We wrote last week that stock selection by construction, e.g., using factors such as stock fundamentals, does not trade off risk and return but does explicitly and transparently tilt a portfolio toward the desired stock characteristics or risk factor(s). When we just trade off risk and return, such as is the case when volatility minimization is used to build a low-volatility portfolio, the methodology does not take into account the individual stocks’ characteristics. As a consequence, the methodology could be adding unwanted risk(s) that come from the stock characteristics “preferred” by the risk-return methodology. The risk-return methodology of portfolio construction, therefore, could lead to an implicit (versus explicit) tilt toward certain risk factors. We concluded last week’s article with the statement that, in contrast to the lack of clarity noted in the article, a stock-selection scheme and a risk-return methodology necessarily come with explicit objectives and a clear way of judging how well the portfolio performs vis a vis its market-cap-weighted index (or a suitable market-cap-weighted benchmark). In the current article we highlight two ways of using stock selection and risk-return tradeoffs to build a better smart-beta fund portfolio.
Clark and Kenyon  demonstrate a way to build two different smart-beta fund portfolios: (1) generate a series of monthly portfolios that outperformed the S&P 500 over the past 30 years, and (2) generate a set of monthly portfolios that outperformed the Russell 1000 Growth index over the past 15 years.
The constraints Clark and Kenyon worked with were: (1) turnover is not to exceed 8% per month; (2) the minimum stock position is set at 0.35% of the net asset value of the portfolio; (3) the maximum stock position is set at 4% of the net asset value of the portfolio; and (4) there is a target market-capitalization constraint, where the average market capitalization of the portfolio must be greater than the average market capitalization of all stocks available to purchase in the current month (this last constraint means both portfolio sets will be “large-cap.” The S&P 500 and the Russell 1000 Growth are large-cap indices). The final common constraint Clark and Kenyon faced was to choose stocks that maximize the scores generated by a multi-factor stock model. (This constraint typifies the use of fundamental financial data to select stocks that are potential candidates for the monthly portfolios.)
There was one additional constraint regarding the Russell 1000 Growth smart-beta fund portfolios: they could not exceed the average book-to-price value of all stocks available for purchase in the current month. Meeting this constraint meant the smart-beta funds generated the required growth portfolios for the Russell 1000 Growth pool.
Clark and Kenyon work with the constraints by using two multiobjective optimization programs (MOPs). A MOP problem differs from a single-objective optimization problem, e.g., classical mean-variance optimization, because it contains several objectives that require optimization. When a single-objective problem is optimized, the best single design solution is the goal. But, for a multiobjective problem with several (possibly conflicting) objectives, there is usually no single optimal solution. Therefore, the decision-maker is required to select a solution from a finite set of possible solutions by making compromises. A suitable solution would need to provide acceptable performance over all objectives.
Clark and Kenyon’s first MOP generated for each month 30 potential portfolios with all the constraints being met except turnover and position limits. The first MOP was, then, a stock-selection scheme. The second MOP evaluated each of the 30 portfolios by trading off the turnover, position, mean return, and variance constraints. The “best” portfolio of the 30 was the one with the highest Sharpe ratio after the constraints of the second MOP were met. The process was repeated each month for the 30 years of S&P 500 data and for the 15 years of monthly data for the Russell 1000 Growth. The second MOP was, therefore, a risk-return methodology.
Clark and Kenyon’s S&P 500-based smart-beta fund portfolio had between 150–200 stocks each month versus the S&P 500’s 500 stocks, a large-cap market capitalization in all periods, statistically significant stock selection as measured by tools such as Zephyr and MSCI Barra, an annualized nonrisk-adjusted return of 13% (after transaction costs) versus the S&P 500’s 9%, and a Sharpe ratio of 1.8 versus the S&P 500’s 1.1.
The smart-beta Russell 1000 Growth portfolio had large-cap market capitalization in all periods, the necessary growth tilt, statistically significant stock selection as measured by tools such as Zephyr and MSCI Barra, an annualized nonrisk-adjusted return of 14% (after transaction costs) versus the Russell’s 10%, and a Sharpe ratio of 0.2 versus the Russell’s 0.1.
Guerard et al. demonstrated the impact of momentum investing on smart-beta portfolios. Their portfolios had tilts toward momentum and value, with momentum being given the larger weight. Their stock selections after optimization outperformed a comparable equal-weighted portfolio and the S&P 500 for the period from January 1998 to December 2007. Similar to Clark and Kenyon, the Guerard et al. portfolios had very significant asset-selection results and high degrees of total active return. The Guerard et al. model also had higher total managed return than either the equal- weighted portfolios or the S&P 500.
In this final article in our series on smart-beta funds we have shown the value of using both stock selection and risk-return trade-off when building smart-beta fund portfolios. The consistency of the outperformance of these portfolios, whether against established benchmarks or an equal-weighted portfolio, suggests manufacturers of smart-beta funds would benefit from taking a closer look at their own methodologies versus the methodologies described here.
 A. Clark and J. Kenyon, “Using MOEAS to Outperform Stock Benchmarks in the Presence of Typical Portfolio Constraints,” Journal of Investing, Volume 21, Number 1.
 The minimum- and maximum-position constraints also imply a cardinality constraint. Dividing 100% by 0.35% yields 286, which is the maximum number of stocks any portfolio can have. Dividing 100% by 4% gives 25, which is the minimum number of stocks any portfolio can have.
 The details and back-testing of the multi-factor stock model can be found in Chapter 3 of Handbook of Portfolio Construction, edited by John Guerard. Clark and Kenyon thank John Guerard for supplying the multi-factor scores and all of the other data used in these models.
 J.B. Guerard, G. Xu, and M. Gultekin, “Investing with Momentum: Past, Present, and Future,” Journal of Investing, Volume 21, Number 1.