## Momentum in SA equities over different lookback periods

It’s been a while since a posted the previous post in which we looked at momentum in SA equities over a 6 month look back period (skipping the latest month). We also showed how the volatility of the highest stock momentum portfolio looked reasonably predictable (or at least wasn’t random noise). Is 6 month’s optimal though for a lookback period? That’s something we want to address in this post.

In general we keep the portfolio construction process the same as in the previous post:

- At the end of each month calculate the momentum (over a specific lookback period) of the top 80 stocks (skipping the most recent month).
- Rank the stocks from highest to lowest momentum placing each stock in one of five portfolios based on this ranking (highest to lowest).
- Equal weight each stock using closing prices of the following trading day (i.e. we are assuming the we readjust the portfolio at the end of the next day).
- Allow the weights to float until the next formation/month (this replicates an actual portfolio – each stock is equal weighted at the beginning of the month but price changes will change the weights during the month).
- Returns are net of dividends and capital adjustments and exclude transaction costs.

**Going long the top momentum stocks**

First we look at portfolios that go long the top quintile of momentum stocks (equal weighted and re-balanced at the end of each month). Below are the cumulative returns (on a log-scale):

It’s a bit messy but we have highlighted the top and bottom two. Interestingly 6 months’ is a rather “middle-of-the-pack” performer. The more longer-term, 12 and 24 month portfolios seem to do better (and consistently so). As expected the longer the lookback period the lower the returns, although too short and the returns are even worse as highlighted by the 2 month portfolio.

We have shown the total return (annualised) and Sharpe ratios below. This further illustrates this “polynomial” relationship – if the lookback period is either too short or too long a (long-only) momentum portfolio’s return degrades. The 12 to 24 month period again seems to be fairly optimal.

**A long-short portfolio**

The above analysis was only for a long-only portfolio (long the top momentum stocks). Here we look at a long-short portfolio: long the top momentum stocks and short the lowest momentum stocks. This will give us a good idea of how sustainable momentum is at different lookback periods and whether mean reversion is more prevalent at specific periods.

We have to be careful here, since the period above only stretches from 2004. Momentum worked really well since 2011 – so no matter which lookback period we used we would have done well. Clearly this isn’t going to continue forever and so we need to contrast post-2011 performance with pre-2011 performance.

The 36 and 48 month portfolios seem to be the worst performers and returns are actually negative until 2011. The best performer is once again the 12 month portfolio (even pre-2011).

The annualised returns and Sharpe ratios highlight a similar relationship to the lookback period, although the 6 – 12 month portfolios seem to be fairly optimal. Returns decline from the 12 month lookback onwards.

**Conclusion**

You can never be sure what the future will hold in terms of optimisations and how these parameters will evolve going forward. However, from both the long and long/short portfolios it seems like 12 months has done pretty well both pre- and post-2011. However, from the charts of the annualised returns and Sharpe ratios it seems like anything between 6 and 12 months is a decent pick as a lookback period.

*Although every effort is made to ensure accuracy in the data and analysis presented on this site, this cannot be guaranteed. Nothing on this site constitutes investment advice, nor should it be taken as such. And obviously, past results do not guarantee future performance.*