Restriction on diversification: $100 million/60 securities

问题如下：

The Epsilon Institute Case Scenario

The Epsilon Institute of Theoretical Physics is a non-profit corporation initially funded from government and private sources. Mitch Lazare is the chairman of the Investment Committee, which oversees the institute’s endowment fund, of which about $750 million is currently under active management. He is currently tasked with finding two additional investment managers to manage a portion of the actively managed funds and, along with his assistant, Brian Warrack, is reviewing the presentations made by several applicants.

John Fraser’s performance is the first that Lazare and Warrack review. Fraser’s fund is constructed with a discretionary approach using the four Fama–French factors; he uses the Russell 1000 Value Index as his benchmark. The most recent 10 years of performance data for both the fund and the benchmark are shown in Exhibit 1.

Exhibit 1

Fraser Fund and Benchmark Average Monthly Performance over the Past 10 years

As part of his evaluation of the applicants, Warrack compiles a record of the Active Share and active risk of the funds that they manage. He observes that the Mattley Fund has relatively high Active Share but relatively low active risk.

Lazare and Warrack make the following comments about Active Share and active risk in the context of a single-factor model:

• The level of active risk will rise with an increase in idiosyncratic volatility.

• The active risk attributed to Active Share will be smaller in more diversified portfolios.

• If the factor exposure is fully neutralized, the Active Share will be entirely attributed to the active risk.

The manager of the Western Fund focuses on smaller companies in the Russell 1000 Value Index and uses the following constraints:

• Size: The capitalization of the average company is $1.8 billion. On average, companies of this size trade 0.90% of their capitalization every day.

• Liquidity: Positions can be no larger than 7% of average daily trading volume.

• Allocation: Positions can be no larger than 1.75% of total assets under management.

• Diversification: The portfolio must contain at least 60 securities.

If the manager of the Western Fund is hired by Epsilon, she will have $100 million of Epsilon’s funds to manage.

Lazare and Warrack turn their attention to the manager of the Herrick Fund, which is the only fund that involves substantial international exposure. Lazare believes that current political events in Country A may result in greater risk exposure than might be appropriate and wishes to investigate further.

The Herrick Fund manager provides them with the information in Exhibit 2, which they use to carry out a risk attribution analysis.

Exhibit 2

The Herrick Fund—Risk Analysis

Question

If the Western Fund manager is hired, which constraint is most restrictive with respect to average position size? The constraint related to:

选项：

A.liquidity. B.diversification. C.asset allocation.

解释：

Solution

A is correct. The most restrictive constraint on position size for the Western Fund manager is the liquidity constraint. It arises from the restriction on average daily trading volume: The average position size cannot exceed $1.13 million.

Average daily trading for the representative company size: 0.90% × $1.8 billion = $16.2 million.

• Restriction on trading volume: 7% × Average daily trading = 7% × $16.2 million = $1.13 million.

• Restriction on allocation: 1.75% × $100 million = $1.75 million.

• Restriction on diversification: $100 million/60 securities = $1.67 million.

Position size is restricted by trading volume, and the fund could hold up to $100 million/$1.13 million = 89 securities.

B is incorrect. With a requirement of at least 60 securities, an investment of up to $100 million/60 = $1.67 million is allowed in any security. The restriction on daily trading ($1.13 million) prevents that much from being acquired.

C is incorrect. The allocation restriction is 1.75% of funds under management = 1.75% × $100 million = $1.75 million. However, the restriction on daily trading ($1.13 million) prevents this amount from being acquired.