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Ella · 2024年11月13日

risk weight怎么算

NO.PZ2023100703000107

问题如下:

The manager of the fixed-income desk of an investment bank is examining the current term structure of swap rates and believes that the 5-year swap rate is too low relative to the 2-year and 10-year swap rates. The manager asks a risk analyst to design a hedged butterfly trade in which the bank is the payer in a 5-year swap contract and the receiver in 2-year and 10-year swap contracts. The analyst decides to perform a principal components analysis (PCA) of the term structure of swap rates and use the results of the PCA to construct the butterfly trade. The principal components (PCs) identified as having the greatest impact are the level, the slope, and the short rate. The results of the PCA, stated as the change in bps in the swap rates due to a 1 standard deviation increase in the PC, are given in the table below:

The analyst also notes that these three PCs explain over 99.5% of the variability in the swap rates, with the level PC having the greatest impact, the slope PC having a smaller impact, and the short rate PC only having an impact on very short-term swap rates.

To construct the hedged butterfly position, the analyst collects the current swap rates and DV01s of the 2-year, 5-year, and 10-year swaps, shown in the table below:

After receiving this information from the analyst, the manager instructs the analyst to construct a butterfly position with a notional amount of EUR 100 million in the 5-year swap in such a way that exposures to the level and slope PCs are neutralized. What notional amounts of the 2-year swap and the 10-year swap should be included in the butterfly and what are the risk weights of the two swaps relative to the DV01 of the 5-year swap?

选项:

A.Choice A B.Choice B C.Choice C D.Choice D

解释:

Solving for the face values of the 2-year and 10-year swaps requires using a system of two equations and two unknown variables.

Notional amount of 5-year swap is 100.

Equation1 that neutralizes exposure to level PC is:

F(2) * (DV01(2)/100) * LevelPC(2) + F(10) * (DV01(10)/100) * LevelPC(10) + 100*(DV01(5)/100) * LevelPC(5) = 0

Equation1 using the information in the tables is:

F(2) * 0.0014421 + F(10) * 0.00396933 + 100 * 0.00296112 = 0

Solving for F(2):

F(2) = ( -0.296112 - F(10) * 0.00396933) / 0.0014421

Equation2 that neutralizes exposure to slope PC:

F(2) * (DV01(2)/100) * SlopePC(2) + F(10) * (DV01(10)/100) * SlopePC(10) + 100*(DV01(5)/100) * SlopePC(5) = 0

Equation2 using the information in the table is:

F(2) * -0.00083505 + F(10) * 0.00001462 + 100 * -0.00063488 = 0

Substitute the previously solved for F(2) into Equation2 and solve for F(10)

-0.579051383 * (-0.296112 - F(10) * 0.00396933) + F(10) * 0.00001462 - 0.063488= 0

0.171464063 + F(10) * 0.002298446 + F(10) * 0.00001462 = 0.063488

F(10) * 0.002298446 + F(10) * 0.00001462 = -0.107976063

F(10) * 0.002313066 = -0.107976063

F(10) = -46.68092564 , or a face value of EUR 46.68 million

Substituting this value of F(10) into the equation for F(2) and solving for F(2):

F(2) = ( -0.296112 – -46.68093 *0.00396933) / 0.0014421

F(2) = -76.84626685 , or a face value of EUR 76.85 million

The face value of the 2-year swap receiving should be EUR 76.85 million

The face value of the 10-year swap receiving should be EUR 46.68 million

The risk weight of the 2-year swap relative to DV01 of the 5-year swap is equal to:

(F(2) * (DV01(2)/100))/DV01(5) =0.44155617 or 44.2%

And the risk weight of the 10-year swap relative to DV01 of the 5-year swap is:

0.687978965 or 68.8%

A is incorrect. This answer choice is incorrect in two ways. First, the notional amount of the 2-year swap is incorrectly adjusted so that the notional amounts of the 2-year swap and the 10-year swap add up to 100 to offset the notional amount of the 5-year swap. Second, the risk weights are assumed to sum to 100%, so the percentages are incorrectly adjusted to weight out of 100.

B is incorrect. The notional amount of the 10-year swap is incorrectly adjusted so that the notional amounts of the 2-year swap and the 10-year swap add up to 100 to offset the notional amount of the 5-year swap.

D is incorrect. The risk weights are assumed to sum to 100%, so the percentages are incorrectly adjusted to weight out of 100.

看了经典题视频,还是不太懂

1 个答案

pzqa39 · 2024年11月13日

嗨,爱思考的PZer你好:


这道题是设计一个hedged butterfly trade,银行做5年期互换的payer,同时做2年期和10年期互换的receiver(买入2年期和10年期利率)。需要计算出如何通过2年期和10年期互换的名义金额来对冲Level PC和Slope PC这两个成分的风险敞口,而保留对短期利率(Short Rate PC)的敞口。


对冲Level PC敞口是通过5年期互换的PCA分析结果,可以设定方程使得2年期和10年期互换对Level PC的敞口被完全抵消。

同理,对冲2年期和10年期互换对Slope PC的敞口。


通过解这两组方程,我们能够得到2年期和10年期互换的名义金额(面值),之后计算RWA。


2年期互换的风险权重=[F(2)*DV01/100]/5年期基准交易的DV01

10年期的互换的风险权重=[F(10)*DV01/100]/5年期基准交易的DV01

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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2024-08-06 06:34 1 · 回答