P2.T8. Risk Management & Investment Management. Grinold, Chapter 14: Portfolio Construction

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1 P2.T8. Risk Management & Investment Management Grinold, Chapter 14: Portfolio Construction Bionic Turtle FRM Study Notes By David Harper, CFA FRM CIPM

2 Grinold, Chapter 14: Portfolio Construction DISTINGUISH AMONG THE INPUTS TO THE PORTFOLIO CONSTRUCTION PROCESS EVALUATE THE METHODS AND MOTIVATION FOR REFINING ALPHAS IN THE IMPLEMENTATION PROCESS DESCRIBE NEUTRALIZATION AND METHODS FOR REFINING ALPHAS TO BE NEUTRAL

3 Grinold, Chapter 14: Portfolio Construction Distinguish among the inputs to the portfolio construction process. Evaluate the methods and motivation for refining alphas in the implementation process. Describe neutralization and methods for refining alphas to be neutral. Describe the implications of transaction costs on portfolio construction. Assess the impact of practical issues in portfolio construction such as determination of risk aversion, incorporation of specific risk aversion, and proper alpha coverage. Describe portfolio revisions and rebalancing and evaluate the tradeoffs between alpha, risk, transaction costs and time horizon. Determine the optimal no-trade region for rebalancing with transaction costs. Evaluate the strengths and weaknesses of the following portfolio construction techniques: screens, stratification, linear programming, and quadratic programming. Describe dispersion, explain its causes and describe methods for controlling forms of dispersion. Distinguish among the inputs to the portfolio construction process. The process of portfolio construction has several inputs as covered below: 1. Current Portfolio: This is the only input which can be measured with certainty as it comprises of assets and their weight-age in the portfolio. 2. Alphas: The Alphas, defined as excess return of the asset vis-à-vis benchmark portfolio, is subject to hidden biases and can be unreasonable at times. 3. Covariance Estimates: It is one of the most important inputs that go into portfolio construction because covariance estimates helps in identifying how the returns of assets in a portfolio are related. 4. Transaction Costs: It is the cost associated with the buying/selling of the asset over & above the agreed price and plays a vital role is determining the actual return on the asset/portfolio. 5. Active Risk Aversion: This input should conform to the targeted active risk levels of the portfolio. Most active managers will have a target level of active risk that must be made consistent with an active risk aversion. Active Risk is also known as tracking error and is derived as the standard deviation of excess return (portfolio return less benchmark return). It is important to note about the above inputs that: Alphas, Covariance & Transaction Costs are subject to error. Barring Current Portfolio estimates, none of the inputs can be estimated with complete certainty. 3

4 Evaluate the methods and motivation for refining alphas in the implementation process. The implementation procedure can be simplified if we ensure that our alphas are consistent with our beliefs and goals. With alpha analysis, the alphas can be adjusted so that they are in line with the manager's desires for risk control and anticipated sources of value added. One of the greatest motivations behind refinement of Alpha is to address the constraints faced by the portfolio manager, few of which are covered below: Most institutional portfolio managers cannot take short positions and need to limit the amount of cash in the portfolio. Others may restrict asset coverage because of requirements concerning liquidity, self-dealing, and so on. These limits are hard to avoid and make the portfolio less efficient. Managers often add their own restrictions to the process. o A manager may require that the portfolio be neutral across economic sectors or industries. o The manager may limit individual stock positions to ensure diversification of the active bets. o The manager may want to avoid any position based on a forecast of the benchmark portfolio's performance. By adjusting the inputs, we can replace a sophisticated & complicated portfolio construction procedure with a direct unconstrained mean/variance optimization using a modified set of alphas and the appropriate level of risk aversion. This method is called Constrained Optimization for portfolio construction. Here we will outline some procedures for refining alphas that can simplify the implementation procedure, and explicitly link our refinement in the alphas to the desired properties of the resulting portfolios. Scaling Technique Alphas have a natural structure. This structure includes a natural scale for the alphas i.e. Where, Alpha (a) = Volatility x IC x Score Volatility is the residual risk and Information Coefficient (IC) signifies the correlation between the actual & forecasted outcomes. We expect the IC and volatility for a set of alphas to be approximately constant, with the score having mean 0 and standard deviation 1 across the set. Hence, as per the equation above, the derived alphas should have mean 0 and its standard deviation range or scale being roughly equivalent to the product of IC & Volatility, i.e.: Standard Deviation {a} ~ Volatility x IC 4

5 Consider for instance, an Information Coefficient (IC) of 0.05 and a typical residual risk (volatility) of 30 percent would lead to an alpha scale of 1.5 percent (0.05 x 0.3 = 1.5%). In this case, the mean alpha would be 0, with roughly two-thirds of the stocks having alphas between -1.5 percent and +1.5 percent and roughly 5 percent of the stocks having alphas larger than +3.0 percent or less than -3.0 percent. In Table 1 below, the original alphas have a standard deviation of 2.00 percent and the modified alphas have a standard deviation of 0.57 percent. This implies that the constraints in this example effectively shrank the IC by 62 percent, a significant reduction. Constrained Index Optimal Optimal Modified Stock Weight Alpha Holding Holding Alpha American Express 2.28% -3.44% -0.54% 0.00% -1.14% AT&T 4.68% 1.38% 6.39% 6.18% 0.30% Chevron 6.37% 0.56% 7.41% 7.05% 0.11% Coca-Cola 3.84% -2.93% -2.22% 0.00% -0.78% Disney 3.94% 1.77% 5.79% 5.85% 0.60% Dow Chemical 5.25% 0.36% 5.78% 6.07% 0.22% DuPont 4.32% -1.50% 1.54% 1.67% -0.65% Eastman Kodak 3.72% 0.81% 4.07% 4.22% 0.14% Exxon 5.60% -0.10% 4.57% 4.39% -0.19% General Electric 7.84% -2.80% 0.53% 0.92% -1.10% General Motors 2.96% -2.50% 1.93% 1.96% -0.52% IBM 4.62% -2.44% 3.24% 3.54% -0.51% International Paper 6.11% -0.37% 5.73% 6.15% 0.01% Johnson & Johnson 4.63% 2.34% 7.67% 7.71% 0.66% McDonalds 4.47% 0.86% 5.07% 4.98% 0.14% Merck 3.98% 0.80% 4.72% 4.78% 0.20% 3M 9.23% 3.98% 17.95% 14.23% 0.91% Philip Morris 7.07% 0.71% 7.82% 7.81% 0.12% Procter & Gamble 4.92% 1.83% 6.99% 6.96% 0.44% Sears 4.17% 0.69% 5.57% 5.54% 0.35% There is value in noting this explicitly, rather than hiding it under a rug of optimizer constraints. The scale of the alphas will depend on the information coefficient of the manager. If the alphas input to portfolio construction do not have the proper scale, then rescale them. Trimming Technique The second refinement of the alphas is to trim extreme values. Very large positive or negative alphas can have undue influence. Closely examine all stocks with alphas greater in magnitude than, say, three times the scale of the alphas. A detailed analysis may show that some of these alphas depend upon questionable data and should be ignored (set to zero), while others may appear genuine. Pull in these remaining genuine alphas to three times scale in magnitude. A more extreme approach to trimming alphas is to force them into a normal distribution with benchmark alpha equal to 0 and the required scale factor. Such an approach is extreme because it typically utilizes only the ranking information in the alphas and ignores the size of the alphas. After such a transformation, you must recheck benchmark neutrality and scaling. 5

6 Describe neutralization and methods for refining alphas to be neutral. Neutralization is the process of removing biases and undesirable bets from Alphas. Neutralization is a sophisticated procedure, but it isn't uniquely defined. There are various types of Neutralization Processes as covered below. Benchmark Neutralization The first and simplest neutralization is to make the alphas benchmark-neutral. By definition, the benchmark portfolio has 0 Alpha, although the benchmark may experience exceptional return. Setting the benchmark alpha to 0 ensures that the alphas are benchmark-neutral and avoids benchmark timing. If our initial alphas imply an alpha for the benchmark, the neutralization process rescales the alphas to remove the benchmark alpha. From the portfolio perspective, benchmark neutralization means that the optimal portfolio will have a beta of 1, i.e., the portfolio will not make any bet on the benchmark. For instance, if a portfolio s modified Alpha has a Beta factor of 1.5 then the same value can be brought down to 1 by making the Alpha benchmark-neutral. Cash-Neutral Alphas In the same spirit, we may also want to make the alphas cash-neutral; i.e., the alphas will not lead to any active cash position. It is possible to make the alphas both cash- and benchmark-neutral. Risk-Factor-Neutral Alphas The multiple-factor approach to portfolio analysis separates return along several dimensions. A manager can identify each of those dimensions as either a source of risk or a source of value added. By this definition, risk factors are those for which, the manager does not have any ability to forecast. Therefore, he or she should neutralize the alphas against such risk factors. The neutralized alphas will include only information on the factors the manager can forecast, along with specific asset information. That is to say, the manager must neutralize the factors for which she is not informed adequately. Once neutralized, the alphas of the risk factors will be 0. 6