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7 Interest Rate Risk

1 in order to use interest rate futures to hedge the

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Unformatted text preview: rporate; munis) Flat price = $ 1,231.38 1 = actual/actual (T- Bonds/Notes) Invoice price = $ 1,249.84 2 = actual/360 (T- Bills) Accrued interest = $ 18.46 3 = actual/365 4 = Euro 30/360 Settlement date Maturity date Annual coupon rate YTM Coupon payments/year Macaulay duration = Modified duration = BOND DURATION January 1, 2000 January 1, 2020 6.000% 4.000% 2 12.8758 12.6233 =date(yyyy,mm,dd) =date(yyyy,mm,dd) (decimal) (decimal) =duration(b33,b34,b35,b36,b37)) =mduration(b33,b34,b35,b36,b37)) Ec 174 INTEREST RATE RISK p. 16 of 17 PRACTICE PROBLEMS Problem 1 Table A shows the 15 NOV ’08 YTM on Treasury zeros (stripped coupon interest) with Table A – Treasury Zeros mid- November maturities out to 2012. Year T ry(T) ft A) Find implied forward rates ft. (Use continuous compounding.). 2009 1 0.0062 B) Suppose your company enters an FRA to lend $750,000 during 2010 at rk = f2010 from Table A. Find the gain or loss if r2010 = 1.5%? 2010 2 0.0083 2011 3 0.0098 Problem 2 A $1,000- par bond pays 7%/yr coupon interest semiannually and matures in T = 4.00 2012 4 0.0179 years. If YTM = 6%: A) Find the bond’s current price. (Use EXCEL spreadsheet) B) Compute the bond’s duration and modified duration. (Use EXCEL spreadsheet) C) What change in bond price do you expect if yields drop by 25 basis points to 5.75% tomorrow? Problem 3 Treasuries (Mar 9, 2009) It is March 9, 2009. RATE MATURITY PRICE YLD A) At what invoice price can you buy the November 2018 T- bond listed at right if 3.750 15 Nov ‘18 107:09 2.8825 M = $1,000 and interest is paid semiannually? B) How much interest will you receive per year? C) What is your annual rate of return if you hold the bond until maturity? Problem 4 It is January 30, 2009. You are managing a bond portfolio worth $6 million. The modified duration of this portfolio is Da* = 8.2 years. The September 2009 Treasury bond futures price F0 = 108- 15, and the cheapest- to- deliver bonds will have a modified duration Db* = 7.6 years. How should you hedge your portfolio value against interest rate risk over the next 6 months? Problem 5 Table B shows December 31, 2008, rates or yields for loans of varying Table B – LIBOR (12/31/08) maturities, appropriate for constructing a pure “LIBOR- Zeros” yield curve. A T (Year) ry(T) ft large, credit- worthy financial institution can both borrow and lend 1 (2009) 1.890% 1.890% (including issue and purchase zero- coupon bonds) at these rates. 2 (2010) 1.981% A) Use continuous compounding/discounting to find the missing yields 3 (2011) 2.170% 2.548% ry(T) and forward rates ft in Table B. 4 (2012) 2.922% You are a hedge fund risk manager and you know today that you will borrow $3.5 million for a one- year period from January to December 2012. You decide that the 2012 forward rate (2.922%/yr) is attractive. Show in 5 (2013) 2.545% detail two ways that you can lock in this rate for your future borrowing. B) One way to lock in this forward rate is by use of a Synthetic...
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