Nicole Seaman

Director of FRM Operations
Staff member
Learning objectives: Describe and evaluate the low-risk anomaly of asset returns. Define and calculate alpha, tracking error, the information ratio, and the Sharpe ratio. Explain the impact of benchmark choice on alpha and describe characteristics of an effective benchmark to measure alpha.


20.5.1. Consider the following four portfolios:

I. Albert's portfolio has a high beta and generates high (aka, strong) returns​
II. Betty's portfolio exhibits low volatility with high (aka, strong) returns​
V. Chuck's portfolio exhibits low beta (aka, systematic risk) but generates a high volatility (aka, total risk)​
III. Donald's tracks the market's minimum variance portfolio with low tracking error and generates low (aka, weak) returns​

Which of the portfolio's best illustrates and confirms the low-risk anomaly?

a. Albert's portfolio
b. Betty's portfolio
c. Chuck's portfolio
d. Donald's portfolio

20.5.2. Ang writes that the "information ratio is the ratio of alpha to tracking error"(†) but an FRM recognizes this as an inaccurate expression (why?). In regard to the relationship between alpha, tracking error, the information ratio, and the Sharpe ratio, each of the following is true EXCEPT which is false?

a. The Sharpe ratio is a special case of the information ratio where the benchmark is the risk-free asset
b. The information ratio is the portfolio's average active return (or average alpha) divided by its tracking error (or standard deviation of its alpha)
c. If two funds use the same benchmark, the fund with the higher information ratio must have a lower tracking error
d. If the benchmark is risk-adjusted (i.e., the fund's beta is measured by regressing its excess returns against the benchmark's excess returns), then we can refer to tracking error as idiosyncratic volatility

20.5.3. Analyst William is evaluating a fund that employs a low volatility ("low-vol") strategy. He evaluates this low-vol fund's performance against its traditional benchmark: the Russell 1000. Over the last three years, the low-vol fund's active return relative to its "naive" Russell 1000 benchmark was only +0.28% per year. This active return is the fund's average return in excess of the Russell 1000 benchmark. William tentatively refers to this +28 basis points as the fund's "alpha," but he is not certain the definition is accurate. Let's call this William's initial analysis.

His colleague Emily suggests a possible flaw in the initial analysis: she says that the fund's correct benchmark was a risk-adjusted portfolio that consists of 65.0% of the Russell 1000 plus 35.0% of a risk-free asset (assume the return on the risk-free asset is significantly less than the Russell 1000). If William re-evaluate the fund's performance (over the same historical period) using this risk-adjusted portfolio as the benchmark, in comparison to the initial analysis, which of the following is the most likely outcome of his revised analysis?

a. The fund's alpha will increase
b. The fund's beta will increase
c. The fund's active return will decrease
d. The fund's information ratio will decrease because its tracking error will increase

Answers here:

Andrew Ang, Asset Management: A Systematic Approach to Factor Investing (New York: Oxford University Press, 2014).
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