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Quiz I Practice

# Quiz I Practice - dollars worth of bond X and Bond Y should...

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Quiz I Practice 1) You own a bond that has an 8% yield to maturity and has a modified duration of 15 and a convexity 40. Approximately how much will this bond’s price change if it’s yield to maturity decreases to 7%? Answer: Recall that approximate percentage price change corrected for convexity is -(Modified Duration)*(yield change) + (VEX)*(yield change) 2 Plug in MD = 15 and VEX = 40 and a yield change of -.01 to get: -(Modified Duration)*(yield change) + (VEX)*(yield change) 2 = -(15)*(-.01) + (40)*(-.01) 2 = .15 + .004 = .154 or a 15.4% increase in price . 2) Bond A has a modified duration of 10 and a convexity of 50. Bond B has a Modified Duration of 20 and a convexity of 60. You have \$4million invested in bond A and \$6 million invested in bond B. There exist two government bonds. Bond X is a zero coupon bond with a modified duration of 8 and a convexity of 40. Bond Y is a zero coupon bond with a modified duration of 18 and a convexity of 60. How many

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Unformatted text preview: dollars worth of bond X and Bond Y should you sell short to immunize your portfolio from interest rate movements? Answer: What is the MD and VEX of your portfolio? Your portfolio is worth \$10 million and you have 40% invested in Bond A and 60% invested in Bond B. MD of portfolio = .4*10 + .6*20 = 16 VEX of portfolio = .4*50 + .6*60 = 56 Let Wx = percent of money to invest in Bond X and Wy = percent of money to invest in Bond Y. Find Wx and Wy such that the MD and VEX of your government portfolio is the same as the portfolio you wish to hedge. Wx*8 + Wy*18 = 16 Wx*40 + Wy*60 = 56 Solve these 2 equations and 2 unknowns for Wx = .2 Wy = .8 Thus, if you invested \$10 million in the government bond portfolio with \$2 million in Bond X and \$8 million in Bond Y you would have a portfolio with a MD = 16 and VEX =56. To immunize your portfolio you must therefore sell short \$2million worth of bond X and \$8 million worth of Bond Y....
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