为什么分母不是excess return ，即portforlio return -benchmark return?

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.

1. Both mutual funds and ETFs can be purchased on margin.

2. Investors can take short positions in ETFs but not in mutual funds.

3. 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%).