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
选项：
解释：
SolutionAs 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.
最终成本的比计较，取决于2个方面：①获得杠杆的成本+②在2个市场交易的成本
对于①获得杠杆的成本，可能有些异议。
关于①，在ETF获得杠杆的成本，我的理解，有2个途径。
途径1：利用1元cash作为margin，借入2元的ETF，获得3元的ETF敞口。
途径2：利用1元本金作为margin，在libor市场借入2元cash，并直接购买3元的ETF产品，获得3元的ETF敞口。
答案直接假设了途径1。
但是，在future市场加杠杆的方法，答案采用的是途径2的思路（在LIBOR市场借入cash，然后买入future）
途径1，其成本应该是更低的，也就是 （5M*0.667*1.8%）/5M=1.2%。
这里，1.8%是3m libor的成本。
请问一下，我对答案理解是否正确，即
- 在ETF市场获得杠杆，默认的是采用途径1，而没有用途径2？
- 实际上，也可以采用途径2，获得3被杠杆的ETF敞口？
- 因为题目暗示的ETF 借贷利率，所以采用了途径1的计算方法？
- 如果题目也暗示了future的借贷利率，那么future的成本，也要采用途径1的方法？
