The following four procedures comprise most of the institutional portfolio construction techniques: screens, stratification, linear programming, and quadratic programming. In each case the goal is the same: high alpha, low active risk, and low transaction costs.
An active managers value depends on her ability to increase returns relative to the benchmark portfolio that are greater than the penalty for active risk and the additional transaction costs of active management.
(portfolio alpha) (risk aversion) x (active risk)2 (transaction costs)
Screens are just what you would expect; they allow some stocks through but not the rest. A screen can be designed in many ways, but two examples will illustrate how a screen might be used with alpha values to select portfolio stocks (given a universe of 200 stocks). Consider a screen that selects the 60 benchmark stocks with the greatest alphas. We could then construct a portfolio of these high-alpha stocks, either equal- or value-weighted.
Another screening method is based on assigning buy, hold, or sell ratings to all the stocks in the managers universe of investable stocks. For example, we could assign a buy rating to the 60 stocks with the greatest alphas, a hold rating to the 40 remaining stocks with the next highest alphas, and a sell rating to the remaining stocks under consideration. One way to rebalance the current portfolio would be to purchase any stocks on the buy list not currently in the portfolio and to sell any portfolio stocks on the sell list. Portfolio turnover can be adjusted by adjusting the sizes of the categories.
Stratification refers to dividing stocks into multiple mutually exclusive categories prior to screening the stocks for inclusion in the portfolio. For example, we could divide the portfolio into large-cap, medium-cap, and small-cap stocks and further divide these categories into six different industry categories; giving us 18 different size-sector categories. By using percentage weights of these size-sector categories in the benchmark portfolio we can match the benchmark portfolios size and sector coverage.
Stratification is a method of risk control. If the size and sector categories are chosen in such a way that they capture the risk dimensions of the benchmark well, portfolio risk control will be significant. If they are not, risk control will not be achieved.
Stratification will reduce the effects of bias in estimated alphas across the categories of firm size and sector. Flowever, it takes away the possibility of adding value by deviating from benchmark size-sector weights. Using stratification, any value from information about actual alphas (beyond their category) and about possible sector alphas is lost.
Linear programming is an improvement on stratification, in that it uses several risk characteristics, for example, firm size, returns volatility, sector, and beta. Unlike stratification, it does not require mutually exclusive categories of portfolio stocks. The linear programming methodology will choose assets for the optimal portfolio so that category weights in the active portfolio closely resemble those of the benchmark portfolio. This technique can also include the effects of transaction costs (which reduces turnover) and limits on position sizes.
Linear programmings strength is creating a portfolio that closely resembles the benchmark. However, the result can be a portfolio that is very different from the benchmark with respect to the number of assets included and any unincluded dimensions of risk.
Quadratic programming can be designed to include alphas, risks, and transaction costs. Additionally, any number of constraints can be imposed. Theoretically, this is the best method of optimization, as it efficiently uses the information in alphas to produce the optimal (constrained) portfolio. However, estimation error is an important consideration. Consider that for a universe of 400 stocks, quadratic programming will require estimates of 400 stock volatilities and 79,800 covariances. The quadratic program will use the information in the estimates to reduce active risk.
Small estimation error in covariances will not necessarily reduce value added significantly. But even moderate levels of estimation error for the covariances can significantly reduce value added; with 5% estimation error, value added may actually be negative. The importance of good estimates of the relevant inputs, especially covariances, cannot be over emphasized.