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Ruthlessbaby · 2020年02月27日

问一道题：NO.PZ2019100901000020

  1. CFA III
  2. 机构IPS

问题如下：

MegaWorld Bancorp has an equity capital ratio for financial assets of 9%. The modified duration of its assets is 2.0 and of its liabilities is 1.5. Over small changes, the yield on liabilities is expected to move by 85 bps for every 100 bps of yield change in its asset portfolio.
Compute the modified duration of the bank’s equity capital.

选项：

解释：

Using Equation 8, A ÷ E = 1/0.09 = 11.11; (A ÷ E) –1 = 10.11; D*A = 2.0; DL* =
1.5; and Δi ÷ Δy = 0.85.
Therefore, the modified duration of shareholders’ capital is:

DE* = (11.11 × 2) – (10.11 × 1.50) × 0.85 = 9.33

为什么资产的Da不需要乘以Δi /Δy呢

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1 个答案

发亮_品职助教 · 2020年02月27日

嗨，爱思考的PZer你好：


“为什么资产的Da不需要乘以Δi /Δy呢”

这个系数乘一次就好了。

这里是这样，我们是想算Equity的Duration，利用恒等式：A = D + E，我们算一下利率变动时，资产价值的变动、负债价值的变动，然后资产价值的变动减去负债价值的变动，就能得到利率变动时Equity价值的变动，这就是Equity价值对利率的敏感度Duration。

但是，在上面这个链条里，我们认为影响资产、负债的利率是同一个利率；但实际上并不是，有可能影响资产的利率变动1bp，影响负债的利率只会变动0.65bp；

所以，我们乘以一个系数即可，这个系数代表，如果资产的利率每变动1bps时，负债的利率变动多少bp。

例如，本题就是资产的利率每变100bps，负债的利率会变动85bps（85 bps for every 100 bps ），这样的话，如果资产的利率变动1bp，我们就知道负债的利率变动0.85bps。

所以Δi /Δy只用给Asset yield乘一次，就会得到负债利率的变动，不用给资产乘。


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