Dimensions Of Expected Return: Patience Is A Virtue

by: Mark Hebner


Academic finance has discovered four factors or "premiums" that offer investors superior investment performance.

There is no free lunch: these factors bear higher risk as well.

Time diversification helps us capture these premiums.

Giving investment advice should always aim to meet investors at their level of understanding. I do not expect everyone to have a Ph.D. in economics, so it is important to focus on big ideas that are the most crucial to understand. This can include ideas such as diversification, costs and discipline.

With that said, I also recognize that many investors who have been engaged in their finances for some time or have a longstanding relationship with their wealth advisor deserve to continually learn more about investing. Today, we are going to delve further down the rabbit hole with the investment strategy that I recommend to investors.

The dimensions of expected return are a finer topic that most investors are unaware of. It is hard enough motivating individuals to embrace a passive investment strategy let alone speaking about multiple regressions and time-tested data. Nonetheless, it is extremely important not only from an academic standpoint, but also from a successful investment experience standpoint.


Starting in the 1960s, financial economists began researching the behavior of stock prices. Two major events led to this particular movement in the field of economics: the development of computers and the establishment of the Center of Research in Security Prices (NASDAQ:CRSP) at the University of Chicago. In other words, economists now had the most comprehensive dataset of stock prices and large machines that could make many computations in a reasonable amount of time. You put these two things together and all of a sudden you have an entirely new concentration in the field of economics.

Decades of research and thousands of peer review academic studies into the drivers of stock market returns have led to amazing discoveries about how different types of stocks move in relation to one another. We can slice and dice the market by different factors such as market capitalization, fundamentals like book value or sales compared to market price, and region to see how different types of stocks compare to one another. From a practical standpoint, in terms of being able to translate academic findings into actual investment strategies, 4 factors or "premiums" have been found within stocks and successfully implemented (there are 2 factors that drive the behavior of bond prices):

That is, we know that historically stocks have outperformed bonds, small cap stocks have outperformed large-cap stocks, value stocks have outperformed growth stocks, and stocks that have high profitability have outperformed stocks with low profitability. Furthermore, we have been able to design investment strategies around these different factors.

Now we are not suggesting that focusing on these "premiums" is a free lunch: quite the contrary. Traditional economic theory would suggest that higher expected returns must be associated with higher risk, which we believe for the most part is accurate. Other theories have suggested that these premiums may be associated with behavioral biases, but unfortunately, proponents of the behavioral theory have not presented an economic model to support it.

Regardless, both theories still point to passive investing as the prescription. We are in essence pursuing different areas of the market that have been shown to reward investors but that involve taking risk. As we will show later on, there are periods of time where investors are not rewarded for pursuing these areas in the market, which is why they are considered to bear "risk premiums." It is important for investors and advisors to have a healthy respect for these risk premiums when suggesting a particular asset allocation.

Why These 4 in Particular?

Before we go further, it is important to understand that there have been many factors found in academic research, but we stick with these particular 4 factors for the following reasons:

  • They are sensible
  • Persistent across time periods
  • Pervasive across markets
  • Robust to alternative specifications
  • Cost-effective to capture in a diversified portfolio

In other words, there is a very high degree of confidence that investors will benefit from focusing on these particular factors. From a fiduciary standpoint, it is crucial that we only do things that have been shown to be successful through rigorous scientific inquiry.

Historical Performance of These Factors

We now have a general understanding about dimensions of expected return. Historically, investors who have focused on these particular factors within equities have been rewarded with higher returns. Below we see the historical size, relative-price and profitability premiums for US, International/Developed and Emerging Markets using the longest dataset available for each market.

For example, within Emerging Markets Stocks, value stocks have outperformed growth stocks (relative price premium) by approximately 4.47% per year from 1989-2014. The highest premium has been the profitability premium in Emerging Markets, delivering 7.12% per year from 1996-2014. The smallest premium has been the size premium in the Emerging Markets, delivering 1.82% per year from 1989-2014.

No Such Thing as a Free Lunch

As we mentioned earlier, pursuing these different premiums in the market is no free lunch. If we want to be rewarded with higher expected return, then we have to take risk. While we should expect these premiums to be positive in any year, there are periods of time where they do not. Many clients of IFA are probably well aware that the relative price premium (value stocks) in US stocks did not deliver for the last 10-year period ending 12/31/2015. The charts below show the annual performance for each premium in the US from 1928-2014. A blue bar indicates a positive premium while a red bar indicates a negative premium.

As you can see, there are definitely more blue bars than red bars, but there are time periods where there are multiple years in a row where different premiums do not show up.

Although the average premium observed over time has been positive, there is extreme variation around that average. For example, just looking at the relative price premium in the US, we can see that the historical average has been 3.64%. There have only been 9 years out of 87 where the observed premium was within 2% of the historical average. See the chart below.

The dashed line represents the arithmetic average (3.64%). The gray area around the dashed line represents the 2.00% range around that average. The dark blue bars represent the annual observations that fall within the range (1.64%-5.64%).

While the average relative price premium in the US has been less than 5%, it is more likely that you will experience a much higher or much lower premium in any given calendar year. The same conclusions hold for the size and profitability premiums in the US as well as all of the premiums around the world.

Patience is a Virtue

While many investors are well aware of diversification in terms of investments, many people cannot fully grasp diversification in terms of time. I recommend diversifying investments as a risk control. Because we do not know with a high degree of certainty which area of the market is going to be the next winner, we hold many different types of stocks. Diversification has been shown to improve returns in terms of risk. Time diversification is the idea of following a particular investment style over time. As we mentioned before, premiums do not always show up in any given year, but the longer we hold onto them, the likelier we are to capture their benefits.

If instead of looking at 1-year returns we now looked at 5-year rolling returns, how do the premiums look?

Each bar shows the 5-year period ending in that particular year. For example, the first red bar under the "market premium" is for the 5-year period ending 1932. The next red bar is the 5-year period ending 1933 and so on and so forth. What do you notice? Compared to the 1-year annual returns shown above, there are far fewer red bars in the 5-year rolling returns. In other words, once we move from looking at premiums from 1 year to 5 years, the probability of seeing a positive premium increases.

Again, just to highlight the relative price premium in the US, below is a chart showing the historical 5-year annual rolling returns.

Looks like a smoother ride for the investor versus annual returns.

Following the same logic, what if we looked at 10-year rolling periods, what do we expect to find?

As you can see, this looks even better than the 5-year rolling returns. Very few red bars across all 4 premiums.

Once again, just to highlight the relative-price premium in the US, below shows the 10-year annual rolling returns.

As you can see, once we present the data in terms of 10-year periods, the pursuit of this premium looks very attractive. From 1941-1995, there was not a single 10-year rolling period where value stocks underperformed growth stocks. With that said, you can also see that in the 10-year period from 2005-2014, the value premium did not deliver.

The table below shows the historical performance for the market, size, relative-price and profitability premiums in the US in terms of having a positive observation.

For example, looking at historical 15-year rolling periods for the market premium, there have been positive premiums 96% of the time. You can also see that across every single premium, the number of positive observations increases as we increase the time horizon.

Things Can Turn Quickly

We have already discussed the extreme variability around the historical averages for each premium. This variability means that things can quickly turn either positive or negative, highlighting the importance of long-term discipline when pursuing these risk premiums within a portfolio. The chart below shows the historical 10-year annual rolling observations for the relative-price premium sorted from lowest to highest.

You can see that for the 10-year period from 2005-2014, the value premium was slightly negative (-0.78%). This isn't odd, as you can see other 10-year periods in history where the value premium was significantly negative. But if we go back just one more year and look at the 10-year period from 2004 to 2013, the value premium switches to being slightly positive (0.79%). This just emphasizes the importance of having a long-term focus when deciding to pursue these risk premiums within your portfolio.


As advisors, it is our duty to constantly educate our clients into understanding the reasoning behind their particular investment strategy. This not only allows us to be transparent, but it is crucial in building long-term discipline of the investment process. Beyond investing in index funds, academic research has found certain factors or premiums within the market that explain the variation in its returns. By pursuing these premiums we can increase the expected return of the portfolio for our investors, but this does not come without accepting a higher degree of risk or variability of returns.

Because there is significant volatility around these premiums in any given year, it is important to maintain a long-term focus. Historically, the number of positive observations for each premium around the world increases as we increase the time horizon. Because I believe in a long-term approach to the investment process, I believe that pursuing these premiums within portfolios will be beneficial for investors, with the ultimate goal of creating a positive investment experience.

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.

Additional disclosure: We utilize strategies from Dimensional Fund Advisors in the portfolios that we build for our clients. There are no profit-sharing arrangements between my firm, Index Fund Advisors, Inc., and Dimensional Fund Advisors, LP.