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Unconstrained Minimum Variance Portfolio: Tools, Performance, and Constraints

Explore the tools used in Minimum Variance (MinVar) Portfolio construction, comparative performance against benchmarks, and impact of style/sector constraints. Discover alternative methods for style tilts. Historical evidence and performance analysis provided.

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Unconstrained Minimum Variance Portfolio: Tools, Performance, and Constraints

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  1. Variations on Minimum Variance Ruben Falk, Capital IQ Quantitative Research March 2011

  2. Agenda • Quick overview of the tools employed in constructing the Minimum Variance (MinVar) Portfolio • Features of a basic unconstrained MinVar Portfolio and comparative performance against the main benchmarks • Impact on performance of imposing constraints such as style or sector neutrality • Alternative methods for imposing style tilts within the minimum variance framework

  3. The Tools • Capital IQ US Fundamental Risk Model • 140 Alphaworks factors aggregated into 8 style factors: Value, Momentum, Earnings Quality, Analyst Expectations, Historical Growth, Capital Efficiency, Volatility, Size • Other factors: Market factor and 24 industry factors based on GICS • Responsiveness: Based on daily returns with serial correlation adjustment • Capital IQ ClariFI Mean-Variance Optimizer • State of the art solver for Mixed Integer Quadratically Constrained Quadratic Programming problems • Capital IQ ClariFI Portfolio Attribution Framework: Classic side-by-side factor based risk and return attribution

  4. Historical Evidence • Early work from HAUGEN/BAKER (1991). For the period covering the years 1972 to 1989 the authors found that a MinVar portfolio would outperform the Wilshire 5000 at lower risk • Many studies followed the original paper. For the US stock market CHAN/KARCESKI/LAKONISHOK (1999), SCHWARTZ (2000) and JAGANNATHAN/MA (2003) and CLARKE/SILVA/THORLEY (2006) found both higher returns and lower realized risks for the MinVar portfolio versus a capitalization weighted benchmark • For global equity markets GEIGER/PLAGGE (2007), POULLAOUEC (2008) and NIELSEN/AYLURSUBRAMANIAN (2008) all find similar results • SCHERER (2010) shows that 79% of the variation of the MinVar portfolio’s excess return can be attributed to exposure to low market beta and low stock specific risk. Value and size are other characteristics noted

  5. The Anomaly Security Market Line Empirical MinVar Portfolio Efficient Frontier Return Market Portfolio Theoretical MinVar Portfolio Risk

  6. Base Case Minimum Variance Portfolio • Portfolio size $1.5BN (initial), long only • Monthly rebalancing, Apr. 1998 to Oct. 2010 • Objective: Minimum Variance at each rebalancing • Risk Model: Capital IQ US Fundamental Medium Term • Universe: S&P 1500 • Max 100 Holdings (not always binding) • Max trade size: 10% of ADV • Trade costs: 25bps • Max holding size: 3% of portfolio per name • Threshold holding and trade size: $50k

  7. Base Case MinVar Performance

  8. Base Case MinVar Performance Note: The annualized risk numbers in this presentation are based on monthly returns. Using daily returns, the risk of the Base Case MinVar portfolio is 13.4% and the S&P 500 is 21.8%

  9. Base Case MinVar Portfolio Factor Attribution The Base Case MinVar portfolio has a low average beta of 0.48 and derives most of its return from stock specific sources

  10. Base Case MinVar Sector Attribution against S&P 1500 The Base Case MinVar portfolio on average overweightstraditionally defensive sectors such as Consumer Staples and Utilities while underweighting IT and Financials

  11. Base Case MinVar Cap. Group Attribution against S&P 1500 The unconstrained MinVar portfolio heavily underweights the top market cap. decilewhile, on average, overweighting decile 2-5 and staying neutral to the bottom half market cap names in the S&P 1500. However on average, the top Market cap. decile still represents 34% of the MinVar portfolio by value

  12. Base Case MinVar v. Fama-French 3 Factor Model Returns Market and Value (but not Size) loadings were statistically significant at the 95% level in explaining the returns of the Base Case MinVar portfolio. The Market beta was about the same as when using the CIQ risk model at 0.5 while the exposure to Value was positive which is consistent with the results of Scherer (2010)

  13. Optimal Turnover & Holding Period (Base Case)

  14. Implementing Sector & Style Neutrality & Style Tilts • Imposing sector neutrality on the Base Case with respect to the S&P 1500 (+/-2%) has the effect of pushing up the market exposure which increases risk while return suffers as we can’t achieve a defensive sector allocation • Imposing strict style neutrality on the Base Case shows some promise in terms of providing higher returns and return/risk ratio but the problem often isn’t feasible • Three scenarios for style neutrality with flexible tilts (lower bound of the style exposure is zero but no upper bound) • Earnings Quality tilt • Value Tilt • Both Value & Price Momentum Tilt

  15. Performance of MinVar Portfolios with Value Style Tilts • The tilted MinVar portfolios generally outperform both on absolute and risk adjusted return • The sources of outperformance are: more efficient market exposure, higher stock and industry specific returns, and the fact the style contributions to return are mostly negative when not constrained

  16. Market & Style Exposures: Base Case v. Single Tilts

  17. Style Exposures: Price Momentum & Value Tilt The style factor exposures have ICs of 0.08 and 0.13 with respect to 1-month forward factor returns of Price Momentum and Value respectively. The Value exposure IC is statistically significant at the 95% while the Price Momentum exposure IC is only statistically significant at the 84% level

  18. MinVar with Flexible Style Tilts Spreads Cumulative Active Return vs. S&P 500

  19. Global MinVar Performance • Base Case and Value tilted global MinVar portfolios constructed using the same parameters as for the US portfolios except drawn from the S&P 1200 universe *Pre transaction costs. Transaction costs impact annual returns by 0.7% in the Base Case **Capitalization weighted Note: Returns are compounded

  20. Base Case Global MinVar Country Attribution vs. S&P 1200

  21. Summary • From Apr. 1998 to Oct. 2010, our MinVar portfolio without sector or style constraints easily outperforms the S&P 500 and S&P 1500 with much lower risk • Portfolio construction with a minimum variance objective naturally lends itself to a large cap. but not mega-cap. bias • During this period, the minimum variance objective has the effect of over allocating to traditionally defensive sectors such as Consumer Staple and Utilities while under allocating to Financials and Technology • Imposing sector constraints has the effect of lowering returns and increasing risk • Style constraints, however, when combined with certain specific style tilts, enhance the performance of the MinVar portfolio • As a side effect, the style factor exposures that are generated from minimum variance portfolio construction provide useful input for factor switching strategies, at least in the case of Value and Price Momentum • The results are quite robust for different style tilts which suggests that many existing strategies could use minimum variance as a performance enhancing overlay • Initial results appear generally consistent for global portfolios

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