NO.PZ202207040100000602
问题如下：
Sapphire Bay Foundation Case Scenario
Edward Cullen advises the board of directors of the Sapphire Bay Foundation (Sapphire) regarding all aspects of the investment portfolio of Sapphire’s endowment fund. Traditionally, Cullen drove the selection of active investment managers for the various asset classes. Despite historically ranking well among peers, several of the managers have performed below the level of their respective benchmarks in the past few years. Cullen’s colleague Paige Stapleton recommends that some passive management should be introduced into Sapphire’s investment mix using pooled investments. They agree to introduce the idea to Sapphire’s board at its next meeting.
At the next board meeting, Cullen begins by introducing passive investing to Sapphire’s board. He states that open-end mutual funds and exchange-traded funds (ETFs) are appropriate approaches. Both alternatives are readily available, offer a broad spectrum of investment choices, and are easy to buy and sell. He makes the following comments comparing the two alternatives.
Both mutual funds and ETFs can be purchased on margin.
Investors can take short positions in ETFs but not in mutual funds.
Both mutual funds and ETFs have the same degree of liquidity.
Stapleton then begins a description of factor-based strategies. These include common equity factors, such as value, size, and quality, and they can be used either in place of or to complement market-cap-weighted indexing. She points out that relative to market-cap weighting, factor-based strategies tend to diversify risk exposures; are transparent in terms of factor selection, weighting, and rebalancing; but can be copied by other investors, which can reduce the advantages of a strategy.
Cullen provides Sapphire’s board with an example comparing the performance of the River Valley Fund, a factor-based fund, with its benchmark portfolio (Exhibit 1). The fund uses benchmark segments of four mutually exclusive sub-categories. Cullen calculates the percentage of River Valley’s excess return that resulted from active factor-weighting decisions.
Exhibit 1
Attribution Data for River Valley Fund and Benchmark
For the large-cap US equity portion of Sapphire’s investment portfolio, Cullen believes that there are some existing passive indexed-based funds that track the S&P 500 Index that the foundation should consider. Cullen presents Exhibit 2 to Sapphire’s board.
Exhibit 2 S&P
500 Index Funds
For the international portion of the investment portfolio, Stapleton suggests that Sapphire invest in an MSCI EAFE index portfolio specifically tailored for the foundation rather than investing in an existing index fund. Anne Rowland, Sapphire’s board chair, asks her how this could be accomplished, given that the initial allocation is only $15 million. Stapleton suggests that Sapphire hire a manager to purchase a portfolio of securities that are a mutually exclusive yet comprehensive subgroup of the index designed to track the index return and risk characteristics.
Question
In Exhibit 1, the percentage of the excess return of the River Valley Fund arising from active factor weighting is closest to:
选项：
A.18.18%. B.–0.04%. C.–0.22%.解释：
Solution
A is correct. The percentage of excess return arising from active factor weighting is 18.18%. In comparing the weights between the fund and the benchmark, the factors with different weights are Growth and Quality. The total contribution to the return caused by active factor weighting is
(Underweighting of the Growth factor + Overweighting of the Quality factor) ÷ Total effect
= (–0.24% + 0.20%) ÷ –0.22% = –0.04% ÷ –0.22% = 18.18%.
The fund’s holding of Momentum securities was less than the benchmark’s (24 versus 30), and thus, the fund incurred active security selection risk. But it did not incur active factor risk, since the factor weight is the same as that of the benchmark.
B is incorrect. The candidate did not divide the sum of the difference due to factor weights (–0.04%) by the total effect (–0.22%).
C is incorrect. This is the value of the total effect (–0.22%).
中文解析：
本题考查的是指数投资组合excess return归因分析。这道题目要求我们计算River
Valley基金的超额收益中，来自主动因子加权决策的比例。根据Exhibit 1的数据显示，River
Valley基金与基准投资组合在不同因子的权重和回报上存在差异。我们需要分析这些差异对超额收益的贡献。
正确答案是A。计算超额收益中来自主动因子加权的比例，需要首先确定因子权重的差异对收益的贡献。从表格中可以看到，River Valley基金与benchamrk的权重差异主要集中在“成长”和“质量”因子上。
1. 在成长因子上，River Valley基金的权重为22%，低于基准的25%，所以有一个-0.24%的贡献。
2. 在质量因子上，River Valley基金的权重为29%，高于基准的26%，贡献为+0.20%。
将这些差异相加，得到总贡献为-0.04%。将这个差异除以总超额收益（-0.22%），我们得到比例：-0.04% ÷ -0.22% = 18.18%。因此，来自主动因子加权的超额收益占比是18.18%。
选项B（-0.04%）错误，因为这是因子加权的差异，而不是超额收益中来自因子加权的比例。
选项C（-0.22%）错误，因为这是总的超额收益，而不是因子加权的贡献。
–0.036% ÷ –0.22% = 16.36%，就算算对了也不敢选A啊，
