financial Institutions 3e Chapter 8 Copyright John C Hull 2012 9 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 WeightTime Weight 0 554 7090 0500 025 1 054 4350 0470 047 1 554 1760 0440 066 2 053 9330 0420 083 2 553 7040 0390 098 3 010573 2560 7782 333 Total13094 2131 0002 653 Duration Continued lWhen the yield y is expressed with compounding m times per year lThe expression is referred to as the modified duration Risk Management and Financial Institutions 3e Chapter 8 Copyright John C Hull 2012 11 Convexity Page 168 169 The convexity of a bond is defined as Risk Management and Financial Institutions 3e Chapter 8 Copyright John C Hull 2012 12 Portfolios lDuration and convexity can be defined similarly for portfolios of bonds and other interest rate dependent securities lThe duration of a portfolio is the weighted average of the durations of the components of the portfolio Similarly for convexity Risk Management and Financial Institutions 3e Chapter 8 Copyright John C Hull 2012 13 What Duration and Convexity Measure lDuration measures the effect of a small parallel shift in the yield curve lDuration plus convexity measure the effect of a larger parallel shift in the yield curve lHowever they do not measure the effect of non parallel shifts Risk Management and Financial Institutions 3e Chapter 8 Copyright John C Hull 2012 14 Other Measures lDollar Duration Product of the portfolio value and its duration lDollar Convexity Product of convexity and value of the portfolio Risk Management and Financial Institutions 3e Chapter 8 Copyright John C Hull 2012 15 Starting Zero Curve Figure 8 3 page 173 Risk Management and Financial Institutions 3e Chapter 8 Copyright John C Hull 2012 16 Parallel Shift Risk Management and Financial Institutions 3e Chapter 8 Copyright John C Hull 2012 17 Partial Duration lA partial duration calculates the effect on a por