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moon · 2022年04月05日

bond future

* 问题详情,请 查看题干

NO.PZ201601050100001803

问题如下:

Six months later, Uff has since closed out both the equity index futures contract position and the interest rate swap position. In response to market movements, he now wants to implement a tactical rebalancing of the Fund’s portfolio.

Exhibit 3 presents the current and target asset allocations for the Fund’s portfolio.


Uff decides to use equity index and bond futures contracts to rebalance the portfolio. Exhibit 4 shows selected data on the Fund’s portfolio and the relevant futures contracts.


Determine how many equity index and bond futures contracts Uff should use to rebalance the Fund’s portfolio to the target allocation. Identify whether the futures contracts should be bought or sold.

选项:

解释:

Uff needs to reduce the equity allocation by €13,202,500 (= €201,384,000 – €188,181,500).

The number of equity index futures contracts required to rebalance the Fund’s portfolio to the target allocation is calculated as follows:


Uff needs to move to a notional “cash” position (βT = 0) to reduce equity exposure, and the portfolio beta is βS = 1.28. The beta of the equity index futures contract (βf ) is 1.00, so the number of equity index futures contracts required is calculated as follows:


Because the number of futures contracts (Nf ) is negative, Uff should sell 483 equity index futures contracts (after rounding).

Uff needs to increase the bond allocation by €13,202,500 (= €101,328,500 – €88,126,000).

The number of bond futures contracts required to rebalance the Fund’s portfolio to the target allocation is calculated as follows:


where


Now, starting with a notional “cash” position (BPVP = 0) provided by the reduction in equity exposure above, and noting that BPVCTD = €91.26 and CF = 0.733194, the number of bond futures contracts is calculated as follows:


Because the BPVHR is positive, Uff should buy 49 bond futures contracts (after rounding).

中文解析:

本题考察的是使用股指期货合约和债券期货合约进行资产配置。

根据题干的意思可知,现在想要降低股票在组合中的占比,增加债券在组合中的占比。

因此第一步是通过卖出股指期货合约来降低股票头寸,第二步再通过买入债券期货合约来增加债券头寸。具体合约的份数按照上述公式计算即可。

老师,想问下答案说:Now, starting with a notional “cash” position (BPVP = 0) provided by the reduction in equity exposure above, and noting that BPVCTD = €91.26 and CF = 0.733194, the number of bond futures contracts is calculated as follows:


这里为啥说“tarting with a notional “cash” position (BPVP = 0) "??

2 个答案

Hertz_品职助教 · 2022年04月08日

嗨,努力学习的PZer你好:


同学你好

看一下咱们计算BPVHR的公式哈,使用的是BPV,而91.26刚好就是CTD对应的BPV啦(表4倒数第二行)。

另外BPV=MDur * MV *1bp,本身就是乘以了修正久期MDur的哈

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加油吧,让我们一起遇见更好的自己!

Hertz_品职助教 · 2022年04月06日

嗨,从没放弃的小努力你好:


同学你好~

咱们再一起梳理一下题干哈:他是说想把现在组合中股票和债券的权重调整到一个目标的权重上,对应题干中的表3,在这里可以看到,是要将201384000的头寸调整到188181500的头寸,然后将债券头寸由88126000调整到101328500。

因此需要调整的金额是13202500,这部分金额是要先从股票通过调整β,调整到现金;然后再通过调整duration调整到债券可以看到这个过程是需要现金做媒介的,而现金的β和久期都为0.

所以才有了“starting with a notional “cash” position”的表述,其实就是现金在中间做媒介的意思啦

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

vivianlsq · 2022年04月08日

请问BTV-CTD计算的时候,为啥直接就是91.26?不是应该还要乘以MDUR-CTD(久期)吗?

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