Successful active management comes from two components; investment selection and portfolio construction. Very crudely, the former is about maximising long-term returns and the latter is about ensuring there are no surprises on the way. Effective diversification requires identifying feasible scenarios that could impact a portfolio and determining portfolio weights that make it as resilient as possible.

The minimum
number of securities required to achieve adequate diversification is a
recurring question among investors and academics. It depends on an investor’s
risk tolerance, and the scenarios most relevant to the securities in the
portfolio. But one scenario that *all*
portfolios are exposed to is that of idiosyncratic shocks in individual
securities. Concern for exposure to single-name events drives investors to
prefer larger portfolios to smaller ones, however the relevant risk is not
usually well quantified, and the distribution of weights is as important as the
portfolio size.

To explore
this, we develop a metric that quantifies the single-name risk of a portfolio
by establishing its *effective size*.
While several metrics exist that quantify portfolio concentration, they
generally lack interpretability in terms of risk[1]. Our
metric is based on the chance of experiencing losses from single-name shocks, thus
it goes straight to the heart of the matter[2].

We review some well-known indices in the table below and find their effective sizes to be much smaller than the headline number of assets[3]. This is a result of weight being unevenly distributed and concentrated in a relatively small number of holdings. In these examples, the effective size is well approximated by 2 x the number of assets covering 50% of the portfolio, which drives home the fact that it is the size of the largest positions that determines the exposure to single-name risk and not the number of assets in the portfolio.

Index | Number of assets | Effective size | Largest weight | Sum (number) of weights > 5% | Number covering 50% | Gini coefficient |

FTSE100 | 100 | 25 | 11.3% | 24.7% (3) | 11 | 0.59 |

NASDAQ | 100 | 22 | 9.7% | 36.9% (4) | 9 | 0.61 |

S&P500 | 500 | 99 | 3.6% | 0% (0) | 50 | 0.60 |

Rather than working with simulations, heuristics often form the basis of practical approaches to managing diversification. One well established rule is the 5/10/40 restriction placed on most UCITS funds which says that no single weight can be greater than 10%, and weights greater than 5% must total less than 40%. This equates to a minimum effective size of ~15-18[4]. It is interesting to note that these rules are relaxed specifically for UCITS schemes that replicate indices, and the FTSE100 and the NASDAQ are frequently at odds with them[5]. Therefore, products that track these indices can, and do, take positions that are prohibited for an active manager.

We conclude that
it is important to look past the number of assets in a portfolio in order to assess
risk. Equity funds that contain ~25 stocks will generally be referred to as
‘concentrated’ by the industry, but as we have seen here these portfolios may have
lower risk levels than those with a much larger number of assets. Working with
metrics that meaningfully quantify the risk you are concerned with is key to
effective risk management.

[1] For example, the
Gini coefficient compares portfolio weights to those of an equally-weighted
portfolio of the *same size*. This does
not help to understand the risk associated with portfolios of different sizes,
as seen in the table.

[2] We simulate 10^{6}
10y futures in which each asset in a portfolio has a 1% chance of experiencing
complete loss in a single year. We quantify exposure to large losses with a
weighted-count of 10y losses >15%. Effective size is defined as the size of
an equally weighted portfolio with the same exposure to large losses, using the
same methodology. Using like-for-like analysis makes the effective size metric
robust to the underlying assumptions of the simulations.

[3] Index weights are as of 31/12/18, 15/02/19, and 14/02/19 for FTSE100, NASDAQ and S&P500 respectively. Multiple share classes for the same issuing body are combined.

[4] The higher of these considers that it is not practical to maintain weights exactly at the boundaries of what is permissible.

[5] For example, the FTSE100 largest position is currently 11.3%. Further, as of 16/11/2018, the NASDAQ had 41.0% of its weight in just 4 positions with the largest at 11.9%.