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nicole 麦子🌳 · 2025年03月28日

为什么期末cash outflow要基于期初cash inflow来计算

NO.PZ2022071101000011

问题如下:

A bank buys a bond on its coupon payment date. Three months later, in order to generate immediate liquidity, the bank decides to repo the bond. Details of the bond and repo transaction are as follows:

If the repo contract expires 6 months from now, what is the bank’s expected cash outflow at the end of the repo transaction?

选项:

A.

USD 94,497

B.

USD 95,702

C.

USD 97,630

D.

USD 100,739

解释:

中文解析:

B是正确的。

repo初期的现金流=notional value*(current bond price%+coupon rate*3/12)*(1-repo haircut)=(100,000)*(98%+5%*0.25)*(1-5%) = 94,288; repo到期的现金流=期初流入*(1+repo int rate*6/12)=94,288*(1+3%*0.5)=95,702。

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B is correct. Cash inflow at beginning of repo: (100,000)*(98%+5%*0.25)*(1-5%) = 94,288; Cash outflow at end of repo: 94,288*(1+3%*0.5)=95,702

A is incorrect. Left out the accrued interest of 5%*0.25 in the correct equation for cash inflow.

C is incorrect. Used 1 instead of 98% for price in the correct equation for cash inflow.

D is incorrect. Left out haircut of 5% in the correct equation for cash inflow.

期初根据计算收到现金94288,6个月后repo到期,不是应该按照6个月后的市价再加上notional 100000元的interest还给对方把bond要回来吗?就是假如6个月后市价为98元,那就是100000*0.98+100000*3%*0.5


那bond在repo期间的6个月内也有产生coupon,这个coupon不在最终cash outflow减掉么?就是

outflow = 100000*0.98+100000*3%*0.5 - 100000*5%*0.5


谢谢老师

1 个答案

李坏_品职助教 · 2025年03月28日

嗨,努力学习的PZer你好:


假设我是repo方,对手是你。repo相当于我期初找你借入一些现金,期末我肯定要还你钱,而且是根据期初借入的现金来计算期末我需要偿还的利息和本金。

期初我从你那里借入的现金 = 债券的full price * (1- haircut) = (债券的clean price + accrued Interest)*(1-5%)。clean price就是债券现在的报价98,而accrued interest是应计利息,距离上次支付coupon已经过去3个月,所以应计利息 = 3/12 * coupon rate。


期末我需要还给你本金+利息,本金就是期初借入的钱,利息是本金*repo rate * 6/12


期间这个bond产生的coupon依然是属于你的,不属于我,所以不计入我最终的cash outflow。

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