问一道题：NO.PZ2016082406000050 [ FRM II ]

Assume thyou have entereinto a fixefor-floating interest rate swthstarts toy anen in six years. Assume ththe ration of your position is proportionto the time to maturity. Also assume thall changes in the yielcurve are parallel shifts, anththe volatility of interest rates is proportionto the square root of time. When woulthe maximum potentiexposure reache In two months In two years In six years In four years anfive months ANSWER: B Exposure is a function of ration, whicreases with time, aninterest rate volatility, whiincreases with the square root of time. fine T the originmaturity ank a constant. This gives σ(Vt)=k(T−t)t\sigma{(V_t)}=k{(T-t)}\sqrt tσ(Vt​)=k(T−t)t ​. Taking the rivative with respeto t gives a maximum t=T3t=\frT3t=3T​. This gives t=63=2t=\frac63=2t=36​=2years. 这里不是说ration会随着时间增长而增加吗 那个1/3的结论不是说到期ration的效果减少吗，那是不是没有摊销效应