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fdzh · 2023年10月23日

看不懂答案，麻烦解释一下

  1. FRM I
  2. Valuation And Risk Models

NO.PZ2023091701000090

问题如下：

A portfolio manager invests $100 million in a 5-year inverse floater paying 18% – 2 × LIBOR. Assume that the modified duration of a 6% 5-year bond is 4.5 years, and the inverse floater is just before a reset day. The worst change in yields at the 95% level over a month is 0.66%. What is the VaR of this inverse floater at the 95% level over a month?

选项：

A.$3.0 million B.$5.9 million C.$8.9 million D.$10.5 million

解释：

18% – 2 × L = 3 × 6% – 2 × L

(18% – 2 × L) + (2 × L) = 3 × 6%

DIF = 3 × D6% = 3 × 4.5 = 13.5

VARIF = D × P (worst change in yields) = 13.5 × 100million × 0.66% = 8.91million

如题

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1 个答案

DD仔_品职助教 · 2023年10月26日

嗨，爱思考的PZer你好：


同学你好，

计算inverse floater久期的思路是：一个普通的固定利息债券（题目给了是6%的coupon bond） = 一个libor浮动利息债券 + 一个libor反向浮动债券，

假设浮动利息债券的权重是w1, 反向浮动利息债券的权重是w2：

  1. w1 + w2 = 1，
  2. 我们要让浮动利息和反向浮动利息加起来正好等于题目给你的6%的coupon, 所以w1 * (L+spread) + w2 * (18%-2L) = 6%，等式左边带有L这个浮动利息的项目必须消掉，这样才能等于右边的固定利息6%，所以w1 * L - 2*w2 * L=0, 所以w1 = 2w2，结合上面的等式，解出来w1=2/3, w2 = 1/3.
  3. 固定利息债券的久期=4.5， 所以4.5 = w1 * 浮动利息债券的久期 + w2 * 反向浮动利息债券的久期，题目还说“just before a reset day”，所以浮动利息债券的久期为0，所以4.5 = 0 + w2 * 反向浮动利息债券的久期，所以反向浮动利息债券的久期 = 3 * 4.5 = 13.5

最后inverse floater的VAR = D × P (worst change in yields) = 13.5 × 100million × 0.66% = 8.91million

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梦梦 · 2024年11月11日

“结合上面的等式，解出来w1=2/3, w2 = 1/3.”咋解出来？为啥直接就把spread当成0了？

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NO.PZ2023091701000090 问题如下 A portfolio manager invests $100 million in a 5-yearinverse floater paying 18% – 2 × LIBOR. Assume ththe mofieration of a6% 5-yebonis 4.5 years, anthe inverse floater is just before a resety. The worst change in yiel the 95% level over a month is 0.66%. Whisthe Vof this inverse floater the 95% level over a month? A.$3.0 million B.$5.9 million C.$8.9 million $10.5 million 18% – 2 × L = 3 × 6%– 2 × L (18% – 2 × L) + (2 ×L) = 3 × 6% F = 3 × % = 3 × 4.5 = 13.5 VARIF = × P (worst changein yiel) = 13.5 × 100million × 0.66% = 8.91million 这里计算vaR为什么没有用95%置信区间1.645

2024-11-08 17:08 1 · 回答

NO.PZ2023091701000090问题如下 A portfolio manager invests $100 million in a 5-yearinverse floater paying 18% – 2 × LIBOR. Assume ththe mofieration of a6% 5-yebonis 4.5 years, anthe inverse floater is just before a resety. The worst change in yiel the 95% level over a month is 0.66%. Whisthe Vof this inverse floater the 95% level over a month? A.$3.0 millionB.$5.9 millionC.$8.9 million$10.5 million 18% – 2 × L = 3 × 6%– 2 × L (18% – 2 × L) + (2 ×L) = 3 × 6% F = 3 × % = 3 × 4.5 = 13.5 VARIF = × P (worst changein yiel) = 13.5 × 100million × 0.66% = 8.91million 老师好，“一个普通的固定利息债券（题目给了是6%的coupon bon = 一个libor浮动利息债券 + 一个libor反向浮动债券”这是为什么？什么原理？

2024-09-04 21:16 8 · 回答

NO.PZ2023091701000090 问题如下 A portfolio manager invests $100 million in a 5-yearinverse floater paying 18% – 2 × LIBOR. Assume ththe mofieration of a6% 5-yebonis 4.5 years, anthe inverse floater is just before a resety. The worst change in yiel the 95% level over a month is 0.66%. Whisthe Vof this inverse floater the 95% level over a month? A.$3.0 million B.$5.9 million C.$8.9 million $10.5 million 18% – 2 × L = 3 × 6%– 2 × L (18% – 2 × L) + (2 ×L) = 3 × 6% F = 3 × % = 3 × 4.5 = 13.5 VARIF = × P (worst changein yiel) = 13.5 × 100million × 0.66% = 8.91million

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