Does the size effect exist? Probably.

Does the size effect exist? Probably.

July 2, 2014 Key Research, Research Insights, Value Investing Research
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Executive Summary:

Case for NO Size Effect

The traditional small-minus-big value-adjusted long/short factor (SMB) developed by Gene Fama and Ken French has arguably added NO value over time. Performance over the past 30 years has been flat and highly volatile (1983-2013).

smb
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.

We create an extreme size value-adjusted factor (E-SMB), which is formed based on quintile splits on size (the original SMB factor is based on median splits). If size is a contributing factor to long-term returns, we should see an even larger premium associated with E-SMB.

The data say otherwise: our results show WORSE performance for E-SMB relative to SMB.

These baseline results question the validity of the “small-cap effect.”

Case for a Size Effect

But why has older research (e.g., Banz’s 1981 Journal of Finance Economics paper) identified a size effect? Turns out the the devil is in the details.

Older research looks at microcaps and the spread between long portfolios sorted on size. For example, the researchers will compare the performance of a long-only small-cap portfolio and a long-only large-cap portfolio. In more recent work, researchers look at long/short portfolios, or portfolios such as ESMB and SMB.

Examining long/short portfolios (Fama/French method) produces different insights than comparing long-only portfolios (Banz method).

When one examines the size effect using the techniques used by older research articles (i.e., Banz 1981) there is still a size effect. The data suggest there are large spreads between small firms and large firms. Moreover, even after controlling for value, one can still identify large spreads between small firms and large firms.

What’s the bottomline?

Identifying a size effect depends on the methodology employed!

From the perspective of a buy and hold investor, the size effect is still alive and well.

Intuitively, there should be SOME premium to buying small cap stocks due to their limited liquidity and transparency relative to larger firms.


Strategy Background:

Here is a brief description of the Fama/French Factor construction:

  • The Fama/French factors are constructed using the 6 value-weight portfolios formed on size and book-to-market. (See the description of the 6 size/book-to-market portfolios.)
  • SMB (Small Minus Big) is the average return on the three small portfolios minus the average return on the three big portfolios. NOTE: SMB is not simply small firms minus big firms—there is adjustment that averages the returns for portfolios sorted on value. It also breaks stocks out based on median size, which is a coarse measure.
    • SMB =1/3 (1+2+3) – 1/3 (4+5+6). (See graphic below)
  • HML (High Minus Low) is the average return on the two value portfolios minus the average return on the two growth portfolios,
    • HML =1/2 (Small Value + Big Value) – 1/2 (Small Growth + Big Growth).
  • MOM is the average return on the two high prior return portfolios minus the average return on the two low prior return portfolios,
    • MOM =1/2 (Small High + Big High) – 1/2(Small Low + Big Low).
  • Rm-Rf, the excess return on the market, value-weight return of all CRSP firms incorporated in the US and listed on the NYSE, AMEX, or NASDAQ that have a CRSP share code of 10 or 11 at the beginning of month t, good shares and price data at the beginning of t, and good return data for t minus the one-month Treasury bill rate (from Ibbotson Associates).
  • LTR = 10-Year Total Return

2014-06-30 13_40_38-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)

–> SMB is a value-adjusted size factor
–> HML is a size-adjusted value factor
–> MOM is a size-adjusted momentum factor

The FF size Factor (1/1/1927 to 4/30/2014)

Factor Summary Statistics

  • SMB is the poorest performing factor.
2014-06-30 13_42_31-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)
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.

Invested Growth (1/1927 to 4/2014)

  • Size has performed over the long-haul, but with extreme volatility.
2014-06-30 13_45_01-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)
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.

Invested Growth vs. Factors (1/1927 to 4/2014)

  • SMB is the worst performing factor.
  • MOM incurs extreme drawdowns.
2014-06-30 13_46_19-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)
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.

Rolling 5-Year CAGRs (1/1927 to 4/2014)

  • Highly cyclical.
  • SMB has acted as a hedge for HML at certain times in history (e.g. late 60’s, late 70’s and early 80’s)
2014-06-30 13_47_45-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)
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 FF Size Factor — Recent 30 Years (10/1/1983 to 4/30/2014)

Factor Summary Statistics

  • SMB has poor performance.
2014-06-30 13_49_48-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)
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.

Invested Growth (10/1983 to 4/2014)

  • Poor performance over the past 30 years.
2014-06-30 13_50_59-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)
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.

Invested Growth (10/1983 to 4/2014)

  • The worst performing factor
2014-06-30 13_51_58-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)
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.

Rolling 5-Year CAGRs (10/1983 to 4/2014)

  • More correlated to the value factor than in previous periods.
  • Highly cyclical.
2014-06-30 13_53_46-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)
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 Extreme Size Factor (1/1/1927 to 4/30/2014)

We examine the Fama-French 25 portfolios and construct an “extreme SMB” factor, or E-SMB.
Construction:

  • E-SMB (Small Minus Big) is the average return on the five small portfolios minus the average return on the five big portfolios, E-SMB =1/5 (1+2+3+4+5) – 1/5 (21+22+23+24+25). (See graphic below)
  • Prediction: If the size effect exists, it should be stronger for E-SMB relative to SMB.

–> E-SMB is a value-adjusted extreme size factor

2014-06-30 13_55_27-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)

Summary Statistics (1/1927 to 4/2014)

  • E-SMB has low CAGR and extremely high volatility
2014-06-30 13_57_44-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)
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.

Invested Growth (1/1927 to 4/2014)

  • E-SMB and SMB are highly correlated.
  • The long leg looks a lot like a high volatility version of the short leg.
2014-06-30 13_58_40-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)
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 FF Size Factor — The “Banz” Period (1/31/1936 to 12/31/1975)

  • We examine the period studied by Banz’  in his 1981 Journal of Financial Economics paper, “The Relationship Between Return and Market Value of Common Stocks.”
  • Banz finds strong evidence for a “small-cap” effect. (He has a unique testing environment that we will discuss later in this report).

Construction:

  • SMB (Small Minus Big) is SMB =1/3 (1+2+3) – 1/3 (4+5+6). (See graphic below)
  • E-SMB (Small Minus Big) is the average return on the five small portfolios minus the average return on the five big portfolios, E-SMB =1/5 (1+2+3+4+5) – 1/5 (21+22+23+24+25). (See graphic below)
  • Prediction: If the size effect exists, it should be stronger for E-SMB relative to SMB.

–> E-SMB is a value-adjusted extreme size factor

2014-06-30 14_00_52-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)

Factor Summary Statistics (1/1936 to 12/1975)

  • E-SMB or SMB are poor long/short portfolios.
2014-06-30 14_01_58-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)
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.

Was Banz Crazy? — Size Deciles and Quintiles (1/1/1936 to 12/31/1975)

We look at the returns to small and large quintiles and deciles (NYSE break-points for market capitalization) over the same time period as the Banz paper (1936 – 1975).

Overall we find that the way you weight the portfolios, such as value-weight or equal-weight, has a large impact on the so called “size effect.”

Value-weighting the portfolios produces a spread between small and large firms of 2.73% and 4.36% for the quintile and decile portfolios, respectively. However, equal-weighting the portfolios produces a spread between the small and large firms of 7.19% and 9.98% for the quintile and decile portfolios, respectively.
Banz was correct in describing the outperformance of small stocks over his time period.
Banz creates the long/short portfolios using the following methodology:

As an illustration, consider putting equal dollar amounts into portfolios containing the smallest, largest and median-sized firms at the beginning of a year. These portfolios are to be equally weighted and contain, say, ten, twenty or fifty securities. They are to be held for five years and are rebalanced every month. They are levered or unlevered to have the same beta.

Results:

The average excess return from holding (ten) very small firms long and very large firms short is, on average, 1.52 percent per month or 19.8 percent on an annualized basis.

So the large difference between large and small caps is generated using 20 firms (10 long, 10 short) as well as leverage (unsure how much).

–> Using 100 stocks (50 long and short), the paper finds about a 12% difference between small and large firms, which is similar to our 9.98% spread for the decile portfolios.

Banz is correct that there is a significant difference (if you use equal-weighting) between small and large firm returns during the 1936 – 1975 time period.
Last, a quote from the Banz paper:

There is no theoretical foundation for such an effect. We do not even know whether the factor is size itself or whether size is just a proxy for one or more true but unknown factors correlated with size.

VW Size Portfolios (1/1936 to 12/1975)

  • Small caps generate outsized returns, but also have extreme volatility.
2014-06-30 14_05_53-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)
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.

EW Size Portfolios (1/1936 to 12/1975)

  • Large CAGR outperformance; large volatility increases.
2014-06-30 14_07_11-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)
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.

Was Banz Crazy? — Size Deciles and Quintiles (1/1/1927 to 4/30/2014)

We look at the returns to small and large quintiles and deciles (NYSE break-points for market capitalization) over the entire time period (1927 – 4/2014).
Overall we find that the way you weight the portfolios, such as value-weight or equal-weight, has a large impact on the so called “size effect.”

  • Value-weighting the portfolios produces a spread between small and large firms of 2.50% and 3.85% for the quintile and decile portfolios, respectively.
  • However, equal-weighting the portfolios produces a spread between the small and large firms of 5.97% and 8.53% for the quintile and decile portfolios, respectively.
  • Also, the small cap quintile (decile) has a higher Sharpe and Sortino ratio than the large cap quintile (decile) over the entire time period (1927 – 4/2014).
    • Thus, equal-weighting the portfolio appears to enhance the “small cap” effect.

VW Size Portfolios (1/1927 to 4/2014)

  • A clear size effect for CAGRs.
2014-06-30 14_09_51-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)
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.

EW Size Portfolios (1/1927 to 4/2014)

  • Higher CAGR; higher volatility
2014-06-30 14_11_15-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)
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.

Size and Value Interaction (1/1/1927 to 4/30/2014)

We examine the Fama-French 25 portfolios.

  • Small Growth is portfolio 1.
  • Small Value is portfolio 5.
  • Large Growth is portfolio 21.
  • Large Value is portfolio 25.

We find that the way you weight the portfolios, such as value-weight or equal-weight, has a large impact on the so called “size effect.”

  • Value-weighting the portfolios produces a spread of 14.65% between small value and small growth, and a spread of 1.95% between large value and large growth.
  • Equal-weighting the portfolios produces a spread of 17.78% between small value and small growth, and a spread of 3.41% between large value and large growth.
    • The spread between value and growth is largest for microcap stocks.

Small Value has the CAGR, Sharpe and Sortino. Also has larger standard deviation than the large cap portfolios.

  • Identify “size” effect by comparing vertically (control value)
  • Identify “value” effect by comparing horizontally (control size)

2014-06-30 14_13_42-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)

Summary Statistics VW (1/1927 to 4/2014)

  • Small value has the strongest performance; SG-LG, SV-LV = Size Effect; LG-LV, SG-SV = Value Effect
2014-06-30 14_14_52-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)
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.

Summary Statistics EW (1/1927 to 4/2014)

  • Small value has the strongest performance; SG-LG, SV-LV = Size Effect; LG-LV, SG-SV = Value Effect
2014-06-30 14_15_50-Size Study_New deck - Microsoft PowerPoint (Product Activation Failed)
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.

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About the Author

Wesley R. Gray, Ph.D.

After serving as a Captain in the United States Marine Corps, Dr. Gray received a PhD, and was a finance professor at Drexel University. Dr. Gray’s interest in entrepreneurship and behavioral finance led him to found Alpha Architect. Dr. Gray has published three books: EMBEDDED: A Marine Corps Adviser Inside the Iraqi Army, QUANTITATIVE VALUE: A Practitioner’s Guide to Automating Intelligent Investment and Eliminating Behavioral Errors, and DIY FINANCIAL ADVISOR: A Simple Solution to Build and Protect Your Wealth. His numerous published works has been highlighted on CBNC, CNN, NPR, Motley Fool, WSJ Market Watch, CFA Institute, Institutional Investor, and CBS News. Dr. Gray earned an MBA and a PhD in finance from the University of Chicago and graduated magna cum laude with a BS from The Wharton School of the University of Pennsylvania.