In smart beta strategies, defining the set of rules to filter a list of potential stocks is just the first step. To optimize portfolio performance, selecting an appropriate weighting method also plays a crucial role.

Algotrade’s Common Weighting Methods

Below are 03 weighting methods commonly used by Algotrade in smart beta strategies:

Equal weighting;
Market-capitalization weighting;
Industry market-capitalization weighting.

1. Equal Weighting

With the equal weighting method, capital is evenly allocated among the constituent stocks, with the weight calculated as follows:

where:

- w_iis the weight of the capital allocated to stock i;

- N is the number of stocks in the portfolio.

This method is simple, easy to understand, and easy to implement, providing good diversification while avoiding excessive concentration in a few stocks. However, it may potentially allocate too much capital to small-cap and less liquid stocks, leading to increased transaction execution costs.

2. Market-Capitalization Weighting

In the market-capitalization weighting method, the weight of each constituent stock is determined by dividing its market capitalization by the total market capitalization of all the stocks in the portfolio. Market capitalization is calculated by multiplying the number of shares outstanding by the market price per share.

The formula for market-capitalization weighting is as follows:

where:

- w_i is the weight of the capital allocated to stock i;

- Q_i is the number of outstanding shares of stock i;

- P_i is the price of stock i at the time of calculation;

- N is the number of stocks in the portfolio.

The market-capitalization weighting method allocates investment capital proportionally to the market capitalization of the stocks, prioritizing large-cap and high liquid stocks. This method helps minimize trading execution costs and facilitates easy scaling for large portfolios, which is common in index funds. However, this method might lead to excessive concentration in a few large-cap stocks, reducing portfolio diversification. It may also overlook the growth potential of smaller-cap stocks.

3. Industry Market-Capitalization Weighting

This method combines market-capitalization weighting and equal weighting while considering industry classification factors, helps to optimize capital allocation and reduce concentration risk. The weight of each constituent stock is calculated as follows:

After identifying potential stocks, classify them into industry groups based on the ICB or GICS (level 1).
Apply the market-capitalization weighting method to allocate capital to industry groups with constituent stocks. Industry groups without any stocks meeting the selection criteria will have a weight of 0.
Within each industry group, allocate capital evenly to the constituent stocks using the equally weighting method.

This method utilizes the advantages of both equal weighting and market-capitalization weighting. It reflects the market value of each industry group while ensuring diversification within each group.

Overweight or Underweight

Depending on the stock screening criteria and market conditions, there is a possibility that in some portfolio rebalancing periods, very few stocks will meet the criteria. This can result in overweighting a few stocks. Additionally, when using the market-capitalization weighting method, capital may be disproportionately allocated to some stocks compared to others. To mitigate this situation, algorithmic traders can establish a maximum capital weight limit for each stock.

For instance, a smart beta trading strategy employing market-capitalization weighting with a maximum individual stock weight limit of 0.25. Assuming an investment portfolio with 05 stocks that meet the screening criteria, the calculated market-capitalization weights of these 05 stocks might be as follows:

The weights of stocks A and B under the market-capitalization weighting method are w_A^Cap=0.35 and w_B^Cap=0.30, respectively. Since both weights exceed 0.25, applying a weight limit condition sets the portfolio weights for stocks A and B at w_A=0.25 and w_B=0.25.

The excess weight portion for both stocks A and B (0.15=0.35-0.25+0.3-0.25) will be allocated to other stocks or cash.

If the algorithmic trader chooses to allocate the excess portion to other stocks in the portfolio, the weights of the remaining 03 stocks can be increased as follows:

The table below shows the adjusted weights following the implementation of a weight limit condition of 25%:

In addition to setting a maximum weight limit to avoid overweighting capital in a few stocks, the algorithmic trader also needs to consider a minimum weight limit to prevent underweighting capital in a stock. To address this issue, the algorithmic trader can set a minimum weight limit for stocks in the portfolio. For example, if the minimum limit is 0.5%, any stock with a weight less than 0.5% will either be removed from the portfolio or its weight will be increased to this minimum level.

Weighting With Stocks on the Priority List

Stocks on the priority list in the context of smart beta trading strategies are stocks actively selected by the investor to increase their capital allocation in the portfolio, based on information or in-depth analysis beyond the stock screening rules.

At Algotrade, the weighting of priority stocks in smart beta strategies is determined based on the parameter set [f_i; k_i] provided by investors for each stock.

Where:

- f_i is the fixed capital allocation priority for stock i, regardless of whether it meets the stock screening criteria;

- k_i is a multiplier coefficient used to adjust the allocation weight for stock i according to 1 of the 3 allocation methods mentioned above.

For example, an investor designates stock A as a priority stock with the parameter A[f_A;k_A] = A[10%;1.5]. If the investment portfolio includes 03 stocks that meet the screening criteria: A, B and C, the calculated market-capitalization weights before considering the priority stock as follows:

When applying the priority stock condition, the capital weight of stock A is calculated as follows:

The capital allocation weight for stocks B and C is calculated as follows:

Therefore, to implement the smart beta strategy, algorithmic traders can apply the simplest weighting strategy using equal weighting or opt for more complex strategies such as market-capitalization weighting or industry market capitalization-weighting. In practice, combining these weighting methods with minor adjustments can generate numerous different weighting strategies. The general principle is to select the appropriate weighting strategy according to the context, achieve investment objectives, and ensure alignment with the ability to execute the strategy.