Different strategic allocation strategies employ different ways of: (1) estimating future values of key asset variables (return, volatility, correlation); and, (2) combining these variables to set future allocations. Each strategy thus produces a distinct return stream. Does it therefore make sense to diversify across strategies? In his February 2012 paper entitled “Diversifying Diversication Strategies: Model Averaging in Portfolio Optimization”, Felix Miebs examines three approaches for diversifying across strategic allocation strategies: (1) naive average (equal weighting), (2) expected variance minimization; and (3) preceding measurement interval return weighting (strategy momentum weighting). He illustrates the three strategy diversification approaches with a set of eight individual minimum expected variance allocation strategies applied to U.S. stocks (industries or individual stocks). He benchmarks results against a simple equal weighting of the industries or stocks. Using 45.5 years of simulated monthly returns for sets of assets similar to U.S. stocks and empirical monthly returns for four sets of U.S. industries and a set of the largest 250 U.S. stocks during July 1963 through December 2008, *he finds that:*

- While none of the individual minimum variance allocation strategies consistently beat equal weighting on a gross risk-adjusted basis, all three strategy diversification approaches do.
- The performance gains for diversifying across strategies derive from: (1) persistent benefits of diversification across the eight individual minimum variance strategies; and, (2) for the third strategy diversification approach, empirical autocorrelation (momentum) in the returns of these eight strategies.
- Specifically, for the empirical data, the three strategy diversification approaches generate Sharpe ratios 20% to 75% higher than that of the benchmark simple equal weighting strategy. An investor using the simple equal weighting strategy would be willing to pay annual management fees of 1.9% to 4.9% to obtain the improvement.
- The three strategy diversification approaches, particularly the momentum-like approach, involve relatively high turnover, such that their advantages over a simple equal weighting strategy diminish with increasing trading friction. Depending on specific strategy diversification approach and set of industries/stocks data, breakeven (based on Sharpe ratio) one-way trading friction relative the simple equal weighting strategy ranges from 0.05% to 1%.

In summary, *evidence from both simulation and empirical tests indicates that second-order diversification across multiple equity diversification strategies is beneficial for risk-adjusted gross performance.*

Cautions regarding findings include:

- The computational burden described in the paper may be material for many investors.
- Breakeven trading frictions do not seem high relative to estimated trading frictions over much of the sample period (see “Trading Frictions Over the Long Run”).
- Data snooping bias may be material for the best net performance (1% breakeven trading friction relative to a simple equal weighting strategy) of the three strategy diversification approaches across five sets of industries/stocks return data.
- It is possible that applying second-order diversification across asset classes rather than within U.S. equities might affect findings.

All in all, results suggest that simple, first-order diversification via equal weighting is suitable for many investors.

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