 Okay, we’re sold on a closet-indexing approach to the markets. Now we’re investigating a variety of smart-beta 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?

Everyone seems to have a story these days for the “best” way to weigh an index. In this study we look at simple ways to weigh a large-cap stock index using prices only. 

We enter 4 different weighting schemes in our asset allocation weight horse race:

• Equal-weight (EW):  Each stock 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 risk-parity technique applied to the top 250 firms, ignoring covariance between firms.  The volatility weights constructed using the past 12-month idiosyncratic volatility of daily returns (regressed against the value weight market return). Higher volatility = lower weight (explained in detail below).
• Value-weight (VW): Calculated as market cap divided by total market cap of the top 250 largest firms.

Bottom-line up front: Low volatility worked the best on a risk-adjusted basis over the past 87 years. However, low volatility, was close followed by momentum, equal-weighting, and value-weighting, 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 1927-2014).

4 weighting schemes:

• Equal-weight (EW)
• Momentum weight
• Volatility weight (see below)
• Value-weight (VW)

Rebalance: monthly

### Why use a 250 Stock Universe?

We use the top 250 stocks for the following reason: