By now, we’re sold on a closetindexing approach to the markets. Now, we’re investigating a variety of smartbeta products available in the market that weigh a large portfolio of stocks with some algorithm. But a natural question arises when trying to pick smart beta ETFs:
What is the Optimal Method to Weigh an Index?
These days, everyone seems to have a story for the “best” way to weigh an index. In this study, we look at simple ways to weigh a largecap stock index only using prices. [1]
We enter four different weighting schemes in our asset allocation weight horse race:

Equalweight (EW): Each stock is given a weight of 1/250.

Momentum weight: Each stock’s momentum is measured over past 12 months. Momentum score (1+momentum) calculated for top 250 firms. The momentum weight is given by momentum score divided by sum of all momentum scores. Higher momentum score = higher weight.

Volatility weight: Simple riskparity technique applied to the top 250 firms, ignoring covariance between firms. The volatility weights constructed using the past 12month idiosyncratic volatility of daily returns (regressed against the value weight market return). Higher volatility = lower weight (explained in detail below).

Valueweight (VW): Calculated as market cap divided by total market cap of the top 250 largest firms.
Bottomline up front: Low volatility worked the best on a riskadjusted basis over the past 87 years. However, low volatility was close, followed by momentum, equalweighting, and valueweighting, respectively. Across the board, results are similar.
Let’s dig into the details on the different strategies we test in this study.
Asset Allocation Weight Approaches — List of the Strategies and Details
Universe: largest 250 domestic stocks every month (99.5% correlated w/S&P 500 from 19272014).
4 Weighting Schemes:

Equalweight (EW)

Momentum weight

Volatility weight (see below)

Valueweight (VW)

Rebalance: monthly
Why use a 250 Stock Universe?
We use the top 250 stocks for the following reason:
In the 1920s and 1930s, there were fewer stocks (around 500 total). We want to focus our results on larger firms, so we pick the top 250 stocks.
Our goal is to identify a weighting scheme that works for a large pool of capital. We want to minimize the impact of poor liquidity and frictional costs, which can be substantial.
In the end, our choice of a 250 stock universe doesn’t matter that much:
From 7/1/1927 – 12/31/2014, the valueweight returns to the top 250 stocks each month is 99.5%, correlated with the S&P 500 returns (valueweight index). Summary statistics are shown below:
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.
Asset Allocation Weighting Scheme Detail — Volatility Weight
To construct volatility weights, we estimate the volatility (σ_i ) of all available stocks (using data up to month t1) and set the portfolio weight in asset class i to:
We estimate σ_(t,i ) as the 12month idiosyncratic volatility of daily returns (regressed against the value weight market return). The number k_t is the same for all stocks and controls the amount of leverage of the volatility weighting portfolio. The unlevered volatility weights (we only study unlevered returns in this report) are obtained by setting:
This portfolio overweights less volatile assets and underweights more volatile assets.
Example: Let’s say that we have 3 stocks A, B, and C which each have volatilities 5%, 10%, and 20% respectively (this corresponds to σ above). Then,
So stock C, with the highest volatility, gets the lowest weight at 1/7; while stock A with the lowest volatility gets the highest weight at 4/7.
Core Results

Results are gross, no fees are included

All returns are total returns and include the reinvestment of distributions (e.g., dividends)

Portfolios are rebalanced monthly
Legend
Top 250 EW = Equalweighting the largest 250 firms
Top 250 Vol = Volatilityweighting the largest 250 firms
Top 250 Mom = Momentumweighting the largest 250 firms
Top 250 VW = Valueweighting the largest 250 firms
SP500 = S&P 500 Total Return Index
Hypothetical performance results have many inherent limitations, some of which, but not all, are described in the disclosures at the end of this document. No representation is being made that any fund or account will or is likely to achieve profits or losses similar to those shown herein. In fact, there are frequently sharp differences between hypothetical performance results and the actual results subsequently realized by any particular trading program. Indexes are unmanaged, and do not reflect management or trading fees, and one cannot invest directly in an index.
Monthly Rebalance — Full Sample: 7/1/1927 – 12/31/2014
Over the entire time period, Volatility and Momentum weighting have the highest performance (CAGR, Sharpe, Sortino ratios).
Equalweighting, Volatilityweighting techniques and Momentumweighting all beat the standard valueweighting technique.
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.
Monthly Rebalance — First Half: 7/1/1927 – 12/31/1971
Over the first half of the sample, Volatility and Momentum weighting have the highest performance (CAGR, Sharpe, Sortino ratios).
Equalweighting, Volatilityweighting techniques and Momentumweighting all beat the standard valueweighting technique.
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.
Monthly Rebalance — Second Half: 1/1/1972 – 12/31/2014
Over the second half of the sample, Volatility and Momentum weighting have the highest performance (CAGR, Sharpe, Sortino ratios).
Equalweighting, Volatilityweighting techniques and Momentumweighting all beat the standard valueweighting technique.
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.
And the winner of our asset allocation weight horse race is…
Volatility weighting has the highest Sharpe and Sortino Ratio in all periods and has the highest riskadjusted returns.
Momentum weighting has the highest CAGR in all periods, but follows volatility weighting on a riskadjusted basis.
Equal weighting works better than the value weight index, but the effect is marginal.
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.
What Have We Learned?
Our three alternative weighting techniques all have better CAGR, Sharpe and Sortino ratios, compared to the standard valueweighting technique. However, we must point out that investors must account for trading costs and taxes — a value weight index can minimize both. If an investor decides to use an alternative index weighting technique, they may want to consider using ETFs to accomplish this goal.
‘What Asset Allocation Weights are Most Effective?’ was originally posted by Wesley R. Gray at Alpha Architect. Please read the Alpha Architect Disclosures at your convenience.
DISCLOSURE: The views and opinions expressed in this article are those of the authors, and do not represent the views of equities.com. Readers should not consider statements made by the author as formal recommendations and should consult their financial advisor before making any investment decisions. To read our full disclosure, please go to: http://www.equities.com/disclaimer
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