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hyi725 · 2023年08月12日

公式

  1. CFA III
  2. Derivative

* 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。

在算出48.69以后为什么不需要再乘 （1320500/35000）了呢？ 公式里不是还有后缀吗

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1 个答案

pzqa31 · 2023年08月13日

嗨，爱思考的PZer你好：


没有后缀，公式如下：

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努力的时光都是限量版，加油！

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