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# 请老师解答一下这个问题看了答案都不明白

 A portfolio manager invests \$100 million in a 5-year inverse floater paying 18%-2*LIBOR. The modified duration of a 6% 5-year bond is 4.5 year. What is the 95% VaR of the inverse floater if the yield volatility is 0.66%? a) \$3.0M b) \$5.9M c) \$8.9M d) cannot be determined 答案是： 18%-2L=3*6%-2L 18%-2L+2L=3*6% D=3*4.5=13.5 VAR=13.5*100*0.66%=8.91 不懂中间为什么可以两边+2L

 本帖最后由 cashking 于 2015-6-3 09:05 编辑 该答案是乱写。我认为正确解答应当是这样： the cash flow of the inverse floater can be replicated by a portfolio that: 1, longs 300 million 5-year fixed-rate bond, coupon rate 6%; 2, shorts 200 million 5-year floating-rate bond, coupon rate equals libor. It is simple to show that the net interst cash flow of the portfolio is 300m*6%-200m*libor=100m*(18%-2*libor), which equals the coupon of the inverse floater, and the priciple cash flow of the portfolio is 300m-200m=100m, which equals the principle of the inverse floater. Therefore, the inverse floater's duration shall equal the portfolio duration, which is the weighted average of the component durations: D=4.5*(300/(300-200))+0*(-200/(300-200))=4.5*3+0*(-2)=13.5 By linear approximation, the 95% VaR of the inverse floater is 1.65*0.66%*13.5*100m=14.7m
 本帖最后由 cashking 于 2015-6-3 09:05 编辑 该答案是乱写。我认为正确解答应当是这样： the cash flow of the inverse floater can be replicated by a portfolio that: 1, longs 300 million 5-year fixed-rate bond, coupon rate 6%; 2, shorts 200 million 5-year floating-rate bond, coupon rate equals libor. It is simple to show that the net interst cash flow of the portfolio is 300m*6%-200m*libor=100m*(18%-2*libor), which equals the coupon of the inverse floater, and the priciple cash flow of the portfolio is 300m-200m=100m, which equals the principle of the inverse floater. Therefore, the inverse floater's duration shall equal the portfolio duration, which is the weighted average of the component durations: D=4.5*(300/(300-200))+0*(-200/(300-200))=4.5*3+0*(-2)=13.5 By linear approximation, the 95% VaR of the inverse floater is 1.65*0.66%*13.5*100m=14.7m

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