Market Returns was the title of the last article in this series. It reviewed the historical performances of a broad selection of stocks and bonds. This article looks at portfolio diversification or what combining different assets does to both return and risk.

Portfolio diversification deals with holding more than one asset or mutual fund in a portfolio. It generally reduces the risk and the returns.

Before looking at some numbers, it is important to understand risk.

Human Beings and Risk

Positive returns are good. People like them to be larger rather than smaller. Yet the volatility of returns is not considered good. If people only focused on returns they would choose that investment that had the highest expected return. Instead, people behave in a manner that takes the volatility or uncertainty of returns into account.

Humans are “pre-configured” to like return and dislike risk. Some show more caution (risk aversion) than others, but we are all risk averse to varying degrees. This statement holds even for those who take pride in being risk takers.

To illustrate, I relay an example I used in the classroom. Students consider themselves bullet-proof and risk-averse (pre-SnowFlake era).

The class, individually, is offered a choice to receive $1.00 or the opportunity to flip a coin which would pay $3.00 if heads turned up and nothing if tails did. The offer was one-time only. The expected value of the coin flip is $1.50 and the expected value (certain value) of the alternative is $1.00. Most of the class voted to play the game, supposedly nullifying risk aversion.

There were several likely reasons for this choice. The trivial amount was likely a major one Another was the fact that win or lose, their life would not change. The fact that they could not lose anything and the diversion of class time to an irrelevant activity also played roles.

Then the offer was changed by a factor of 10. Now I would hand you $10 or you could flip a coin with the chance of winning $30 or zero. Fewer people were willing to flip the coin, preferring the certain $10. There were still holdouts, so the game increased by another factor of 10. Ask and you can have a $100 bill or flip a coin with the chance of three of them or nothing. Most chose the $100 instead of running the risk of nothing.

There were always some holdouts who loved the spotlight. For them, the game was raised by a factor of 100 this time. You can ask and receive $10,000 or flip a coin with a head producing $30,000 or a tail, zero. Usually, at this point everyone accepts the sure thing. If not, we go to $1,000,000 vs gambling between $3,000,000 or zero. Even those with great bravado realize their silliness and begrudgingly take the $1 million. 

Admittedly artificial, the above-demonstrated risk aversion even for the unabashed confidence (or truculence) of youth.

Portfolio Diversification

The existence of portfolios is further proof of risk aversion. If we were not risk averse, we would all hold only one asset and that asset would be the one we deemed to have the highest expected return.

Combining two assets where one has a higher expected return than another produces less expected return than holding just the one. Yet people combine different assets (and many more than two) when they construct a portfolio.

However, so long as the two assets are not perfectly correlated, the volatility of returns diminishes. Portfolios exist not to maximize returns but to obtain returns at reasonable risk.

A Simple (Unrealistic) Example

To dramatize the effects of diversification, let’s assume there are only two “states” to the economy. By “states” we mean conditions. In this simplification, the two states of the economy are good and bad. There is no in-between.

Suppose you are in the dog grooming business. When the economy is good, so is your business. You earn $10,000 when the economy is good and $0 when bad (people groom their pets less in bad economies). You have a friend who in a different business. He is in the car repossession business. When the economy is bad, his business thrives. Good economies produce fewer defaults. For simplicity, he earns $0 in good economies and $10,000 in bad economies.

The two businesses are both risky. Both earn $10,000 or $0. But look what is possible if you combine them. Risk falls to zero and you earn $10,000 with certainty each year!

The real world is more complex than this pedagogical example. There are infinite states of the economy and it is virtually impossible to find businesses whose profits/losses move opposite each other for all states.

Some Commentary on Correlation

This information is conceptually important only to understand diversification. There is no need to be able to calculate correlations between assets

Assets that are perfectly correlated (in statistical terms, a correlation coefficient of 1) provide no risk reduction. No assets is perfectly correlated with another. Some may be highly correlated but no asset has a correlation coefficient of one with another. Likewise, no asset is perfectly negatively correlated with another (a correlation coefficient of -1).

Stocks of different companies are not perfectly correlated. Some have high correlation coefficients (close to 1) and provide little benefit in terms of diversification. Others have correlation coefficients near zero, which means the stocks are not correlated. Some (few) have negative correlation coefficients which mean they move opposite, to some degree, to each other.

When searching for risk reduction via portfolio construction, negative correlations or low positive correlations provide greater risk reduction than higher correlations. Stocks tend to be highly correlated with other stocks in their industry and less so in unrelated industries. Bonds tend to be less correlated to stocks than each other. Stocks in different countries tend to be less correlated than stocks in the same country.

At the risk of scaring some off, I present a correlation table. Do not worry, you need not know how to calculate these numbers.

The table shows the correlation between four ETFs: VTI, VNQ, GLD, and BND as calculated over about a 12-year period. These assets are generally not considered to be highly correlated with one another.

Correlation Table

A perfectly correlated asset would show a coefficient of 1. The closest to this figure is VNQ and VTI at 0.77. All other numbers are close to zero. Bonds show minor negative correlation to VTI and VNG. These low correlations suggest they would produce good risk reduction effects for a portfolio.

A caution should be noted re correlation coefficients. They are not stable for all types of markets.  As an example, here is how the correlation between VTI and GLD moved based on 60-day calculations:

The range in this correlation coefficient over time is from greater than +0.50 to smaller than -0.50. Market panics — up or down — tend to move all coefficients closer to 1. People desperate to get in or get out of markets generally buy or sell everything they can. Thus, well-planned diversification often breaks down during hectic periods.

To demonstrate in more conventional terms, the following table shows how returns of different asset classes move around:

This table came from Gabriel Potter who also provides an additional resource on portfolio diversification.

Simple Portfolio Diversification

Let’s return to our two index assets — stocks and bonds — as viewed in the last article, Market Returns. The effects of combining the two will show in both returns and risk.

In this scenario, we will look at three combinations of stocks and bonds. We know what each returns held separately from the last article. What happens now if we hold these combinations: 80% stocks and 20% bonds, 60 – 40% and 40 – 60% where each of the latter two represent decreasing percentages of stock and increasing percentages of bonds?

Here are the results where Portfolio 1 represents 80-20, Portfolio 2 60-40 etc.

The results show that combining stocks and bonds, at least the indices we chose to combine for the period we chose to cover, reduces risk and also reduces return. Were you to have invested your beginning $100,000 nest egg in all stocks in 1993 you would have ended up with just over one million dollars by Feb 1, 2019. This result occurs despite two of the worst periods in US stock history. In both periods, you would have huge drawdowns if you had only been in stocks (dot-com bubble beginning 1999 and the near-financial collapse beginning 2008).

The results of the stock/bond portfolios all earn less than the all stocks portfolio. Furthermore, they earn less as the percentage of bonds in the portfolio increases. This relationship is to be expected. What is surprising from the results is the minimal risk reduction obtained.

Risk reduction, as evidenced by standard deviations, does decline. The maximum drawdowns also reflect risk reduction, perhaps the most important to an investor. These drawdowns are still very large. Even the portfolio of 40% stocks and 60% bonds has a drawdown of 12%. When one looks at the fact that one sacrifices $400,000 in ending value from this portfolio compared to others, one wonders whether the “safety” is worth it.

The effects of diversification shown above are not encouraging.

But Wait!….

“But wait,” as they annoyingly say in television ads. We have just begun. There is no reason to be discouraged as you will see in subsequent articles. You will be able to accumulate substantial wealth and do so at a comfortable risk level.

For now, just some parting observations:

• The diversification shown above is simplistic. A broad portfolio of US stocks was combined with a broad portfolio of US bonds (government and corporate of all maturities).  No classes of uncorrelated sectors were included in the portfolio.
• The covered period consisted of some of the greatest rallies and losses in US stock market history. No other period other than the 1930s produced greater swings than the first decade of this new century.
• A review of the portfolio growth curve shows that the safest portfolio (60% bonds) worked during the first major drop (2003) but failed in the second (2009). By failing, I mean it did not mitigate the drawdowns of the other portfolio growth curves.
• The purpose of diversification is to reduce profits and risks. Diversification that does the first without the second is harmful.