The extent to which a skilful manager can outperform varies with time. It depends, primarily on the dispersion of security returns in a measurement period as we will explain here.  If we want to judge investment skill, we need to be aware of the effect of market dispersion.   The market’s composition also plays a role as we will discuss in a future post.

To simplify our explanation, we assume that portfolios only trade at the start and end of a measurement period, or that the measurement period is short enough so that trading within the period is negligible1.

We measure performance against the unbiased capitalisation-weighted benchmark.  The explanation is, however, equally applicable when considering performance relative to a peer group.

What is dispersion?

Dispersion is the degree of variation in the underlying security returns, or simply a measure of how scattered the individual security returns are relative to that of the benchmark. To illustrate this, consider a market consisting of four shares with equal market capitalisations. We compare a low to a high dispersion period. The benchmark gives a return of 2% in both cases. First a chart of the low dispersion period:

(The benchmark return is calculated as 25%x1% + 25%x2% + 25%x2% + 25%x3% = 2%.)

The high dispersion period with more scattered returns looks like this:

In the high dispersion period a long-only active manager’s portfolio with, for example, 50% invested in Stock A and 50% invested in Stock B, yields 5% and outperforms the benchmark by 3%. In the low dispersion period, the highest possible outperformance an active portfolio can deliver is 1%, but only if the portfolio is 100% invested in Stock D.

So, the more dispersed (or scattered) the underlying security returns are relative to the benchmark, the more the performance of actively managed portfolios can deviate from the benchmark.  On the contrary,  if all securities give the same return over the measurement period the dispersion is zero. The most skilful investor can then only deliver benchmark performance.  In a following post, we propose methods for quantifying market dispersion.

How does dispersion benefit a skilful manager?

What drives this dispersion in markets?  We decompose a security’s return into two factors.

      • Firstly, new price sensitive information causes security prices to change. The higher the volume and significance of security specific information during a measurement period, the more dispersed the performances of securities.
      • Secondly, assuming that markets are not efficient, security prices would move towards or away from their fair values during any measurement period. How material these unwarranted price changes are would depend, for example, on the ratio of informed to uninformed participants during the period as I discussed here, or even the complexity of new information.

In summary,

Price change  = Change due to new information + Unwarranted change

According to John Maynard Keynes (1936)2: “Day-to-day fluctuations in the profits of existing investments, which are obviously of an ephemeral and non-significant character, tend to have an altogether excessive, and even an absurd, influence on the market. It is said, for example, that the shares of American companies which manufacture ice tend to sell at a higher price in summer when their profits are seasonally high than in winter when no one wants ice.

It is reasonable to assume that the more dispersed security returns are, the more likely it is that they are being mispriced. Or, put differently, if the volume and impact of price sensitive information is high the likelihood of mispricing increases. It takes time and might be difficult for market participants to account for news. See, for example, Heston & Sinha (2017)3, who used neural networks to detect news that is persistently under-incorporated into current stock prices.

Therefore, the higher the dispersion in returns the greater the extent of outperformance skilful managers can potentially deliver. There are more opportunities available, but only if the dispersion results, in part, from mispriced securities returning towards fair value.

The effect of dispersion on relative performance has been analysed by the Brandes Institute using fund returns for the US and global markets over 20 to 30 years, depending on the dataset. During calendar years with above-normal dispersion, top quartile managers delivered considerably better returns than what top-quartile managers delivered in below-normal dispersion years.  Also, the range of returns from top- to bottom-quartile managers was larger during the above-normal dispersion years.

Yet each calendar year’s top managers could just have been lucky. The improved relative returns is an inherent outcome of the increase in dispersion, as is evident from my simple example. Hence, the improved outperformance of top managers during high dispersion periods does not demonstrate skill. Skill can, for example,  be demonstrated through performance persistence studies, which is a topic we will cover in future posts.

Also, note that an increase in dispersion does not imply an increase in the percentage of active managers that outperforms. I describe the factors that could influence the ratio of outperforming versus underperforming portfolios in a following post.

In the next post, we will explain how the market’s composition affects the potential of skilful managers to outperform.


1Even if market dispersion is low over a measurement period, it might be high for short subperiods within the full period, and managers can take advantage of this. If measurement periods are therefore too long, this could invalidate comparisons of dispersions between two periods, for the purpose of examining portfolio returns. I will propose a way to deal with this in a future post.

2Keynes, John M. (2017).  The General Theory of Employment, Interest and Money. p138. 2016 edition, Atlantic Publishers and Dist. (see here)

3Steven L., Sinha, Nitish Ranjan (2017). News vs Sentiment: Predicting Stock Returns from News Stories. Financial Analyst Journal  73(3), 67 -83, CFA Institute. (see here or here)