中译 本科银行管理课件chapter 6

Managing Interest Rate Risk: Duration GAP and Market Value of Equity


This chapter examines the management of a bank’s interest rate risk position in terms of duration gap and the sensitivity of the market value of stockholders’ equity to changes in interest rates. In this framework, interest rate risk refers to the volatility in the market value of stockholders’ equity attributable to changes in the level of interest rates. 本章讨论以久期缺口表示的银行利率风险以及股票市值随利率变动的敏感 性. 在本章中，利率风险是指股票市值由于利率变动而引起的波动风险。 A bank that assumes substantial risk will see its value of equity rise or fall sharply when interest rates change unexpectedly. 一家银行若利率风险较大，随着意料外利率变动时市值变动越大。
There are four steps in duration gap analysis: 久期缺口分析的四个步骤
1. 2.
Management develops an interest rate forecast.预测利率 Management estimates the market value of bank assets,


Duration gap and market value of equity sensitivity analysis represent alternative methods of analyzing interest rate risk. They emphasize the price sensitivity of assets and liabilities to changes in interest rates and the corresponding impact on stockholders’ equity. 久期缺口和股票市值分析是另一种分析利率风险的方法。着重于 分析资产和负债的价格对于利率的敏感性以及对于股东持有的股 票的影响。
Duration GAP Model





Unlike static GAP analysis, which focuses on rate sensitivity or the frequency of repricing, duration gap analysis focuses on price sensitivity. 久期缺口分析着重于价格敏感性，而缺口分析重于重新定价频率 A bank’s interest rate risk is indicated by comparing the weighted average duration of assets with the weighted average duration of liabilities. 通过比较平均资产久期和平均负债久期来衡量利率风险水平 As with GAP analysis, the sign and magnitude of DGAP provide information about when a bank potentially wins and loses, and the magnitude of the interest rate bet. DGAP反映了银行潜在的盈利和损失，以及利率变化对其影响。


Modified duration=D/(1+i) ∆P/P=-D/(1+i) * ∆i
Duration ΔP Δi P (1 i)
Effective Duration


The concept of effective duration is used to estimate how price sensitive a security is when the security contains embedded options. It compares a security’s estimated price in a falling rate environment with an estimated price in rising rate environment relative to the initial price times （乘积）the assumed rate differential （利率变动幅度）. 有效久期是用于计算含期权证券的价格的利率风险。等于利率下 降时证券价格减去若利率上升时价格的差除以原价格，再乘以预 期的利率变动幅度
Macaulay’s Duration


Macaulay’s duration (D) is computed as a weighted average of the time until cash flows are received. The weights equal the present value of each cash flow as a fraction of the security’s current price. And time refers to the length of time in the future until payment or receipt. It is measured and quoted in units of time. Conceptually, duration measures the average life（平均期 限) of an instrument. (P133) 麦考利久期(即久期D)是各付息期时间的加权平均，直到还本付 息。每期的权重系数等于当期现金流现值除以证券现价。各付息 期时间等于签发到已过时间。久期的数值代表单位付息期的倍数。 所以久期其实衡量的是一种证券的平均期限。(书133页)
确定资产，负债以及股票的市值。股票市值(MVE)等于资产市
值加上负债市值。
There are four steps in duration gap analysis:
3.
4.
Management estimates the weighted average duration of assets and weighted average duration of liabilities. The effects of both on- and off-balance sheet items are incorporated. 计算出资产平均久期以及负债平均久期(包括表内 表外业务) Management forecasts changes in the market value of stockholders’ equity across different interest rate environments.在不同的利率预期变化的环境下，分别计算各种 情况下股票市值的变化。
Duration GAP Model


Duration gap (DGAP) models focus on managing net interest income or the market value of stockholders’ equity, recognizing the timing of all cash flows for every security on a bank’s balance sheet. 久期缺口(DGAP)模型着重于管理净利息收入和股票总 市值，并且将资产负债表中每个证券的现金流时间价 值都列入考虑。
liabilities, and stockholders’ equity. The market value of equity
(MVE) equals the amount that makes the market value of assets equal to the market value of liabilities plus MVE.
Chapter 6 Managing Interest Rate Risk: Duration GAP and Market Value of Equity 管理利率风险:久期缺口和股票市值
2011.10.10
Managing Interest Rate Risk: Duration GAP and Market Value of Equity
Measuring Interest Rate Risk with Duration GAP 通过久期缺口衡量利率风险


Duration gap analysis compares the price sensitivity of a bank’s total assets with the price sensitivity of its total liabilities to assess whether the market value of assets or liabilities changes more when rates change. 久期缺口分析是将资产价格(不是利息收入)对于利率 的敏感性与负债价格对于利率敏感性程度进行对比， 以进一步计算出哪方随着利率变动，价格变动幅度更 大。

Eff Uur=(Pi- - Pi+)/ P0(i+ - i-)
P i Pi Eff Dur P0 (i i)
Effective Duration



Where公式中: Pi- = price if rates fall, 若利率下降时价格 Pi+ = price if rates rise,若利率上升时价格 P0 = initial (current) price,原价格(现价) i+ = initial market rate plus the increase in rate, 原利 率加上利率增加值 i- = initial market rate minus the decrease in rate.原 利率减去利率下降值
Modified Duration


Modified duration equals Macaulay’s du来自百度文库ation divided by (1+i). It has the useful feature of indicating how much the price of a security will change in percentage terms for a given change in interest rates. 修正久期等于久期除以(1+i),i为利率。修正久期用于反映当利率 变动固定值时，计算价格变化率(价格变化率=(-1)*利率变化*修 正久期)
Duration, modified duration, and effective duration 久期，修正久期以及有效久期


Market participants often use three different duration measures-Macaulay’s duration, modified duration, and effective duration-as if they were the same. In fact, while the interpretations are similar, they differ in terms of how they are calculated and how they should be used. 市场参与者经常将久期，修正久期以及有效久期这三 者混淆，尽管由来相同，实际上他们计算和应用方面 却不一样。