Investment management is a zero sum game. The source of outperformance for a market’s outperformers is the underperformance of the same market’s underperformers. Properly measured, the weighted average sum of the winners’ gains is exactly equal (before costs) to the weighted average sum of the losers’ losses. This identity, along with the professionalization of the investment management business globally, helps explain why our SPIVA reports consistently show that most active managers underperform most of the time.

Wins and losses might be, but need not be, distributed symmetrically. If half the assets in a market underperform by 3%, then the other half (on average) will outperform by 3%. But if 70% of assets underperform by the same 3%, the average outperformance of the winners will be a much more impressive 7%. A simple example will illustrate an important principle: **if stock returns are skewed and portfolios are concentrated, most assets will underperform.**

Exhibit 1 shows a simple model of positively-skewed returns; we assume a market with five stocks, one of which outperforms the others. Assuming each stock has the same capitalization, the market’s overall return is 6.0%, with a narrow dispersion.

In Exhibit 2, we use these five stocks to build portfolios of different sizes. There are, for example, five possible one-stock portfolios, four of which underperform the market. Alternatively, there are five possible four-stock portfolios, four of which outperform. Since the market, in this example, is up 6%, the average return of the portfolios is also 6%—if the market gives us 6%, it doesn’t matter how we slice it up. What changes is the distribution of returns across portfolios.

Exhibit 2 suggests that two things happen as portfolios become more concentrated:

- The probability of outperformance falls.
- The gap between the winners and losers grows; the winners’ alpha rises, albeit for a smaller number of winners.

These differences become more pronounced as the dispersion of returns grows. Exhibit 3 shows a hypothetical market with the same average return, similar skewness, and wider dispersion than in Exhibit 1.

If we repeat our portfolio construction exercise, Exhibit 4 shows identical probabilities of success, but with much wider gaps between winners and losers.

As before, concentration lowers the odds of success, but dramatically raises the payoff for the relatively small number of winners.

Why is this simplistic exercise relevant to the real world?

- As is the case in most years, returns for 2020 look to be positively skewed, as the median stock in the S&P 500 underperforms the average.
- Most active portfolios
*are*relatively concentrated. Coupled with skewness, higher concentration implies that the majority of assets are likely to underperform. - Dispersion is well above historical average for every equity market we cover. This implies big gaps between winners and losers.

As the year draws to a close, we should expect to hear reports of spectacular successes. Don’t let the well-advertised big wins obscure the more dismal landscape of active underperformance.

The posts on this blog are opinions, not advice. Please read our Disclaimers.