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moon · 2022年07月25日

老师，想问下这个公式的原理是什么？

  1. CFA III
  2. 机构IPS

NO.PZ2019100901000018

问题如下：

Meura Bancorp, a US bank, has an equity capital ratio for financial assets of 12%. Meura’s strategic plans include the incorporation of additional debt in order to leverage earnings since the current capital structure is relatively conservative. The bank plans to restructure the balance sheet so that the equity capitalization ratio drops to 10% and the modified duration of liabilities is 1.90. The bank also plans to rebalance its investment portfolio to achieve a modified duration of assets of 2.10. Given small changes in interest rates, the yield on liabilities is expected to move by 65 bps for every 100 bps of yield change in the asset portfolio.

Calculate the modified duration of the bank’s equity capital after restructuring. Show your calculations.

选项：

解释：

The modified duration of the bank’s equity capital after restructuring is 9.89 years:


老师，想问下这个公式的原理是什么？

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1 个答案

lynn_品职助教 · 2022年07月26日

嗨，从没放弃的小努力你好：


这个公式就是计算Equity的Duration，我们知道银行最重要的管理之一就是要让资产和负债相匹配，管理短借长贷的风险。因此这个公式的原理即利用恒等式：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65bps（65 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0.65bps。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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