We have already documented the returns to generic momentum investing strategies. Within the fund marketplace, many investors focus on fees and less on process. For example, Morningstar highlights the fees as “cost-efficient” for a specific momentum fund, MTUM. However, fees are only one part of an investment decision–process also matters–especially when it comes to momentum-based stock selection strategies. Here we hope to document how portfolio construction (number of stocks, holding period, and weightings) affects returns.
Our bottomline is as follows:
- Holding period matters: more frequent trading increases gross returns
- Portfolio size matters: more concentration increases gross returns
Our analysis of momentum investment strategies
We examine the top 1,000 largest US-exchange-traded firms each month. We calculate the momentum variable as the cumulative returns over the past 12 months, ignoring the past month (academic construction). We allow the portfolio construction to vary across two dimensions:
- First, we examine the returns by varying the number of firms in the portfolio. We allow the portfolio size to vary from 50 to 500 stocks (Universe is 1,000 stocks).
- Second, we examine the returns by varying the holding periods. We allow the holding periods to vary from 1 month to 12 months.
We select the top x number of firms ranked on momentum, every month. Here, the number of stocks x can be 50, 100, 150, 200, 250, 300, or 500. These firms are held in the portfolio for y months. The holding period (number of months) y varies from 1 to 12. Portfolios with holding periods over 1 month are formed by creating overlapping portfolios. (see Jegadeesh and Titman 1993).
The returns runs from 1/1/1970 to 12/31/2014 (momentum was calculated on 12/31/1969 for initial portfolio). Results are gross of fees. All returns are total returns and include the reinvestment of distributions (e.g., dividends).
Value-Weight Portfolio Performance
The results below reflect the compound annual growth rates for the various strategies from 1970-2014. The monthly rebalanced 50 stock momentum strategy earns 18.00% CAGR, whereas the annually rebalanced 500 stock portfolio earns 11.20% CAGR. Important to note, all of these results are GROSS of transaction costs.
For context, there are no concentrated high-turnover momentum funds with which we are aware (we are actively looking to solve that problem via our quantitative momentum philosophy). However, there are many examples of diworsified, lower-frequency momentum funds in the market place. See Gary Antonacci’s analysis of momentum-based stock-selection strategies for examples.
In the chart below we look at results benchmarked against the 50 stock monthly rebalanced results. For example, the 500 stock annually rebalanced portfolio has a CAGR that is 6.80% less than the 50 stock monthly rebalanced momentum portfolio.
Clearly, there is a relationship between the number of firms, the holding period, and returns.
- The holding period is important. Holding the number of firms constant, the lower the holding period, the higher the CAGR. Examining the 50 stock portfolios, the CAGR falls from 18.00% when holding the stocks for 1 month, to 11.91% when holding the stocks for 12 months.
- The number of firms is important. If we keep the holding period constant, the less firms in the portfolio, the higher the CAGR. Examining the portfolio with a holding period of one month, the CAGR falls from 18.00% when selecting the top 50 stocks, to 12.46% when selecting the top 500 stocks.
Overall, there is a near monotonic relationship along both dimensions (holding period and number of firms). The results are almost identical when equal-weighting the portfolios (higher CAGRs, similar pattern).