请老师解答一下这个问题看了答案都不明白

zrj1018

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

cashking

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

cashking

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