Optimal Stock Quantity, Selection and Weights for Momentum Investing

By Rujeko Musarurwa

To try and maximise return the correct recipe of ingredients must be brought together. Not only do we have to look at the quality of stock selection, but the weights and quantity of stocks required for maximising returns and minimising risk. Momentum investing looks to invest in top performing stocks and combining this technique with good diversification skills and portfolio optimisation should result top performing portfolios. An added benefit is that transaction costs will be minimised if the correct stocks are picked right from the beginning as less buying and selling will have to be done in the future.

This article will aim to answer the following three questions:

  1. How to pick the right amount of stocks to optimize a portfolio?
  2. How to pick the best stocks to include in the portfolio?
  3. How to get the weight for each stock in the portfolio right?

1. Picking the correct amount of stocks for your portfolio

Picking the correct number of stocks to place in a portfolio has been debated upon for a large number of years now. I believe that the ultimate number of stocks should be 15 stocks for our model regardless of the investment strategy used and I will go into detail in the following paragraphs as to why this is my belief.

  • A case for more stocks – Many researchers have supported the idea of using a large volume of stocks (greater than 50), believing that the more stocks you have, the greater the diversification and thus the lower the risk. A major issue however is that although the stocks are many, if they are highly positively correlated with each other then the portfolio may not be as highly diversified as it should be and the risk to the portfolio is still high. Additionally, having too many stocks and thus too much diversification can hinder potential profits and higher returns as usually lower risk is associated with lower returns. In the case of momentum investing, having too many stocks in a portfolio would not be advisable because it is nearly impossible to find that many stocks all performing really well at the same time and to foresee all these stocks continue to grow in the future.
  • A case for fewer stocks – On the other side of the coin many researchers believe in having a concentrated portfolio of stocks where a few number of stocks are carefully selected and risk can still be diversified by taking time to analyse them thoroughly. Looking at the figure below, we can see that after 20 stocks the amount of risk that can be diversified away becomes significantly less and less and adding more stocks at this stage actually hinders returns more than limiting risk. Many believe that holding too little stocks is too risky but as stated by Lazardnet (2015), most diversification benefits are realized after only adding a few selected stocks to the portfolio.

Std dev vs. no. of stocks

  • Optimal number of stocks – Focusing on the two opposing views above, it would make sense to go with the latter. It seems more beneficial to pick between 15 and 20 stocks because in this area we can see that the standard deviation would more or less be the same as taking 30 stocks. I personally feel that 10 stocks would be too little to achieve a good level of diversification and 20 stocks seem to have same risk as 15 stocks and thus I would further agree with my view earlier on that 15 stocks is ideal.
    Lazardnet (2015) also mentions that adding extra stocks to a portfolio is not a beneficial or only means of method for diversifying a portfolio but that the combining diversified cash flows approach is a better method. With his approach, 20 companies with different operations and objectives are placed in a portfolio in order to combine best ideas and not just top ideas of analysts. This approach furthermore aims to achieve, “the optimal combination of stocks by understanding the revenue, earnings, cash flow and balance sheet contribution of each individual company,” (Lazardnet, 2015) and will be discussed in detail as the next section of this paper.

2. Picking the best stocks for portfolio optimisation

Finding the best performing stocks with sustainable long term performances is the end goal of this paper. A desirable outcome would be a portfolio that not only increases returns but minimises risk of picking the wrong factors and maximises exposure to outperforming factors.

For diversification and portfolio optimization we take a look at the following:

Economic & other factors

  • Past performance and stock price movements – Investors should have a look at the historical chart 52-Week high for stocks that have performed well. Additionally it is also advisable to invest in stock prices that make significant positive movements and not ones that are stagnant or only increase slightly every year.
  • Geography – a portfolio should consist of stocks from different countries. In this way, should a disaster happen in one country it won’t affect your portfolio as much as it would if all your stocks were from that one country.
  • Industry – same as the above, if portfolio is diversified and stocks are from different industries, if one industry does badly, your portfolio will not be as affected.
  • Transaction costs – these costs can lessen the profits made from a portfolio. The better the stocks that are picked, the less the buying and selling and the less the transaction costs.

Company characteristics

Picking sustainable top performing stocks will be achieved by investing in companies with good characteristics (quality and value) driving their increased performance. According to a study by Sagi (2007), firms with the following characteristics showed a positive relationship between past and future returns i.e. momentum and thus higher returns:

  • Firms with high revenue growth volatility
  • Low cost of goods sold
  • High market-to-book value
  • Momentum profits are increasingly higher during market expansion.

Additional company characteristics to consider are:

  • Value ratios – Combining several value ratios into an investment strategy can be very beneficial to portfolio returns and research by James O’Shaughnessy shows that relying on one metric only can hinder profits. A metric that works now e.g. PE ratio might not give the best indication for the future and thus a combination of value ratios should be considered and analysed.
  • Company risk profile – this involves reading and analysing market news and company specific news to see if the company will be susceptible to any future risks. For example if a company might be taken over in the future, or if a new legislation will be coming into action that will negatively impact the company and thus the company’s stock price.

Risk factors

Ideally, portfolios that perform well are ones with high risk, high Sharpe ration and portfolios that include stocks that are highly negatively correlated and thus fully diversified.

Modern portfolio theory states that returns are normally distributed and that higher returns are associated with higher risk. However a lot of research has proved that this does not have to be the case and that high returns do not have to be associated with higher risk.

  • Risk vs. Return – According to a study carried out by Capital Ideas (2012), greater returns were achieved without added risk. This high return, low risk outcome was accomplished by stocks with strong negative correlation between momentum and value within and across different assets as compared to a higher risk associated with individual investment strategies used on their own.
  • ETFs – Economic noise (n.d.) states that their method for achieving high returns and minimising risk that works is that every month they analyze each asset class and select the best two performing ones that show the most potential looking forward. They then purchase low-cost, highly liquid ETFs that give their investors exposure to each of the selected asset classes and place equal weights on each of the two.
  • Dual momentum – A study mention by Advisory Group (2014)’s article that was carried out by author Gary Antonacci is one based on dual momentum and is said to be the best form of investing according to their research. Dual momentum is the combination of relative strength and trend-following, i.e. not only following past performance but picking best performing stocks compared to their peers. In this study, Gary Antonacci found that the best performing strategies are not always ones with the highest risk and that higher return does not necessarily have to follow from high risk. As we can see in the figure below, Global equity momentum strategy produced the highest return of about 17.5% but with a risk of only  about 12.8% whereas the Relative Momentum strategy had the highest risk of about 16.3% but did not attain the highest returns.
    The figure below also shows that the strategy that performed the best, Global Equity Momentum strategy was the one that was a combination and inclusive of the other three strategies proving once again that a combination of strategies performs better than the strategies on their own.

Risk vs Return profile

3. Getting each stocks portfolio weight right

I would encourage all investors to ask themselves the following questions:

  • How would it benefit investors to place the correct weights on each stock in a portfolio from inception?
  • How much more would it benefit investors to know the right moment in which to shift stock weights i.e. buy or sell a stock in order to gain higher returns?

Traditionally, stocks in a portfolio were equally weighted as a way of diversification but after some additional research a much better approach was found to be one were heavier weighting was placed on the stocks that would perform better than the rest of the group. An approach to further improve this method could possibly be to divide the stocks equally amongst industries and economies and then pick the strongest performing ones within that industry and place the most weighting on them in contrast to placing heavier weights on stocks that may all be in the same industry.

No researcher has yet to mention an exact weighting that should go towards the best performing stock and as time goes by and the portfolio is monitored, the weightings will change and therefore there not need to be a reason to have a set percentage for a particular stock. Some researchers use a proportional method where the percentage weighting depends on the size on each individual company’s market capitalization but the main problem with this technique is that the largest company may not be the best performing one and thus heavier weight should not be placed on it.

Practical tests for stock weighting

Qusma (2012) assessed a relative strength and momentum approach that used factor momentum in an attempt to tilt the allocation towards factors showing strong momentum and away from factors with weak momentum.
The way in which this approach worked is that they decomposed returns into their principal factors (e.g. inflation or growth) and based a weighting algorithm on factor momentum and this had the effect of having a portfolio that only included the factors required. Target betas were set and then the difference between target betas and realized betas minimized given a set of weights and using the following formula:
Formula 1

Qusma (2012), stated that a future more beneficial method to stock weightings would be to better their model by means of finding a more lucrative way of calculating betas taking each factor’s volatility and momentum into account. This view is closely similar to Gestaltu (2013)’s view that weighting portfolio assets according to their individual risk contribution improves portfolio performance.

  • Gestaltu (2013)’s study used momentum score as a weighting tool. They applied a Gaussian transform to the cross-sectional momentum across lookback horizons and their formula however different from Qusma (2012)’s formula, resulted in similar results that momentum weighting resulted in higher portfolio returns.
    The Gaussian method uses the formulas below to determine asset weights:

formula 2



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Sagi, J., 2007. The myths of momentum investing. Vanderbilt University. [online] Available at: http://www.owen.vanderbilt.edu/faculty-and-research/vanderbilt-business-inbrief/the-myths-of-momentum-investing.cfm [Accessed 19 June 2015]

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