Thucydides at the Bazaar

“Self-control is the chief element in self-respect, and self-respect is the chief element in courage.” ―Thucydides, The History of the Peloponnesian War

Current geopolitical events lead me to reflect on the writings of Thucydides. The connection is meaningful albeit indirect. For example, is it credible to infer from Russia’s recent annexation of Crimea and its subsequent military positioning on the Ukrainian border that the Kremlin is inclined to respect the 1994 Budapest Memorandums on Security Assurances, confirmed in 2009 by Russia and the U.S., in which Ukraine surrendered its nuclear arsenal in exchange for respect of its territory? The pattern of recent events suggests otherwise.

Unfortunately, what we are witnessing in Ukraine is reminiscent of the battle on the island of Melos during the Peloponnesian War. In that battle, Athens expanded its empire at the expense of the Melian soldiers who gave their lives fighting in an alliance with Sparta only to leave their wives and children widowed and orphaned slaves. As Simon Critchley explains in a recent NY Times piece (“Abandon (Nearly) All Hope”), the Melians believed Sparta would come to the rescue in their resistance to the Athenian invasion, but that assumption proved fatal. In the “Melian Dialogue,” Thucydides illustrates “realism,” the school of political thought attributed to this 5^th century B.C. philosopher. Time will tell whether the U.S. and NATO will replay Sparta to Ukraine’s Melos. In the meantime, the tumultuous history of the region appears unending.

Reflecting on realism as a mindset in turn leads me to the topic of investing. Fundamental to realism is an appreciation (in my amateur philosopher interpretation) for the nature and balance of relationships. In the case of the array of crises brewing in the East, the relationships in question relate to the balance of political and military power. In investing, the relationships relate to the implicit trade-off in any investment decision between risk and return.

The ordinary investor likely would agree that risk and return are two sides of the same coin; that one should expect an investment return only when assuming some degree of financial risk. While this metaphor is helpful, the assumed corollary is that the relationship between investment return and risk is linear; that is, that the more risk one takes, the greater the return one may reasonably expect, regardless of the starting point. The relationship between risk and return is more complex and nuanced than the ordinary investor is likely to have had the opportunity to dissect.

The chart below illustrates one such nuance in the relationship between investment returns and risk. Using data from 1926 through 2012^[1], the blue line represents the long-term average annual return for portfolios with asset allocations of varying percentages of stocks shown along the horizontal axis. For example, the point on the far left on the blue line represents the 5.5% average annual return for a portfolio consisting 100% of bonds and 0% stocks. The point on the far right on the blue line represents the 10% average annual return for a 100% stock portfolio. These long-term average annual returns fall along the left vertical (“y”) axis.

The red line represents the range of historical returns for portfolios of varying asset allocations of stocks and bonds. In other words, the red line represents risk in that each of the eleven points along this line represent the difference between the best and worst annual return for portfolios with the stock allocations shown along the horizontal axis. The point on far left of the red line represents the 40.7 percentage-point difference between the best and worst annual returns for a 100% bond portfolio over this period. The best annual return was 32.6%, and the worst was -8.1%. The point on the far right on the red line represents the 97.3 percentage-point difference between the best and worst annual returns for a 100% stock portfolio. The best annual return was 54.2%, the worst -43.1%. These average annual returns fall along the right vertical (“y”) axis.

The trajectory of the two lines shows the non-linear relationship between risk and return. With each incremental 10 percentage-points of stock allocation in the portfolio, the historical average annual return increases, although the blue line tapers some as the stock allocation approaches 100%. On the other hand, with each incremental 10 percentage-points of stock allocation to the portfolio, the incremental risk as measured by the range of historical returns for that allocation shifts upward at a point of inflection around the 40% stock allocation.

Of course, history is not predictive, but this illustration using 86 years of historical data offers two lessons. The first is that portfolio risk as measured by the range of returns falls as the stock allocation increases from zero to 20%. The slight bow in the red line toward the left reveals this phenomenon, which suggests that most investors should consider holding at least some stocks. The second is that the incremental increase in portfolio risk accompanying incremental increases in stock allocation (above 20%) is significantly higher after the point of inflection (around 40%).

On the one hand, the 2.8% in incremental average annual return historically registered when increasing the stock allocation from 0% to 50% accompanies an increase in the range of returns from 40.7 to 54.8 percentage points. The spectrum of returns over the historical period grew by more than a third with this shift in stock allocation. On the other hand, the 1.7% in incremental average annual return registered when the raising the stock allocation from 50% to 100% comes at the price of an increase in the range of returns from 54.8 to 97.3 percentage-points. The range of returns over the historical period grew by nearly four-fifths with this shift in stock allocation.

In other words, taking incremental risk by adding stocks to the portfolio has historically meant accepting greater incremental risk as the stock allocation increases roughly beyond 40%. On the margin, the relationship between risk and return is not at all linear.

The implication is that a balance of stocks and bonds offers the ordinary investor the best chance of optimizing the implicit trade-off in the assumption of risk with the expectation of return. With a balance of stocks and bonds tailored to his risk appetite, the ordinary investor has the best chance of prudently (self-) controlling his portfolio risk.

The comfort afforded him by controlling for portfolio risk in turn emboldens the ordinary investor to focus on more important matters: life.