Authors: Guido Bolliger and Dries Cornilly
We have often been asked by clients and prospects why we are running our equity impact portfolios with 100 to 150 positions. Indeed, our main competitors tend to hold between 30 and 50 positions in their thematic portfolios, as do thematic active EFTs.
Of course, risk diversification (sector, region, and style) is one of the reasons, but we are also convinced that the fundamental law of active management applies when it comes to long-term risk-adjusted performance.
In this short note we recall the fundamental law of active management and apply it to one of the most skilled long-term investors of all-time, Warren Buffett.
The fundamental law of active management
The law was developed by Grinold and Khan. It is designed to assess the added value of active management, measured by the information ratio, by using only two variables. The first variable is the skill of portfolio manager in selecting securities and reflects the quality of the investment manager in selecting the right stocks. Stock selection can be done through a discretionary fundamental approach, a systematic quantitative approach, or a combination of both. At Asteria, we use a quantitative approach. The second variable is breadth, representing the number of independent investment opportunities. In a simplified world, this is the average number of securities in the portfolio. Note that this simplification ignores the likely correlation between equities.
In formula form, the fundamental law of active management reads
𝐼𝑅 =𝐼𝐶 ×√𝑁
- IR: information ratio computed as the manager’s return in excess of the market divided by the tracking-error
- IC: information coefficient or selection skill
- N: number of independent investment opportunities or breadth
Measuring the selection skill of Warren Buffett
Warren Buffet has been successfully running Berkshire Hathaway since 1970. He is probably one of the best investment managers of all time and runs a concentrated US investment portfolio with a value/quality bias. As of December 12th, 2022, there are 20 positions in his portfolio. We use the track-record of the Berkshire Hathaway stock price (BRK/A US Equity) since January 2000 to derive Warren Buffett’s skills. As his portfolio is mostly concentrated in US mega-caps, we use the S&P 500 index as benchmark.
Exhibit 1: Berkshire Hathaway performance (Jan. 2000 to Nov. 2022)
From these numbers we derive that the selection skill of Warren Buffett equals 0.09:
𝐼𝐶 = 0.4/√20 = 0.09.
Fund concentration and implied skill level
Having identified an information ratio of 0.4 as our skilled investor benchmark, we calculate the level of security selection capabilities that are required to reach this value. To do so, we vary the number of holdings from 20 to 150 and calculate which level of skill, or information coefficient, is required to match an IR of 0.4.
Exhibit 2: Number of positions and security selection skill
What does this chart tell us? First, it shows that the level of skill required to reach an information ratio of 0.4 decreases as the number of positions increases. An active portfolio manger with 40 positions needs almost twice the amount of skill than the portfolio manager with 120 positions to reach the same information ratio of 0.4.
Second, the active portfolio manager with 40 positions needs to be almost as talented and skilled (71%) as Warren Buffett to reach the target information ratio. While we probably do not have the security analysis skills of Warren Buffett, we more than make up for it in breadth. In case we have the same skill level as the average impact fund, running a diversified portfolio of 120 equities results in an information coefficient that is about 50% higher than the one usually seen by impact funds with 50 positions.
The average thematic impact funds or ETFs tend to be very concentrated. As we showed, to reach a good long-term risk-adjusted return, significant security selection skills are required. Diversification is probably the only free lunch that exists in investment management. We made the explicit choice of using this free lunch to achieve better long-term information ratios.
The only downside of an approach focused on breadth is that it is more difficult for us to engage in “story telling” with our prospects and investors. We can’t meet the management of the 300 firms that constitute our investment universe. Neither can we develop a specific discounted cash-flow model for each of these companies. However, we believe that our fiduciary duty is to generate above-average risk-adjusted performance with impact on top rather than to tell stories.
 Grinold, Richard, and Ronald Kahn. 1994. Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk. McGrow-Hill Library of Investment and Finance.