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baidu.sina · 2021年04月23日

Equity duration

  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.

解释：

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


Equity duration代表的意思也是利率变化1%带来的价格变化吗？ 答案中9.8年代表什么意思？ 为何Equity duration要远远大于债券duration?是不是说明equity对利息的敏感度要远远大于债券？ 谢谢

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1 个答案

发亮_品职助教 · 2021年04月27日

嗨，从没放弃的小努力你好：


Equity duration代表的意思也是利率变化1%带来的价格变化吗？


是的。


答案中9.8年代表什么意思？


Years这个单位有点多余。Duration是弹性的概念，即，利率变动1单位，价格变动多少幅度。由于是一个系数，所以最准确的说法是没有单位。


Duration其实与Maturity有很强的关系，一般Maturity长的利率产品，他们的Duration都比较大，所以很多地方，会用Maturity、Macaulay duration这些年份的概念来近似充当Duration，所以很多地方都会给Duration加一个Years单位。

这种情况在一些教科书以及财经报道上都看到过，给Duration加一个years，其实用法不规范。


9.8就是代表利率的敏感度是9.8，应该无单位。


为何Equity duration要远远大于债券duration?是不是说明equity对利息的敏感度要远远大于债券？


注意，这里不是分析股票的利率敏感度，不是2级市场交易的股票利率敏感度。


这里分析的是：银行资产负债表上，Equity（自有资金）的利率风险。


银行的资产多是一些贷款，这类资产是利率的产品，利率一旦改变，资产的价值就会变动；

银行的负债也是利率产品，例如，存款，发行的债券等，利率一旦改变，负债的价值就会改变。

根据恒等式：Asset - liability = equity；我们可以知道，利率改变时，这个Equity的价值也一定会改变，因此，Equity也具有Duration。


这里的Equity duration要大于Asset的Duration，本质原因是杠杆：银行会借钱进行业务，也就是说，银行的Asset有很大一部分都是通过借钱Liability实现的，通过融资（Liability）然后放贷形成资产（Asset）。


那这样的话，其实银行就用了比较少的自有资金，撬动了更大规模的asset，于是，自有资金部分（Equity）面临的利率风险要大于Asset的Duration，这是由于杠杆作用放大的。


这个计算公式，以及计算Equity volatility的公式需要记住哈~~机构IPS里面仅有的可以考计算的地方。

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