What modifications must investors make to minimum variance portfolios to make them more attractive than equal weighting? In their April 2017 paper entitled “Asset Allocation with Correlation: A Composite Trade-Off”, Rachael Carroll, Thomas Conlon, John Cotter and Enrique Salvador assess conditions under which a minimum variance portfolio (requiring only estimates of asset covariances) beats an equally weighted portfolio. In particular, they test minimum variance portfolios that:

- Employ one of three ways (one constant and two dynamic) to estimate future asset return correlations.
- Consider a range of correlation forecasting horizons.
- Do and do not have shorting restrictions.
- Limit turnover by rebalancing only when: (1) any weight drifts outside a fixed percentage band; or, (2) any asset drifts outside a no-trade range based on its volatility, such that each asset has the same probability of triggering (allowing riskier assets more latitude).
- Have rebalancing frictions of either 0.2% or 0.5% of traded value.

These variations enable analyses of trade-offs among parameter estimation error, correlation forecasting horizon, turnover and rebalancing frictions. Their key portfolio performance metrics are volatility, Sharpe ratio and turnover. They consider seven asset universes for forming minimum variance portfolios: 10, 30 or 48 U.S. industry portfolios during January 1970 through December 2013; 20 portfolios of U.S. stocks sorted by size and book-to-market ratio during January 1970 through December 2013; stock indexes for nine developed countries during January 1980 through December 2013; the 30 stocks in the Dow Jones Industrial Average during January 2003 through December 2012; and, the 197 stocks continuously listed in the S&P 500 Index during January 1996 through December 2012. Using daily returns in excess of the risk-free rate for the assets in these universes, *they find that:*

- On a gross basis, dynamic correlation minimum variance strategies emphatically both beat a static correlation minimum variance strategy and equal weighting across datasets.
- The correlation forecasts, not the variance forecasts drive outperformance.
- Short-horizon correlation forecasts are more effective than long-horizon forecasts.

- However, high turnover and rebalancing frictions significantly reduce performance of minimum variance strategies. Restricted short selling and relaxed rebalancing are necessary to enable net outperformance of equal weighting.
- Even for low rebalancing frictions (0.2%), only minimum variance portfolios without short selling statistically outperform equal weighting.
- For higher frictions (0.5%), outperformance is elusive, suggesting that large investors are best able to exploit minimum variance strategies.
- In general, minimum variance portfolio performance improves as rebalancing rules are increasingly relaxed.

In summary, *evidence indicates that exploiting minimum variance effects requires short-horizon dynamic correlation forecasting, exclusion of short positions and rules that suppress portfolio rebalancing.*

Cautions regarding findings include:

- Testing many strategy variations and datasets introduces model and sample snooping biases (sources of luck), such that the best-performing strategy/dataset overstates expectations.
- Several universes consist of indexes or similar aggregations, which do not account for the costs of maintaining tradable assets and therefore overstate returns.
- Dynamic minimum variance portfolio reformation processes are beyond the reach of many investors, who would bear fees for delegating to a fund manager.
- The S&P 500 Index sample incorporates survivorship bias by ignoring stocks removed from the index, thereby likely overstating performance of portfolios formed from this sample.