## Top-Momentum S&P500

The Efficient Market Theory and Random Walk Theory are standard theories in investing. These theories are based on the assumption that markets can quickly and efficiently adjust to new information. Stock prices therefore reflect all information that’s available in the market. Thus, future prices move in a random manner and cannot be predicted.

Momentum, the fact that a trend tends to continue, is the most persistent deviation from these standard theories. It is a so-called Market Anomaly and extensive evidence of its existence can be found in literature. Literature about Factor Investing introduces factors, that can all be seen as Market anomalies. Besides Momentum, Value, Size and Low-volatility are the most important factors. But definitely Momentum is the strongest and most persistent Factor.

With our Single Momentum and Double Momentum Investment strategies, we trie to harvest the benefits of Momentum in the market as a whole. We do so by staying in or out of an Index Tracker (ETF) depending on the actual momentum of the Index.

In this section, we will move beyond ETF’s and construct portfolio’s of individual stocks with high momentum. As we did for SMI and DMI, for these Top Momentum Portfolio’s we will perform backtesting and evaluate returns, volatility and maximum drawdown.

**Construction of Top-Momentum Portfolio’s**

For the construction of our Top-Momentum Portfolio’s, we start with all stocks that constitute the Standard & Poor’s 500 Index at this moment.

For every month starting from january 1986, we calculate a momentum variable for all these stocks. We use the same momentum variable as Fama and French in their well-known 2008 article ‘Dissecting anomalies’. For month j the momentum variable is the 11-month return for j-12 to j-2. Like Fama and French, we skip the return for the month before the return to be explained because of the evidence of negative correlation (reversal rather than continuation) of month-to-month returns.

Next, for every month, we make a ranking of the momentum value of all the stocks considered.

We then construct equally weighted Top-Momentum portfolios with n (5,10, 15, … ,150) stocks with highest momentum. Rebalancing of the portfolio’s can be done every 1 to 12 months.

**Return, Volatility and Max Drawdown of Top-Momentum portfolio’s**

**Analysis**

The more concentrated in Top-Momentum Stocks, the better the annualised return of the portfolio is (Figure 1). Actually the strenght of Momentum is nicely illustrated by the exponential decline in return when larger numbers of different Top-Momentum Stocks are held. A portfolio of only the five best Top-Momentum Stocks has far better returns than a portfolio with the fifty best Top-Momentum Stocks.

The absolute values of the returns are very high compared to the returns of the S&P500 Index. We must admit there is possible bias in our data: survivor bias. We constructed our portfolios starting with all stocks that constitute the Standard & Poor’s 500 Index at this moment. Next for every month starting from january 1986 we ranked these stocks by the value of the momentum variable. Of course, the composition of the S&P500 Index changes over time. Some of the stocks that were removed from the Index might have had excellent momentum values before their removal. If we would have taken all historical constituents of S&P500 into account, some of the Stocks that were later removed, could have been part of the Top-Momentum Portfolios. And we don’t know how these Stocks would have performed afterwards.

Despite survivor bias, we are strongely convinced our Top-Momentum Portfolios do far better than the S&P500 Index. A strong argument is the exponential growth in return in more concentrated Top-Momentum Portfolios. Moreover, our results are in line with the results described in a very interesting paper* by Han Liu, John Mulvey and Tianqi Zhaoz from Princeton University. In their second real data experiment the authors apply an investment strategy to a large data set including 1500 stocks over a 34-year investment horizon from 1981 to 2014. In the first step they implement a momentum-based investment procedure to preselect 50 stocks. The authors report an annulized return of all 50 stocks of 27.66% (table 4.5 in the article). As can be seen in our Figure 1, this is comparable to the returns of our Top-Momentum Strategy with 50 Top-Momentum Stocks.

* Han Liu, John Mulvey & Tianqi Zhao (2016) A semiparametric graphical modelling approach for large-scale equity selection, Quantitative Finance, 16:7, 1053-1067, DOI: 10.1080/14697688.2015.1101149

Of course, return is not the only outcome parameter of interest. As can be expected Volatility is higher (Figure 2) and Maximum Drawdown is more negative (Figure 3) in more concentrated porfolios. Thus, the Top-Momentum Strategy offers no protection against Volatility or large Drawdowns.

When looking at different rebalancing periods, we see Monthly Rebalancing results in better returns and lower volatility compared to longer rebalancing periods. Maximum Drawdown, though, is more negative with Monthly Rebalancing.

**Parameter settings**

When choosing the settings for our 2 parameters (number of top momentum stocks and rebalancing period), we look for an optimal risk/return ratio.

The Sharpe ratio (excess return (return – riskfree rate)/volatility) is commonly used for this purpose. If we calculate the Sharpe ratio for our TopMomentum Strategies, we get the results, shown in figure 4.

In figure 4 we see the Sharpe Ratio is highest with 10 TopMomentum Stocks and monthly rebalancing. Even if all 10 TopMomentum stocks would be completely uncorrelated (which is impossible), we don’t feel comfortable with a portfolio that’s this minimally diversified. In this case the Maximum Sharpe Ratio doesnot offer a well balanced portfolio since the impact of the phenomenal returns is too high.

Probably a better way to appreciate the risk/return ratio for our TopMomentum Strategies, is shown in the figures below. In figure 5, 6, 7 and 8 the first subplot shows the number of years (from 1986 till 2021) with positive or negative returns; the second subplot shows the years in which the strategy outperformed or underperformed relative to the S&P500 Index. We did the calculations for portfolios with 10 (n10) to 35 (n35) TopMomentum Stocks. The R value in the figures stands for the rebalancing period in months.

The figures show that with monthly rebalancing we have the highest number of years with positive return. We see that for monthly rebalancing there is an optimum around 25 to 27 Stocks. With 25 tot 27 TopMomentum Stocks and monthly rebalancing we have the most years in which returns are positive and in which the strategy outperforms the S&P500 Index.

For longer rebalancing periods the picture is less clear but even with yearly rebalancing we see most outperformance of the strategy in portfolios with 28 to 30 TopMomentum stocks.

**TopMomentum Portfolios of choice**

In our premium section we provide investors with uptodate information in order to construct the TopMomentum portfolios they prefer with different numbers of TopMomentum stocks and different rebalancing periods. Since we found an optimum around 25 stocks, our portfolios of choice are 25TopMomentumStocks portfolios. Therefore in the following figures we will look more closely at the historical returns of these 25TopMomentumStocks portfolios and compare them with the return of the S&P500 Index.

In figures 12 to 16, we see that for all rebalancing periods the 25TopMomentumStocks strategy rarely underperformed relative to the S&P500 Index. When there is underperformance, the difference is small; when there is overperformance, very often the difference is larger. This observation can be made for the complete period, starting in 1986. It can be seen in the last 10 to 15 years as well. In these last years, the possible survivor bias, we talked about earlier (here), is definitely not at play.

**Top-Momentum Portfolios Conclusions**

Portfolios of Top-Momentum Stocks generate excellent annualized returns. If we look back 36 years, from 1986 till 2021, the more the portfolios are concentrated, the better the annualized returns. When looking for optimal risk-return ratios, we found out portfolios of around 25 Top-Momentum stocks, performed best. With monthly rebalancing these portfolios had negative returns in only 1 out of 36 years. And they underperformed relative to the S&P500 index in only two years. When they underperformed the difference was small; in contrast, when they outperformed the index, the difference was often much higher.

**The practical use of TopMomentum Portfolios**

In our premium section, premium subscribers can find the current composition and returns (YTD) of the Top-Momentum portfolios of our choice. This section also contains all necessary information to build Top-Momentum Portfolios of one’s personal preference.

We believe a thorough study of history will help investers to perform better. We congratulate our subscribers for their choice for scientifically based investing strategies and we wish them a lot of succes