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Cooljas · 2024年04月18日

为什么3450前面是负号啊?

NO.PZ2023091701000174

问题如下:

A risk manager at a fixed-income hedge fund wants to hedge the interest rate risk exposure of a portfolio. The manager has determined that a 1-bp increase in the 2-year spot rate would decrease the value of the portfolio by INR 1,600, however a 1-bp increase in the 5-year spot rate would increase the value of the portfolio by INR 3,450. The manager plans to hedge the portfolio’s exposure using the following two bonds whose key rate 01s (KR01s) are shown below:

Which of the following transactions would most effectively hedge against the portfolio’s interest rate risk?

选项:

A.Buy 38 of Bond A and short 56 of Bond B B.Buy 75 of Bond A and short 29 of Bond B C.Short 38 of Bond A and buy 56 of Bond B D.Short 75 of Bond A and buy 29 of Bond B

解释:

C is correct. A Key Rate 01 (KR01) is the reduction in a bond or portfolio’s value given a 1 basis point increase in a given spot interest rate. Given the information provided, the KR01s of the portfolio to the 2-year spot rate and 5-year spot rate are INR 1,600 and INR-3,450, respectively. The positions in the hedging instruments required to reduce the portfolio KR01s to zero are expressed in the following equations:

1,600 + 48A + 4B = 0

3,450 + 5A + 65B = 0

Simultaneously solving these equations finds that A = 38 and B = 56. Therefore, selling short 38 of Bond A and buying 56 of Bond B would hedge the key rate exposures of the portfolio.

A is incorrect. This reverses the direction of the trades in Bond A and Bond B.

B is incorrect. This is the result found when the equations are set up incorrectly as:

3,450 + 48A + 5B = 0

1,600 + 4A + 65B = 0

D is incorrect. This reverses the direction of the trades in Bond A and Bond B after the equations are set up incorrectly as in B above.



2 个答案

品职答疑小助手雍 · 2024年05月01日

The manager has determined that a 1-bp increase in the 2-year spot rate would decrease the value of the portfolio by INR 1,600, however a 1-bp increase in the 5-year spot rate would increase the value of the portfolio by INR 3,450. 这句其实都已经说得很明白了,前半句说的是利率上升债券价格下降,那意味着key rate久期为正,后半句相反意味着key rate久期为负。

那么题目给的债券久期都是正的,联立二元一次方程即可。

品职答疑小助手雍 · 2024年04月19日

同学你好,因为同样是利率上升1bp,变动是相反的,总得有一个加负号。The manager has determined that a 1-bp increase in the 2-year spot rate would decrease the value of the portfolio by INR 1,600, however a 1-bp increase in the 5-year spot rate would increase the value of the portfolio by INR 3,450. 

Olivia Zhang · 2024年04月30日

为什么负号加在了3450前面,没有加到1600前面。如果负号给了1600,A和B的方向会和答案相反。

Cooljas · 2024年05月01日

为啥不是在1600前面加上负号啊?为了对冲的话

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NO.PZ2023091701000174 问题如下 A risk manager a fixeincome hee funwants to hee theinterest rate risk exposure of a portfolio. The manager hterminetha1-increase in the 2-yespot rate woulcrease the value of the portfolioINR 1,600, however a 1-increase in the 5-yespot rate woulincreasethe value of the portfolio INR 3,450. The manager plans to hee theportfolio’s exposure using the following two bon whose key rate 01s (KR01s)are shown below:Whiof the following transactions woulmosteffectively hee against the portfolio’s interest rate risk? A.Buy 38 of BonA anshort 56 of Bon B.Buy 75 of BonA anshort 29 of Bon C.Short 38 of BonA anbuy 56 of Bon Short 75 of BonA anbuy 29 of Bon C is correct. AKey Rate 01 (KR01) is the rection in a bonor portfolio’s value given a 1basis point increase in a given spot interest rate. Given the informationprovi the KR01s of the portfolio to the 2-yespot rate an5-yespotrate are INR 1,600 anINR-3,450, respectively. The positions in the heinginstruments requireto rethe portfolio KR01s to zero are expressein thefollowing equations:1,600 + 48A +4B = 0−3,450 + 5A + 65B =0Simultaneouslysolving these equations fin thA = −38 anB =56. Therefore, selling short 38 of BonA anbuying 56 of BonB woulheethe key rate exposures of the portfolio.A is incorrect.This reverses the rection of the tras in BonA anBonB.B is incorrect.This is the result founwhen the equations are set up incorrectly as:−3,450 + 48A + 5B =01,600 + 4A +65B = 0is incorrect.This reverses the rection of the tras in BonA anBonB after theequations are set up incorrectly in B above. 能理解利率上升,P变动与KR01、ration正负关系。没理解的是对冲的方向,就48A+4B+1600=0.为例,题干讲int增加1bp,P减少1600.,48A+4B=-1600,这样计算的A、B,怎么能对冲负1600呢?我怎么觉着48A+4B=1600,才能对冲负1600呢。用李老师讲的组合思想,组合X=48A+4B,组合Y=-1600,T=X+Y=0,T=48A+4B+(-1600)=0.所以,我总选A。没想明白,请老师讲解下我这么想,错在哪了。应该怎么想这个对冲方向?

2024-05-05 21:07 1 · 回答