Nicole Seaman

Director of CFA & FRM Operations
Staff member
Learning objectives: Distinguish among the inputs to the portfolio construction process. Evaluate the motivation for and the methods used for refining alphas in the implementation process. Describe neutralization and the different approaches used for refining alphas to be neutral. Describe the implications of transaction costs on portfolio construction.


21.3.1. Grinold's fundamental law says that the expected information ratio of an active investment strategy, IR, is given by the information coefficient (IC) multiplied by the square root of the breadth, BR, which is a measure of diversification. In words, as Grinold says, "High information ratios follow from high levels of skill and/or high breadth or diversification."(†) The presumption is that information ratios are the primary measure of value added. In a subsequent development the transfer coefficient, TC, was incorporated as a multiplier such that the extended fundamental law is given by IR = IC × sqrt(BR) × TC. The transfer coefficient, TC, is a measure of efficiency: to what extend do transaction costs and/or other constraints cause the actual portfolio to vary from the optimal portfolio?

Which of the following is the BEST measure of breadth, BR, in the fundamental law?

a. The number of bets per year
b. The ratio of active return to active risk
c. The number of positions (aka, holdings) in the portfolio
d. The number of securities in the relevant global index; e.g., S&P 1500, Russel 3000 or Wilshire 5000

21.3.2. According to Grinold, information coefficients (IC) are correlations but in practice they are small: forecasting residual returns is hard. An Average Manager (by definition) has an IC of zero. Let's assume a Good Manager has an IC of 0.060 while a Great Manager has an IC of 0.120. Further, assume that a certain stock has a residual volatility of 30.0%. In regard to this stock, a Great Manager has a stock recommendation for which she is highly positive (she makes only a few recommendations per year), and this confidence is quantified with a z-score (aka, expectation) of 1.50. What is the implied alpha of this stock recommendation?

a. 2.40%
b. 3.60%
c. 5.40%
d. 60.0%

21.3.3. Kelly is constructing a portfolio where her initial unconstrained optimization generates two outcomes that violate her fund's style policy. Specifically, the unconstrained optimization implies that the portfolio should hold several short positions; and further that the portfolio should shift to over-weight three positions in particular. Unfortunately, these three positions would then exceed the portfolio self-imposed concentration limit. This rule says that individual positions cannot exceed the benchmark holdings by more than 10.0%. Kelly proceeds to refine the alphas by performing two methods: she scales the alphas and then she trim the extreme alphas.

What is the most likely reason for Kelly to refine the alphas?

a. Performance: the refined alphas generate higher information ratios (IR)
b. Precision: the active risk aversion coefficient is more accurately calibrated
c. Sophistication: the refined alphas are more conducive to quadratic programming
d. Simplification: to be able to size the active positions with a simple unconstrained mean-variance optimization

Answers here:

(†) Richard Grinold and Ronald Kahn, Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk, 2nd Edition (New York: McGraw-Hill, 2000).
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