How Portfolio Construction Affects Momentum Funds

How Portfolio Construction Affects Momentum Funds

November 16, 2015 Active and Passive Investing, Momentum Investing Research

Last updated on January 18th, 2017 at 03:12 pm

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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 common stocks each month (we eliminate REITs, ADRs, ETFs, and Closed-End Funds). 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 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.

vm mom hold period
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

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.

vw mom hold period diff
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

Clearly, there is a relationship between the number of firms, the holding period, and returns.

  1. 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.
  2. 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).

Digging a little deeper into the results

Let’s examine the returns (with some more advanced statistics) on two portfolios. First, we will examine the 50 stock, 1-month holding period portfolio, and compare this to a 100 stock, 6-month hold “low cost” momentum portfolio.

Here are the portfolios we examine:

  1. 50 stocks, 1M hold, VW = Top 50 firms ranked on momentum, held in the portfolio for 1 month. Portfolio is value-weighted.
  2. 100 stocks, 6M hold, VW = Top 100 firms ranked on momentum, held in the portfolio for 6 months. Portfolio is value-weighted.
  3. VW Universe = Returns to the universe of the top 1,000 firms on market capitalization (with 12-month momentum calculation). Portfolio is value-weighted.
  4. SP500 = S&P 500 Total return

Results are gross of management fees and transaction costs. All returns are total returns and include the reinvestment of distributions (e.g., dividends).

Here are the returns (1/1/1970-12/31/2014):

vw mom hold period rets
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

Both momentum portfolios outperformed the index over the past 44 years (also note the high correlation between the universe of stocks and the SP500). This once again documents the out-performance of momentum strategies. However, there is a clear out-performance of the 50 stock, 1-month holding period portfolio, relative to the 100 stock, 6-month holding period portfolio–before fees and transaction costs. Would transaction costs eat the 434 bps spread in returns?

Consider two momentum product offerings:

  • Low scalability, high expected performance strategy: 50 stock monthly rebalanced; 100bps management fee, 25bps rebalance fee
    • 100bps + 12*25bps = 400bps in costs
    • Gross CAGR = 18.00%, Net CAGR ~ 14.00%
  • High scalability, lower expected performance strategy: 100 stock semi-annual rebalance; 25bps management fee, 25bps rebalance fee
    • 25bps + 2*25bps = 75bps in costs
    • Gross CAGR = 13.66%, Net CAGR ~ 12.91%

In the example above, the high octane, high cost momentum fund will have higher net returns relative to the low octane low cost momentum fund.

Of course, we can also come up with scenarios where the benefits of a more concentrated higher-frequency rebalanced momentum fund is negative. For example, if the monthly rebalance costs are 100bps, or 1200bps per year, now the Net CAGR = 18.00% – 13% = 5%, which is worse than the lower cost momentum fund and worse than the overall buy and hold market portfolio. Check out the RAFI piece for more examples and in-depth analysis. The chart below from RAFI shows how important trading costs can be.

momentum transaction costs
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

Learning Points

This simple discussion should highlight a few things:

  • Momentum works on a gross of fee basis.
  • Momentum works even better when it is concentrated and traded frequently.
  • A buyer of momentum products need to consider construction, asset scale, and trading capability of an asset manager before selecting a momentum fund
  • The ideal momentum product built for expected performance is concentrated (~50 stocks), has high turnover (monthly-quarterly rebalance), and limited AUM (<$1B)

Note: This site provides no information on our value investing ETFs or our momentum investing ETFs. Please refer to this site.


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About the Author

Jack Vogel, Ph.D.

Jack Vogel, Ph.D., conducts research in empirical asset pricing and behavioral finance, and is a co-author of DIY FINANCIAL ADVISOR: A Simple Solution to Build and Protect Your Wealth. His dissertation investigates how behavioral biases affect the value anomaly. His academic background includes experience as an instructor and research assistant at Drexel University in both the Finance and Mathematics departments, as well as a Finance instructor at Villanova University. Dr. Vogel is currently a Managing Member of Alpha Architect, LLC, an SEC-Registered Investment Advisor, where he heads the research department and serves as the Chief Financial Officer. He has a PhD in Finance and a MS in Mathematics from Drexel University, and graduated summa cum laude with a BS in Mathematics and Education from The University of Scranton.