How Portfolio Construction Affects Value Funds

How Portfolio Construction Affects Value Funds

May 13, 2016 Value Investing Research, Active and Passive Investing
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(Last Updated On: September 13, 2016)

Value investing is an investment philosophy that has been extensively discussed and examined at least since the days of Ben Graham, who popularized it as a discipline in the 20s and 30s. While there are some who are dismissive of its advantages as a long-term strategy, the historical evidence is compellingly clear: Cheap stocks beat expensive stocks over time (see our simulation study as an example). Of course, on a relative performance basis, value can be excruciatingly painful.

In academia, scholars have gone to great lengths to determine which processes and variations on the value philosophy are most effective. Yet the high-performance strategies identified in academic research are typically not available in the real-world marketplace. There are a number of reasons why this is the case, but they typically boil down to career-risk incentives, scale, and branding. A common mistake by financial service consumers is to focus solely on fees and branding, but little on process. However, while branding is of questionable usefulness, and fees and scale should be considered–process also matters. Here we document how three core elements of portfolio construction can directly affect the historical returns associated with generic value investing strategies (we’ve conducted a similar analysis on momentum):

  1. Number of stocks
  2. Holding period
  3. Portfolio weights

Our bottom line is as follows:

  • The number of stocks matters: more concentration increases gross returns
  • Holding period matters: more frequent rebalancing increases gross returns (not as much as momentum, however)
  • Portfolio weights matter: Equal-weight construction beats value-weight construction

How portfolio construction affects value strategies

In order to explore how these elements have influenced performance historically, we examine mid-large capitalization US-exchange-traded common stocks each month (we eliminate REITs, ADRs, ETFs, and Closed-End Funds), and explore the sensitivity of returns to changes in portfolio construction. In order to insure stocks are adequately liquid (and thus “investable” in a practical sense), we only focus on firms above the 40th percentile for NYSE market capitalization. We calculate a “cheapness” metric using a form of an enterprise multiple; in particular, we calculate EBIT/TEV (similar in spirit to a price-to-earnings ratio, but historically more effective). We use annual fundamentals and update stocks prices (and market capitalization) monthly. We allow the portfolio construction to vary across three 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 over the entire time period).
  • Second, we examine the returns by varying the holding periods. We allow the holding period to vary from 1 month to 12 months.
  • Third, we vary the portfolio position weights using either an equal-weight methodology or a value-weight methodology (i.e., “market-cap” weighted).

We select the top x number of firms ranked on value, 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 12/31/2015 (EBIT/TEV was calculated on 12/31/1969 for the initial portfolio). Results are gross of fees. All returns are total returns and include the reinvestment of distributions (e.g., dividends).

Portfolio Performance

The results below reflect the compound annual growth rates for the various strategies from 1970-2015 for value-weighted portfolios (these portfolios put more weight on larger market-cap companies). The monthly rebalanced 50 stock value strategy (top left) earns 15.37% CAGR, whereas the annually rebalanced 500 stock portfolio (bottom right) earns 12.39% CAGR. It is important to note that all of these results are GROSS of transaction costs. Obviously, as an investor moves up and to the left, transaction costs take a bigger bite out of the gross returns. We leave it to the reader to determine just how big that bite might be.

value funds number of stocks and holding periods 1
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.

The results below reflect the compound annual growth rates for the various strategies from 1970-2015 for equal-weighted portfolios. The monthly rebalanced 50 stock value strategy earns 16.43% CAGR, whereas the annually rebalanced 500 stock portfolio earns 13.86% CAGR. It is important to note that all of these results are GROSS of transaction costs.

value funds number of stocks and holding periods 2
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.

There is a clear relationship between absolute returns and the number of firms, the holding period, and portfolio weightings. In general, it appears that 1) a more frequent rebalance, 2) a more concentrated portfolio, and 3) equal-weighting seem to increase returns, and do so independently.

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, 3-month holding period portfolio (equal-weight), and compare this to a 200 stock, 3-month holding period portfolio (value-weight).

Here are the portfolios we examine:

  1. 50 stocks, 3M hold, EW = Top 50 firms ranked on EBIT/TEV, held in the portfolio for 3 months. Portfolio is equal-weighted.
  2. 200 stocks, 3M hold, VW = Top 200 firms ranked on EBIT/TEV, held in the portfolio for 3 months. Portfolio is value-weighted.
  3. VW Universe = Returns to the universe of our mid to large market capitalization firms (with available EBIT/TEV data). 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 (1/1/1970-12/31/2015):

how portfolio construction affects value funds
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 equal weight and value weight value portfolios outperformed the index over the past 45 years (also note the high correlation between the universe of stocks and the SP500). The spread between the 50-stock and 200-stock portfolio is 1.99%–a number that will definitely make a difference over 45 years. There is also higher volatility associated with the value portfolios; however, as a component in a diversified portfolio structure this risk differential is approximately zero. So the difference between the two value portfolios would primarily be the management fees (and perhaps higher frictional fees): the value weight, more passive closet-index value portfolio will likely having a lower management fee than the equal weight, more concentrated and highly active value portfolio. The optimal long-term expected value portfolio will be determined by the spread in returns between the 1) expected benefits of the active constructed portfolio (~1.99% per year in the example above) and 2) the expected costs (e.g., management fees, frictional costs, etc). If the benefits are ~1.99% and the differential costs are 3.00%, we have a bad deal; if the benefits are 1.99% and the differential costs are 1% we may have a better deal.

Let’s get closer to the real world

Below is an example of two portfolio index constructions (data for the image below was derived on 4/19/2016).

  • The x-axis represents “valuation” based on the percentile rank of EBIT/TEV across the universe of all stocks (1 = cheap, 0 = expensive).
  • The y-axis represents “quality” based on the percentile rank of ROE across the universe of all stocks (1 = quality, 0 = junk).
  • The dots reflect the percentage weight in the respective index.
  • Blue = Quantitative Value Index (based of Wes’ book, Quantitative Value). <50 stock, equal-weight, quarterly rebalance
  • Green = CRSP US Mid Cap Value Index (see methodology here). >200 stock, value-weight, quarterly rebalance
value for scale and for returns
for illustration purposes only

While the fundamental characteristics (cheapness, quality, etc.) of the portfolio holdings are much different depending on how the portfolio is constructed, this is often overlooked by investors. If one believes that firm characteristics, such as cheapness and quality, drive future expected returns, a portfolio construction that is more concentrated on those characteristics will do better than a portfolio that is less concentrated on these characteristics. Of course, these portfolios with more concentration on the characteristics desired will also have more tracking error (and typically more volatility) than a standard benchmark.

Learning Points

This simple discussion should highlight a few things:

  • Value has historically worked on a gross of fee basis.
  • Value works even better when it is concentrated and traded more frequently.
  • Equal-weight portfolios work better than value-weight portfolios (even beyond size exposure)
  • Investors should focus on portfolio construction and holdings characteristics when buying an investment fund.

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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Please remember that past performance is not an indicator of future results. Please read our full disclaimer. The views and opinions expressed herein are those of the author and do not necessarily reflect the views of Alpha Architect, its affiliates or its employees. This material has been provided to you solely for information and educational purposes and does not constitute an offer or solicitation of an offer or any advice or recommendation to purchase any securities or other financial instruments and may not be construed as such. The factual information set forth herein has been obtained or derived from sources believed by the author and Alpha Architect to be reliable but it is not necessarily all-inclusive and is not guaranteed as to its accuracy and is not to be regarded as a representation or warranty, express or implied, as to the information’s accuracy or completeness, nor should the attached information serve as the basis of any investment decision. No part of this material may be reproduced in any form, or referred to in any other publication, without express written permission from Alpha Architect.

Definitions of common statistics used in our analysis are available here (towards the bottom)

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.

  • yg

    very interesting analysis.
    Could you please provide the results (CAGR and sortino) of a portfolio with only 20 stocks (EV) with 3m, 6m and 12m holding periods?
    Many thanks

  • Jack Vogel, PhD
  • Tim Chen

    Thanks for the great post as always.

    When comparing the two value portfolios, why do you focus only on returns vs fees and ignore the difference in volatility? You write that “as a component in a diversified portfolio structure this risk differential is approximately zero.” Since all factor strategies would presumably be held as part of a diversified portfolio, wouldn’t this be grounds for ignoring volatility almost always?

  • Hombre Sinombre

    Terrific post, Jack. I was intrigued to see that returns actually peak under the quarterly re-balancing scenario in the concentrated MW portfolio (convenient, where frictional costs are concerned). I wonder why this quality goes away in the EW portfolio?

  • Hey Tim,
    A lot of the risk won’t diversify away on equity strategies since they all have heavy market exposures (i.e., systematic risk), but the extra risk associated with being more concentrated (i.e., idiosyncratic risk) tends to wash away inside a diversified portfolio. And to directly answer your question, yes, people should invest in a pool of factors and pool them together in a portfolio, however, most investors look at the individual pieces and make decisions based on the performance of a component of their portfolio. If one factor is blowing up they sell it and if another factor is working they buy it. Even though fin pros should have learned why thinking of allocations in isolation (as opposed to the context of a portfolio) is a bad idea, it seems everyone forgets what they learned in school. Weird.

  • Probably just noise. The results in the upper right corner are all about the same

  • Steve

    Just a side point, but it raised my eyebrows slightly.

    Second table (EW CAGR’S)….and only looking at the ’12 month hold’ row (although any row from ‘6 months hold’ onwards will do).

    Over this 45 year period, and assuming a universe of ~1000 stocks (as mentioned)…there was zero difference whether you bought the top decile, top quintile or top tertile (and the top vigintile was no better than the top decile for that matter).

    I just didn’t notice quite the slope downward that I would have expected. Though there is a little bit.

    This might be the universe of large cap stocks. Going out further in market cap might bring more of a pronounced stair step down.

    Anyway, not important – but interesting enough to me. From a practical standpoint, the wider you can go (e.g. top 3 deciles as opposed to top decile) the more opportunity you will have to find quality, momentum or whatever you’re looking for after first finding, ‘cheap’. That is, assuming an investor is using a, ‘screen upon screens’ approach rather than a weighting approach (that Asness argues gets you more exposure to the desired factors) – but now that’s a whole other topic!

  • Arek

    Thanks for the post Jack, I am wondering if these Quant value strategies keep working same good nowadays as they did in the past. Is the Internet a structural change because fundamental data is now much easier to access than 30 years ago? Would it be possible to see a table with the yearly returns for the last 15 or 20 years? Thank you

  • Jack Vogel, PhD

    Good question — all strategies should be examined through the lens of how sustainable they are — here is a post regarding value that you may find interesting:

    Also, even if a strategy has some sustainable edge, it needs investors that are willing to stick with the program.

    I hope that helps.

  • Mark

    Interesting post. I was a little skeptical of the notion that value works better when it is traded more frequently so I set up a test in Quantopian. I tested two algorithms the Magic Formula (a proxy for Quantitative Value) and the Acquirer’s Multiple (a proxy for Deep Value). My test period was from 2007-2016 (not long enough for sure). I also tested with and without the Robust Asset Allocation (RAA) model. Lastly, I used a commission cost of $1/trade and I limited trades to only take 25% of available volume.

    I’ve posted some results, the first chart is for yearly rebalance, MF = Magic Formula, AM = Acquirer’s Multiple. While the second is for a 3month rebalance.

    It seems that a 3 month rebalance adds a little value to the MF strategy, but significantly detracts from the AM strategy. Again this is not a long enough backtest, but it does seem like a reasonable conjecture that a deep value strategy requires a longer holding period for it to perform well.

  • Jack Vogel, PhD

    Thanks for sharing, when you state that you use the RAA model, what signals are you using on the Value stock portfolio?

  • Mark

    Hi Jack,

    Thanks for responding. I believe I’ve implemented the RAA model as described in the DIY investor, that is
    Rule 1 – Test for Time Series Momentum and invest .5 weight of portfolio if Excess Return > 0.
    I use SPY and SHY as proxies for the S&P and T-bill returns

    Rule 2 – Test for Simple MA and invest .5 if current price of SPY is > 12-month MA

    Otherwise stay in cash.

  • Jack Vogel, PhD

    Thanks for sharing, those signals are correct.

    For the buy-and-hold portfolio on our universe, I found the 12-month hold slightly better over that time period as well.

  • Mark

    Hi Jack,

    Is your buy and hold universe an implementation of the Quantitative Value Algorithm described in Wes’s book? My proxy for that (the Magic Formula) seems to do well with more frequent rebalancing, its the deep value portfolio the needs the extra time to outperform.

  • Jack Vogel, PhD

    It is a similar universe — the QV algo requires 8 years of data, while this only requires 1 year. Both only examine what we consider to be mid/large cap stocks (market capitalization above the 40th percentile for NYSE listed firms). The QV algo takes into account the quality of the firm (after already being in the value bucket).

  • Doug01

    Thank you very much for sharing this.

    Equal weighting beats value weighting. That makes sense.

    Fewer stocks beats more stocks. I’ve read a previous post on this forum, where the most concentrated portfolio you tested was 15 stocks, but the risk adjusted return was worse than 30-50 stocks. Patrick O’Shaughnessy did an analysis of the optimal number of stocks, and if IIRC, the optimal risk adjusted number was 20. So a portfolio in the 20-50 stock range also makes sense.

    The greatest uncertainty I have is holding period. I’ve never seen any research, that found you needed less than a 3 year holding period, to get the value premium. And commonly a 5 year holding period works.

    Your research is the first that I’ve found that looks at holding periods of less than one year for value investing. And you’ve found that the shorter the holding period, the greater the return, at least down to a one month period. When I’ve seen research presented on the optimal rebalancing frequency for other stock market anomalies, more frequent rebalancing results in greater return. So that also makes sense.

    When I look at the equal weighted portfolios, I notice the following, with the exception of the 500 stock portfolios. Whether you use a 6 month or 12 month holding period makes little difference. And in the 6-12 month holding period, the returns are similar for portfolio sizes ranging from 50 to 300 stocks. When holding period becomes less than 6 months, it starts to have more of an impact. And the difference due to a concentrated portfolio also become more noticeable with a holding period of less than 6 months.

    But the problem with shorter holding periods are the increased costs. One would be taxes. For American investors, whether you have a holding period of more or less than one year makes a difference, when it comes to cap gains. Multiyear holding periods may result in cap gains tax deferral. When holding periods are less than 1 year, such as comparing 3 to 6 months, tax deferral is not an issue. Short holding periods may allow one to minimize dividends. And if there is a difference between your tax on cap gains and dividends, then that might influence length of holding period. And an ETF wrapper would definitely help, when it comes to cap gains.

    However, transaction costs will increase, as holding period shortens. Transaction costs are difficult to generalize about.

    The above publication examined the issue of transaction costs. It was published in 1995, which may limit its usefulness. The stock universe was about 2500 American stocks between 1963-1988.

    They divide the market into quintiles by price/book and market cap. After 1.0% transaction costs and annual rebalancing, investors would have outperformed the market by 4.82%, if they invested in the 4% of the market that consisted of the smallest and cheapest stocks by quintile. With 2.0% transaction costs, the outperformance was 3.89%. See Table 2.

    What was the optimal rebalancing frequency? Table 3 addresses that question. It assumes 1% transaction costs. Yearly return outperformance for a rebalancing period of 1 year was 5.28%, 2 years 7.14%, 3 years 7.05%, 4 years 6.93%, 5 years 6.32%, 6 years 5.99%, 7 years 5.84%, 8 years 5.35%, 9 years 4.90% and 10 years 4.42%.

    In a taxable account, one can’t exclude that a 3 or 4 year holding period might might be the optimal one.

    Your stock universe is about 1000 mid to large cap stocks. So transaction costs will likely be less of an issue than with 2500 stocks, which will be predominately small cap stocks. Optimal holding period may vary, as a function of the average/median market cap of a portfolio.

  • Thanks for sharing your thoughts. Agree with everything you’ve mentioned. Frictional costs and taxes always matter.
    As you mentioned, ETF structures can deal with the tax problem, but you’re still left with frictional costs. There really isn’t any way around that problem except to say that the amount of capital that can be deployed at any given time will be limited and constrained. And if you have Warren Buffett money, a 5yr holding is probably all you can do–his wallet is simply too fat to allow him to be nimble.