Momentum investing, portfolio optimisation, and diversification

By Rujeko Musarurwa

It is nearly impossible to get the right mix of stocks to achieve maximum returns. A lot of time and effort has been spent trying to renovate and build upon old theories in order for investors to gain maximum returns. Wouldn’t it be ideal to be able to invest in stocks that are increasing in price and will continue to increase into the future? 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? These are just some of the questions that I will aim to answer.

This will be the first article in a 4 part series of articles. I will attempt to come up with a portfolio that will provide the best returns for momentum investing whilst actively managing the portfolio. In this first article I will be discussing the combination of momentum investing, portfolio optimisation and diversification and despite some researchers disagreeing with these two theories working together, most researchers agree that combination of strategies work well together and I will discuss how and why these specific strategies can work jointly. The second article will discuss the diversification method and give you an insight on how to pick the correct stocks and correct number of stocks followed by a third article that will discuss the portfolio optimisation area i.e. the risk-return tradeoff that should give the best stock selection by using normal distribution formula and other methods. The fourth article will combine all the topics previously discussed in order to formulate the ultimate model and discuss why the model should work.

Modern portfolio theory or momentum investing strategies on their own should not be strategies to rely on. A passive portfolio left to wither through equities ups and downs in hope that in the end a good return will still be achieved makes no sense to me at all and neither does going long or short in top performing stocks. Portfolio optimisation and diversification compliments momentum investing and vice versa.

Company characteristics positive impact on success

Research undertaken by Sagi (2007) in partnership with Mark Seasholes provided a new framework for improving momentum strategies. They found that the underlying reason for the strategy’s success lies behind the company’s change in risk overtime caused by specific company characteristics. More importantly they found that profits will be higher for high revenue-volatility, low-cost and high book-to-market companies. Taking this information into consideration, it would be of benefit for me to add this information into the model. Adding this enhanced momentum strategy to portfolio optimisation and diversification may improve a new model by placing heavier stock weightings in a portfolio on companies that exhibit these characteristics.

A detailed look at mutually coupled strategies

According to research done by Larson (2013), momentum is only a strong strategy when additionally added to another core strategy. He advised long-term investors to pick a more stable factor as a core strategy and in this case I would pick portfolio optimisation and diversification to play the role of core strategy. Portfolio optimisation and diversification would assist in the portfolio not only being based on finding the best performing stocks but also taking risk and stock weights into consideration.

In additional research done by Light (2012), he describes momentum as being one of his company’s favourite strategies as it can be coupled with other strategies to beat the market and avoid crashes. He combined momentum with relative strength where relative strength is picking the best performing asset out of a portfolio of assets. His research however did not convince him that the strategy was exceptionally good as yes, it did give him good risk factor results but he felt the lowest point and worst month results were a bit too high. This got me thinking that picking the best performing stocks from portfolios could benefit a newly formed portfolio that included these best performing stocks. This new momentum strategy could then be combined with portfolio optimisation and diversification to form a model that could achieve higher returns and perhaps lower the worst month and lowest point results and provide higher returns.

Opposing research and its rationale

In contrast to the above, Jegadeesh and Titman (1993) used naïve diversification and found that naïve diversification returned better results than passive strategies over a period of 3 to 12 months. However, a major drawback of this research was that it did not take into account transaction costs. Jonsson and Radeschnig (2014) agreed with this study and concluded that portfolio optimization did not necessarily complement momentum investing and did not give significantly higher risk adjusted returns. Their research also found that naïve portfolio diversifies away systematic risk and believe that returns are obtained by holding out-performing assets over quarters. Their research however also has the major flaw of not taking transaction costs into consideration.


To conclude this section, I would say that I agree with the majority of researchers in that the two strategies combined provide better and higher returns and as such I will proceed to try and build a model that incorporates previous findings and add to them ingredients that may be missing that may enhance the model. Thus, in my next article I will be discussing an in depth analysis of the stock selection in reference to momentum investing. The article will attempt to show what characteristics and weightings should apply to each stock in the portfolio to ultimately achieve higher returns.



Jegadeesh, N and Titman, S., (1993), Returns to Buying Winners

and Selling Losers: Implications for Stock Market Efficiency, The Journal of Finance,

Volume 48, Issue 1 (Mar.,1993), pp. 65-91.[pdf] Available at: [Accessed 23 June 2015]

Jonsson, R and Radeschnig, J., 2014. Momentum investment strategies with portfolio optimization. [online]. Available at: [Accessed 19 June 2015]

Larson, R., 2013. Hot potato: Momentum as an investment strategy. Research affiliates. [online] Available at: [Accessed 19 June 2015]

Light, L., 2012. How to Beat the Market: The New Momentum Strategy. Forbes. [online] Available at: [Accessed 19 June 2015]

Sagi, J., 2007. The myths of momentum investing. Vanderbilt University. [online] Available at: [Accessed 19 June 2015]

4 replies
  1. Samit Ahlawat
    Samit Ahlawat says:

    Which strategies are being combined here? Momentum investing with relative strength index? Relative strength index is a technical indicator. Momentum investing depends on the exact method used to identify momentum stocks. Researchers have used returns over past 6 months. Using relative strength index on winnners in momentum portfolio may amount to picking a higher percentile of winners from plain momentum style portfolio. Idea sounds nice though, looking forward to see the next article.

    • Rujeko
      Rujeko says:

      Hi Samit,

      The relative strength I am referring to is when you buy the one stock out of a basket of stocks that has the strongest performance over time and yes this is different to relative strength index. This is very interesting as not just top performers (momentum strategy) are picked to be included in a portfolio but top performing stocks that perform better than their peers in their own portfolios. Light (2012) did an excellent study on this and you can find it available at:

      Thank you very much for your comment and I look forward to you reading my next article.

  2. johan
    johan says:

    Hi there,
    Thank you for highlighting a very interesting topic indeed. Just a few reflections.

    You mentioned some company specific factors (P/B, Rev vol, etc) that Sagi (2007) found correlated with future stock returns. A lot has happened in the field of beta factors since then and there are nowadays quite a vivid flora of beta factors (JPM is using 72 different ones if i remember correctly).
    Hence, it might be beneficial to test some of these in combination with Momentum for the weighting of stocks in the portfolio.

    How do you define Momentum in your models? Do you use the ex-post return between to fixed dates (historical quarterly returns), or MA or MACD or something else?

    Regarding the actual optimisation. My experience is that the portfolio gets very sensitive to changes in exp return and variance. What are your thoughts about how stabilise the optimisation in order to make it robust?

    Kind regards,

    • Rujeko
      Rujeko says:

      Hi there Johan,
      I do believe it would be a good idea to incorporate some of the more currently used beta factors in combination with momentum for our portfolio.
      With regards to your momentum question, we are still looking into what type of calculations to use as there are many to select from.
      Lastly, please kindly clarify your last question for me in order for me to answer it, specifically “My experience is that the portfolio gets very sensitive to changes in exp return and variance.”


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