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Factor Investing Part 2 - Size Factor Thumbnail

Factor Investing Part 2 - Size Factor

In October of 1994, financial advisor Bill Bergen authored a paper titled “Determining Withdrawal Rates Using Historical Data”.  Bill set out to determine, using historical data, what amount of money a retiree could safely withdraw from a portfolio of stocks and bonds over a 30 year retirement and avoid running out of money.  Bill’s research concluded that, after “smoothing” the withdrawals to account for historical periods of high inflation and stock market crashes, that the safe withdrawal rate for a retiree with a portfolio of 50% Large Cap US stocks and 50% intermediate term US government bonds was closer to 4% per year.  Meaning, a retiree with a 30 year time horizon could safely set their withdrawals at 4% of their starting portfolio value, take that amount out every year, and increase that withdrawal annually by the rate of inflation.

It is hard to believe that less than 30 short years ago we did not have this type of insight, but it’s true.  

Prevailing wisdom at the time was that, if you simply assumed that you would get average long-term stock and bond returns and average long-term inflation rates, that a retiree could simply take out the “real” component of their portfolio’s historical average return each year for the rest of their lives and be ok.  

For example, if stocks returned 10.3% average annual returns historically, bonds returned 5.1%, and inflation was 3% - an retiree with a portfolio of 60% stocks and 40% bonds could expect an average compounded rate of return of 8.2%.  The “real” return, meaning the amount of return exceeding inflation, would be about 5%.  Therefore, a retiree applying this logic would infer that they could safely withdraw all of the “real” return from their portfolio each year - about 5% - and do so for the remainder of their retired lives while not worrying about running out of money. 

As Bill's research showed, this withdrawal rate was simply too high and did not adequately plan for seasons of bad returns and high inflation.  Bill's research was among the first acknowledgements that investors don’t experience “average” returns.  Since stock and bond returns can vary greatly from one multi-year period to the next, the actual investment experience that a retiree gets can vary widely based on when they happen to retire.  In other words, we can mostly choose when we retire, but we can't choose what stock and bond returns we are going to get.   We have experienced, and will continue to experience, periods of high returns followed by periods of low returns.  Recessions and expansions.  High inflation and low inflation.  

The research was certainly a leap forward from what retirees and their advisors had accepted previously.  The research, and resultant findings, were dubbed by the financial planning industry as the “4% rule”.  To this day, it is used widely by retirees and their advisors alike.

Image: William P. Bengen

Several years later, Bill revisited his original research to see if the historical withdrawal rates could be improved by adding additional asset classes to the model portfolio.  Recall that the original research was based on a simple 2-asset class portfolio - US Large Cap Stocks and US Intermediate Term Government Bonds.  Surprisingly, Bill found that by adding US Small Cap (small company) stocks to the portfolio, the safe withdrawal rate went from 4% up to around 4.5% - a significant enhancement to his original finding.  What is it about small company stocks that made their addition so impactful to Bill's original findings?  Is there something unique about small company stocks that causes them to outperform large company stocks over long periods of time?

In this edition of the Factor Investing Series, we will dig into small cap stocks, also known as the “size factor”.

Introducing the Size Factor

In Part 1 of this series, we introduced the first factor - Market Beta.  The CAPM Model, the single-asset pricing model developed by William Sharpe, was the financial world's most reliable model to explain the differences in the returns of different investment portfolios. 

But, it was incomplete.  

Over time, academics discovered that the CAPM model only explained about 2/3 of the differences of returns of diversified portfolios.  For example, if Portfolio A returned 10 percent, and Portfolio B returned 13 percent, the difference in the market beta's of the portfolio would only be able to explain 2 of the 3 percentage points of difference.  So, what could explain the other 1 percent difference?  There must be other "factors" at play that drive returns and ultimately explain the deficiencies of the CAPM Model.

In 1981, years before Bengen's finding that adding small caps to his retirement income model improved safe withdrawal outcomes, Rolf Banz of the University of Chicago authored a paper titled "The Relationship Betweeen Return and Market Value of Common Stocks".  In the period he studied between 1936 and 1975, he found that US small cap stocks provided a higher risk-adjusted return than US large cap stocks, and that additional return was not explained by market beta.  Subsequent research that extended the study over longer time periods and other countries has confirmed that small company stocks do add a unique risk "factor" to investment portfolios.  Rolf Banz referred to the premium as the 'size effect'.  We will refer to it as the size factor.

Size Factor in the Data

Now we will examine the “premium” - or the excess return - that investors experienced by being exposed to the size factor.  We simply subtract the return of large cap stocks from the return of small cap stocks to determine whether a premium exists.  For example, if the long-term large cap stocks returned 10% and small cap stocks returned 12%, the small cap "premium" would be 2% (12%-10%).

So, how has the size factor performed empirically?

All charts and data are from Dimensional Fund Advisors.

In Canada, small company stocks factor have outperformed large company stocks in 45% of 1 year periods, 43% of five year periods, and 69% of 10-year periods since 1988 - resulting in a 0.33% average annualized size premium over that period.

1 Year Size Factor Premiums - Canada

Size Factor Outperformance Over Different Time Periods - CanadaIn the US, small company stocks have outperformed large company stocks in 56% of 1-year periods, 61% of 5-year periods, and 70% of 10-year periods since 1926 - resulting in a 1.95% average annualized size premium over that period.

1 Year Size Factor Premiums - US

Size Factor Outperformance Over Different Time Periods - US

Internationally (ex-US), small company stocks have outperformed large company stocks in 63% of 1-year periods, 84% of 5-year periods, and 88% of 10-year periods since 1970 - resulting in a 4.78% average annualized size premium over that time period.

1 Year Size Factor Premiums - ex-US

Size Factor Outperformance Over Different Time Periods - Ex-US

Thoughts on the Size Factor

The size factor can be observed to have positive returns in the historical data in Canada, the US, and Internationally.  It passes the tests of being persistent and pervasive.  Small cap stocks can be less liquid and more expensive to trade, depending on the country an investor wants to invest in.  Small cap ETF's are widely available in the US and Canada, and in most developed ex-US countries.

Now the big question - why do small companies have higher realized historical returns than large cap companies?  Is there something unique about small companies that makes them riskier and, hence, causes them to produce higher returns?

The simple explanation is that small companies are not as stable, not as well-capitalized, and may be less stable in a downturn than larger companies.  They may also have higher borrowing costs, their earnings and cashflows may be more volatile, and they may be less profitable.  Therefore, as compensation for the higher degree of risk that small cap stock returns pose to investors, particularly during recessionary periods or periods of restrictive central bank monetary policy, investors will demand higher returns for holding them.

The additional risk of holding small cap companies can be observed in the data as well.  The volatility, measured by standard deviation, of US Small Cap stocks was 26.58, compared with 18.10 for US large cap stocks between 1926 and today.

Chart Source: DFA Returns Web


By this point, you may be noticing a theme - that over long periods of time, higher returns accrue to investors who are taking higher degrees of risk.  The risks that we have identified so far are:

1. Market risk - the higher risks we take and returns we expect from holding stocks vs. holding treasury bills over long periods of time

2. Size risk - the higher risks that we take and returns we expect from favouring smaller company stocks vs. larger company stocks over long periods of time.

And, as Bill Bengen identified, the pursuit of the size premium in a diversified portfolio can have a positive impact on financial planning investment outcomes if you are prepared to take on that additional risk.

Make sure to check back in if you'd like to follow along with my series on Factor Investing.  Or, you can subscribe to my weekly video newsletter here:


Thanks for reading!


The comments contained herein are a general discussion of certain issues intended as general information only and should not be relied upon as tax or legal advice. Please obtain independent professional advice, in the context of your particular circumstances. This article was written, designed and produced by Mark Walhout, CFP®, an Investment Funds Advisor with Investia Financial Services Inc., and does not necessarily reflect the opinion of Investia Financial Services Inc.The information contained in this article comes from sources we believe reliable, but we cannot guarantee its accuracy or reliability. The opinions expressed are based on an analysis and interpretation dating from the date of publication and are subject to change without notice. Furthermore, they do not constitute an offer or solicitation to buy or sell any securities. 

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