LO 66.3: Assess the impact of practical issues in portfolio construction, such as

LO 66.3: Assess the impact of practical issues in portfolio construction, such as determination of risk aversion, incorporation of specific risk aversion, and proper alpha coverage.
We need a measure of active risk aversion as an input to determine the optimal portfolio. As a practical matter, a portfolio manager does not likely have an intuitive idea of optimal active risk aversion in mind, but will have good intuition about his information ratio (the ratio of alpha to standard deviation) and the amount of active risk (as opposed to active risk aversion) he is willing to accept in pursuit of active returns. An equation that translates those values into a measure of active risk aversion is:
. . information ratio risk aversion = ———- 7—- ;—–
2 x active risk
For example, if the information ratio is 0.8 and the desired level of active risk is 10%, then the implied level of risk aversion is:
0.80 2×10
The utility function for the optimization is: utility = active return (0.04 x variance). Of course, the accuracy of the estimate of active risk aversion is dependent on the accuracy of the inputs, the information ratio, and the preferred level of active risk.
Professors Note: Remember that active risk is just another name for tracking error. Also note that in the risk aversion equation, the desired level o f active risk is measured in percentage points rather than in decimal form.
In addition to active risk aversion, aversion to specific factor risk is important for two reasons. First, it can help the manager address the risks associated with having a position with the potential for large losses. For example, the risk from a portfolio with sector risks that do not match those of the benchmark portfolio. Second, appropriately high risk aversion values for specific factor risks will reduce dispersion (of holdings and performance) across portfolios when the manager manages more than one portfolio. Setting high risk aversion values for factor specific risks will increase the similarity of client portfolios so that they will tend to hold the same assets. Considering these two effects of specific factor risk aversion values will help a manager determine appropriate values to include in portfolio optimization.
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2018 Kaplan, Inc.
Topic 66 Cross Reference to GARP Assigned Reading – Grinold and Kahn, Chapter 14
Proper alpha coverage refers to addressing situations where the manager has forecasts of stocks that are not in the benchmark or where the manager does not have alpha forecasts for stocks in the benchmark. When the manager has information on stocks not in the benchmark, a benchmark weight of zero should be assigned for benchmarking, but active weights can be assigned to these stocks to generate active alpha.
When there is not an alpha forecast for stocks in the benchmark, adjusted alphas can be inferred from the alphas of stocks for which there are forecasts. One approach is to first compute the following two measures:
value-weighted fraction of stocks with forecasts = sum of active holdings with forecasts
(weighted average of the alphas with forecasts) average alpha for the stocks with forecasts = ————;————- ;——————;————— (value-weighted fraction of stocks with forecasts)
The second step is to subtract this measure from each alpha for which there is a forecast and set alpha to zero for assets that do not have forecasts. This provides a set of benchmark- neutral forecasts where assets without forecasts have alphas of zero.
Po r t f o l io Re v is io n s a n d Re b a l a n c in g