Published 06/11/2020

^{1}), or they could be an Amazon or Facebook, which
would have delivered holders incredible returns over the past 10–15 years.

The only thing we know for sure is that there is no way of telling
which path a single, randomly chosen stock will take beforehand. This
uncertainty of whether an individual will become a multimillionaire, lose
everything or something in between, is why we diversify. Diversification
reduces risk.

**Diversification From a Risk Perspective**

The idea that diversification is the only free lunch in investing
is often attributed to Nobel Laureate Harry Markowitz. Instead of the crazy,
uncertain paths in the example above, an investor can invest across the market,
thereby diversifying away company-specific risk, while earning the market
return. Companies go bankrupt all the time, but the entire market will not.
Diversification has allowed investors to have more conviction in their future
outcomes and clarity for their long-term financial plans by building more
efficient portfolios. More return for each unit of risk and less risk for each
unit of return increases the efficiency of a portfolio. Diversification is the
cornerstone of proper investment management.

For example, the average U.S. stock
has a standard deviation of about 35%.^{2} This means that if a stock has an
expected return of 7%, the yearly return will be between –28% (7%-35%) and +42%
(7%+35%) about two out of every three years. A range of –28% to +42% is a very
wide band of possible outcomes. However, if a portfolio is diversified across
all 3,000+ stocks that make up the U.S. market, now the standard deviation is
below 20%. This means that assuming the same 7% expected return, the yearly
outcomes about two out of three times will be between –13% and +27%, a tighter
band than the previous example. In the second example, the company-specific
risk has been diversified away, leaving only the market risk component. In the
single-stock portfolio, the portfolio fully retained both types of risk: market
and company-specific. One thing that Markowitz discovered is that since
company-specific risk is diversifiable, it does not drive additional expected
return. The arithmetic average returns are the same, but the risk of the index
is much lower than the risk of the single stock. This means the diversified
portfolio of U.S. stocks is much more efficient.

In addition, the diversified portfolio has an advantage in growth
of wealth because of “volatility drag” on portfolios that cause geometric or
compounded returns (average returns in dollar terms) to be lower than
arithmetic returns the more volatile a portfolio. The simple logic is that if a
portfolio falls by 20%, then it must increase in value by 25% to get back to
even. Volatility drag is the formal name for the concept that a given
percentage drop has a larger effect on dollar value than the subsequent same
percentage gain.

Assume $100 is invested in the two portfolios from the earlier
example:

1.
Single-Stock Portfolio: 7% expected arithmetic
return, 35% standard deviation

2.
U.S. Market Portfolio: 7% expected arithmetic
return, 20% standard deviation

They will have different geometric returns as approximated by the
following formula:^{3}

Geometric or Compounded Return = Arithmetic Return – (StDev^2)/2

After 30 years, the $100 has turned into:

Reduction of volatility has a dramatic impact on the growth of
wealth, and this is the tangible benefit of diversification. There are two
items worth mentioning about the analysis above. First, it ties out with known
data, as over half of publicly listed stocks have negative total returns versus
Treasury bills over their lifetime.^{4} Second, this analysis
presupposes that the arithmetic returns are the same for an index versus an
individual stock, however, in the next section, we will discover that this is
not true either. The expected arithmetic return for a single-stock holding
should be lower than for an index.

**Diversification From a Returns Perspective**

The benefit of diversification has mostly been researched as a
risk story, but there is a very important return benefit as well. As in the
previous section, we will examine the difference between investing in a single
stock versus investing in an index. If one is picking a stock at random, then
the median stock return should be used as a proxy for the average stock. We
looked back at the data for U.S. stocks from 1927–2017 using the CRSP U.S.
stock database.^{5}

The average yearly U.S. market return over that time period (91
years) was 12.01%. The median stock return was 8.30% on average. This means
that investing in the overall index versus randomly picking a single stock
would have earned on average 3.71% more per year. Again, this is a natural
outcome of stock returns as stock returns are skewed, not uniform. In any given
year, there are a few big winners, while the majority of stocks have returns
that are less than the average. That means it should not be a surprise that the
index would have higher yearly returns than the median stock, but this
phenomenon has not received nearly enough attention.

Further, by looking at a single-stock’s lifetime price return versus
the Russell 3000 Index, going back to 1980–2014, we know that roughly 2/3 of the
universe of single stocks underperformed the Russell 3000. The median stock underperformed
the index by –54%, with the extreme winners being two standard deviations over
the mean as represented by the chart below.^{6}

**Combining Risk and Return**

Going back to the example of compounded annual growth over 30
years, let us evaluate the combined effects of both a higher standard deviation
and a lower expected return.

1.
Single-Stock Portfolio: 4.29% expected
arithmetic return (7% index return – 3.71% historical spread between single
stocks and index returns), 35% standard deviation

2. U.S. Market Portfolio: 7% expected arithmetic return, 20% standard deviation

After 30 years, the $100 has turned into:

**Conclusion**

Most of the financial world understands the benefits of diversification from a risk perspective, but there is a benefit from a returns perspective as well. Investing in single stocks or a concentrated portfolio is significantly riskier (from a standard deviation and long-term outcome perspective) than investing in a diversified index. Additionally, single stocks or a concentrated portfolio have lower returns than index returns, which means that single-stock and concentrated portfolios are less efficient on two dimensions: risk and return. The goal of a well-constructed portfolio is to maximize returns for the lowest amount of risk. Single-stock investing accomplishes the opposite: It lowers returns for greater risk. Single-stock or concentrated-stock investors could get lucky, but the less diversified the portfolio, the more the odds tilt against these portfolios versus a diversified portfolio in the long run.

**Sources**

^{1} “Public Company Bankruptcies From 2005 to 2015.” The Wall
Street Journal, Accessed August 16, 2018.

^{2} “Chart 18: Today’s Ultra-Low SPX Realized Vol Is Driven by
(i) Single Stock Vol at 27yr Lows and (ii) Policy Polarization Crushing Stock
Correl to Levels Rarely Seen Outside of the 90s & the Tech Bubble.” Financial
Times, Accessed August 16, 2018.

^{3} Michael Kitces, “Volatility Drag and Its Impact on
(Arithmetic) Investment Returns in Monte Carlo Analysis.” Nerd’s Eye View at
Kitces.com, December 27, 2017.

^{4} Cormac Mullen, “Lesson of the Century: Most U.S. Stocks
Can’t Even Beat a T-Bill.” Bloomberg, February 1, 2017.

^{5} Data from Dimensional Fund Advisors and CRSP.

^{6} Michael Cembalest, “The Agony & the
Ecstasy: The Risks and Rewards of a Concentrated Stock Position.” Eye on the
Market (Special Edition), J.P. Morgan, 2014.