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大张伟 · 2022年10月05日

关于三倍杠杆的理解

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.

选项:

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.

题目中对于“Investment policy compliant at 3 times leverage”的计算给出的是“ 3 times leverage factor (66.67% borrowed and 33.33% cash usage)”。实在不是很理解,为什么2/3=66.7%就是三倍杠杆了?


是这样理解吗?

A/E=3 然后推出 L=2 E,所以自由资金cash占1/3?

1 个答案
已采纳答案

lynn_品职助教 · 2022年10月08日

嗨,从没放弃的小努力你好:


A/E=3 然后推出 L=2 E=1,所以自由资金cash占1/3?

是的,这句话的表达非常奇怪,但是我们也只能把它的 3 times leverage理解为leverage ratio了。


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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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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