Do any equity asset allocation strategies convincingly outperform equal weighting (1/N) after accounting for data snooping bias and portfolio maintenance frictions? In their December 2016 paper entitled “Asset Allocation Strategies, the 1/N Rule, and Data Snooping”, Po-Hsuan Hsu, Qiheng Han, Wensheng Wu and Zhiguang Cao apply tests based on White’s Reality Check to compare out-of-sample performances of 23 basic allocation strategies and 5,490 combinations of these strategies to that of equal weighting (1/N) after accounting for snooping bias and portfolio frictions. The 23 basic strategies encompass: conventional mean-variance optimization; mean-optimization with parameter shrinkage (to avoid extreme allocations); the capital asset pricing (1-factor) model (CAPM); the Fama-french 3-factor model (market, size, book-to-market); the related 4-factor model (adding momentum); CAPM augmented with a cross-sectional volatility factor; a missing factor extension of CAPM; minimum variance; maximum diversification; equal risk contribution; volatility timing; and, reward-to-risk timing. Strategy combinations use two or three of the basic strategies with weights varied in increments of 10%. They apply these strategies to each of seven sets of equity assets: (1) 25 size and book-to-market sorted U.S. stock portfolios; (2) 49 industry U.S. stock portfolios; (3) the stocks in the Dow Jones Industrial Average; (4) 22 developed country stock indexes; (5) the combination of (1) and (2); (6) 93 long-lived stocks from the S&P 500 Index; and, (7) 100 size and book-to-market sorted U.S. stock portfolios. Specifically, they each month estimate model parameters and asset weights in each dataset based on the most recent 60 months, and then calculate respective strategy performances the next month. They set one-way trading frictions for all assets at either 0.05% or 0.50% to estimate net returns. They focus on associated Sharpe ratios and certainty equivalent returns (CEQ) as strategy performance metrics. Using the specified monthly data mostly since July 1969 (but since July 1990 for developed country markets and since July 1996 for S&P 500 Index stocks) through December 2014, *they find that:*

- Before addressing snooping and portfolio maintenance frictions, or allowing short selling, for the 23 basic allocation strategies:
- The Sharpe ratio of 1/N beats the average Sharpe ratio of the more sophisticated allocation strategies for six of seven datasets.
- The best strategy usually beats 1/N by a large margin.
- The best strategy varies across datasets.

- After addressing snooping and portfolio maintenance frictions:
- For 0.05% one-way trading frictions, only a few of the 23 basic allocation strategies beat 1/N, all within datasets (1) and (7) above.
- For 0.50% one-way trading frictions, the only basic allocation strategies beating 1/N are within dataset (7).
- Outperformances of the best strategies relative to 1/N are much reduced.
- Allowing short selling slightly increases the number of strategies that beat 1/N.
- Including 126 strategies that pick the current strategy based on recent past performance of all 23 basic strategies identifies only a few additional strategies that beat 1/N.
- Including 5,490 combinations of two or three of the 23 basic allocation strategies identifies a few more outperforming strategies.

In summary, *evidence supports belief that simple equal weighting of equity assets is hard to beat on a net basis.*

Cautions regarding findings include:

- The study considers equities and equity portfolios only, mostly for the U.S. market. Findings may differ for other asset classes.
- Actual portfolio maintenance frictions vary considerably over the sample period, generally high early and low late (see “Trading Frictions Over the Long Run”). The assumption of fixed one-way frictions of 0.05% or 0.50% do not account for this variation and may both be too low early in the sample period.
- Data required to execute many of the strategies were likely not available in a timely enough manner early in the sample period to support portfolio reformation assumptions.
- For scenarios that allow short selling, calculations do not account for any costs of short selling or infeasibility of short selling (lack of shares to borrow).
- Analyses do not consider any fees that most investors would bear for delegating execution of sophisticated strategies.
- The significance tests used assume that monthly return distributions are tame. To the extent that returns are wild, these tests lose meaning.

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