Last week, we tried to estimate the number of stocks needed in a portfolio to effectively reduce unsystematic risk.
But most active managers, and most investors in actively managed funds, are looking to achieve the exact opposite outcome: to use concentration and high tracking error to achieve excess returns.
Instead of asking how to diversify away unsystematic portfolio risk, the question becomes: How many stocks should you own in a concentrated factor portfolio if the goal is maximizing expected returns or Sharpe ratio?
We constructed four factor portfolios each year from 1995 to 2022, drawn from the largest 500 US-listed companies and ranked composites of the following metrics:
We then drew the top n ranked stocks for each factor composite from 1995 to 2022, rebalancing annually. The CAGR of each portfolio as n increases is shown below in Figure 1.
Figure 1: Concentrated Factor Portfolio CAGR as n Increases (1995–2022)
Source: Capital IQ, Verdad research
According to our research, both quality and value portfolios exhibit peak CAGRs around 15 to 20 stocks, with returns declining as n increases. (Note that we focused here on large cap stocks; the optimal number for small and micro cap portfolios is significantly higher). Meanwhile, growth portfolios exhibit a below-market CAGR, which approaches the market average as n increases. The size portfolio, which in effect represents no skill (we have no reason to believe that buying larger companies within the S&P 500 should exhibit excess returns) approximates the market return regardless of portfolio size.
For asset allocators, the observations are interesting. For quality and value strategies, higher concentration is better. If the objective is higher returns and a willingness to stomach higher volatility, it seems the optimal portfolio size is somewhere between 15 and 20, in our opinion. As mentioned in last week’s piece, we believe optimal Sharpe ratios are achieved with closer to 200 stocks as tracking error steps down considerably.
For growth strategies, concentration is worse. As we’ve written previously, growth is neither persistent nor predictable, so owning a concentrated portfolio of the trailing growth champions is bound to disappoint.
At very low values of n (<10), the volatility of the portfolios drowns out any excess expected return for each factor. This seems to stabilize with portfolios sizes of around 15–20 stocks, as shown in Figure 2 below.
Figure 2: Concentrated Factor Portfolio Summary Statistics as n Increases
Source: Capital IQ, Verdad research
The optimal relative Sharpe is still achieved at 200–300 stocks, but here the excess CAGR is significantly reduced relative to a more concentrated portfolio. We believe the sweet spot for excess returns in large caps, balancing the elimination of truly wild volatility, seems to be achieved at 15–20 stocks.
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This document may contain forward-looking statements that are based on our current beliefs and assumptions and on information currently available that we believe to be reasonable, however, such statements necessarily involve risks, uncertainties and assumptions, and investors may not put undue reliance on any of these statements.
References to indices or benchmarks herein are for informational and general comparative purposes only. Indexes are unmanaged and have no fees or expenses. An investment cannot be made directly in an index.
The information in this presentation is not intended to provide, and should not be relied upon for, accounting, legal, or tax advice or investment recommendations. Each recipient should consult its own tax, legal, accounting, financial, or other advisors about the issues discussed herein.