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Dichaleeee · 2024年02月01日

为什么futures有借贷成本？

  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.

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.

为什么这里futures默认有借贷成本？我理解futures没有initial cash outflow until settlement, 所以也不存在这个所谓的借贷成本。


如果说cash ETF 要花1.67m的本金，futures是可以把这个1.67m去投资赚risk-free rate的，对他来说成本应该只有unlevered cost partially offset by interest income from investment of 1.67m.

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1 个答案

lynn_品职助教 · 2024年02月01日

嗨，爱思考的PZer你好：


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

为什么这里futures默认有借贷成本？我理解futures没有initial cash outflow until settlement, 所以也不存在这个所谓的借贷成本。

如果说cash ETF 要花1.67m的本金，futures是可以把这个1.67m去投资赚risk-free rate的，对他来说成本应该只有unlevered cost partially offset by interest income from investment of 1.67m.


同学说的是对的，这道题在机构IPS的case里面讲的又是衍生品的知识点，而且出题还不严谨，协会的Case Study in Portfolio Management: Institutional课后题感觉就是为了让大家知道一些知识点，参考意义不大。


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。


· Investment policy compliant at 3 times leverage


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),


看一下就行，同学的分析才是对的。

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