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Brownie · 2022年10月15日

为什么unleveraged cost 不用乘以权重

  1. CFA III
  2. 机构IPS

NO.PZ2022051904000006

问题如下：

In its quarterly policy and performance review, the investment team for the Peralandra University endowment identified a tactical allocation opportunity in international developed equities. The team also decided to implement a passive 1% overweight ($5 million notional value) position in the asset class. Implementation will occur by either using an MISC EAFE Index ETF in the cash market or the equivalent futures contract in the derivatives market.

The team determined that the unlevered cost of implementation is 27 basis points in the cash market (ETF) and 32 bps in the derivatives market (futures). This modest cost differential prompted a comparison of costs on a levered basis to preserve liquidity for upcoming capital commitments in the fund’s alternative investment asset classes. For the related analysis, the team’s assumptions are as follows:

  • Investment policy compliant at 3 times leverage
  • Investment horizon of one year
  • 3-month Libor of 1.8%
  • ETF borrowing cost of 3-month Libor plus 35 bps
Q. Recommend the most cost-effective strategy. Justify your response with calculations of the total levered cost of each implementation option.

解释：

Solution

As the lower cost alternative, the endowment’s investment team should implement the 1% overweight position using futures.

The additional cost of obtaining leverage for each option is as follows:ETF: ($5 million × 0.6667 × 2.15%) / $5 million = 1.43% (or 143 bps) and Futures: ($5 million × 0.6667 × 1.80%) / $5 million = 1.20% (or 120 bps),

where the inputs are derived as follows:0.6667 reflects the 3 times leverage factor (66.67% borrowed and 33.33% cash usage), 2.15% reflects the ETF borrowing rate (3-month Libor of 1.80% + 35 bps), and 1.80% reflects the absence of investment income offset (at 3-month Libor) versus the unlevered cost of futures implementation.

The total levered cost of each option is the sum of the unlevered cost plus the additional cost of obtaining leverage:ETF: 27 bps + 143 bps = 170 bps and Futures: 32 bps + 120 bps = 152 bps.

This 18 bps cost advantage would make futures the appropriate choice for the endowment’s investment team.

The total levered cost of each option is the sum of the unlevered cost plus the additional cost of obtaining leverage:ETF: 27 bps + 143 bps = 170 bps and Futures: 32 bps + 120 bps = 152 bps.


上述答案中，27bp，32bp为什么不乘cash的权重（1/3）？

143bp，120bp，都是unleveraged的cost，他们是乘以借款权重0.6667得出的结果。那么unleveraged 的部分，为什么不乘以cash 的权重0.3333

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3 个答案

lynn_品职助教 · 2023年06月30日

嗨，爱思考的PZer你好：


我理解也许unleverage cost也许指的是交易的税费等成本，主要和交易规模有关，因此，相当于权重就是1


这个理解也可以，题目确实出得很奇怪，其实是为了给我们介绍一个新的知识点。

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

jerryhuqian · 2023年06月29日

我理解也许unleverage cost也许指的是交易的税费等成本，主要和交易规模有关，因此，相当于权重就是1

lynn_品职助教 · 2022年10月16日

嗨，从没放弃的小努力你好：


我们看143bp和120bp的计算，他们计算的是获得杠杆后的成本，The additional cost of obtaining leverage for each option is as follows:ETF: ($5 million × 0.6667 × 2.15%) / $5 million = 1.43% (or 143 bps) and Futures: ($5 million × 0.6667 × 1.80%) / $5 million = 1.20% (or 120 bps),


这道题是原版书Reading 28 Case Study in Portfolio Management: Institutional的一道课后题。



Recommend the most cost-effective strategy. Justify your response with calculations of the total levered cost of each implementation option.



题目让计算一下考虑杠杆后的成本，推荐一个最省成本的策略。就是在计算cost的时候考虑借钱的成本。



视频在课后题Reading28 Question8~9八分钟（两倍速处），整个知识点角度挺奇特的，同学稍稍看一下就可以了不需要花太多时间。

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努力的时光都是限量版，加油！

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