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The science of portfolio concentration

How many stocks you should have in your portfolio for the optimum balance between risk and reward

The science of portfolio concentration

One of the main goals of portfolio construction is to optimise risk vs reward (or returns). As the number of stocks increases in a portfolio, diversification reduces the stock-specific risks involved in the portfolio. However, excessive diversification reduces returns more than it reduces risk, because:

1. Every incremental stock added to the portfolio is likely to be inferior in quality as compared to the previous stocks in the portfolio.
2. In a fundamental-research-based portfolio, the wider the coverage universe, more difficult it is for the research team to conduct deep research.
3. The diversification benefits from every incremental stock added to the portfolio reduce as the number of stocks in the portfolio increases.

So, how many stocks in a portfolio make it optimally balanced? The answer to this question might not be a 'one-size-fits-all' approach. Some of the most successful funds globally call a 30-40-stock portfolio as 'concentrated' and above 50 stocks in a portfolio as being overdiversified. However, there are other successful funds which view a 10-20-stock portfolio as being 'concentrated' and a 30-stock portfolio as being overdiversified.

At Marcellus, we use our proprietary framework for arriving at the number stocks in a portfolio, based on a few factors that drive portfolio concentration. One of the biggest factors in our framework is the 'gradient' of the characteristics that the fund manager seeks within her coverage universe. Here we lay out the science behind this factor to optimise the risk-reward trade-off embedded in our portfolios.

The science of portfolio concentration

The 'gradient' of fund philosophy
There are various ways to make money in the stock market - timing cyclical stocks; buying and holding high-fundamental, high-quality stocks; timing business turnarounds; stock-discovery-based valuation expansion (i.e., P/E multiple expansion); macro-based themes; sectoral themes; disruption-based themes; unicorn hunt; and many more. Hence, every equity fund manager's investment philosophy seeks a different 'characteristic' in the stocks that are selected in their portfolio.

Within the coverage universe of a fund, the fund manager is likely to be more convinced about the characteristics of certain stocks as compared to others. This will typically lead to a gradient of conviction across the coverage universe of such a fund manager at any point of time. As highlighted in the charts, this gradient can either be steep or relatively flat.

The steeper the gradient, the fewer should be the number of stocks in an optimal portfolio. This is because a steep gradient implies that every incremental stock added to the portfolio reduces the quality of the overall portfolio meaningfully. Hence, as shown in chart 'Steep gradient in the coverage universe', the first few stocks added to the portfolio improve the risk-reward because the reduction in risk due to diversification is significantly greater than the compromise on portfolio returns. For instance, a 10-stock portfolio could be substantially less risky and hence offer better risk-reward compared to a three-stock portfolio, despite the average characteristic score of a 10-stock portfolio (and hence the expected returns) being slightly lower than that of a three-stock portfolio.

After adding a few stocks to the portfolio, the marginal risk reduction due to diversification tapers off (as highlighted in the chart 'Steep gradient in the coverage universe'). For instance, the concentration risk of a 30-stock portfolio is not substantially lower than that of a 20-stock portfolio. However, the expected portfolio performance of a 30-stock portfolio could be meaningfully lower than that of a 20-stock portfolio. Therefore, the compromise on portfolio returns becomes a meaningful and avoidable drag on the overall risk-reward of the portfolio after a certain number of stocks have been added in such a portfolio. For such a coverage universe (with steep gradient), it might be prudent to have no more than 10-15 stocks in the portfolio and focus on the fund manager's depth of fundamental research to further reduce portfolio-level risks, rather than relying on adding more stocks to the portfolio.

The flatter this gradient, the greater should be the number of stocks in an optimal portfolio. This is because a flat gradient implies that every incremental stock added to the portfolio does not reduce the quality of the overall portfolio. Hence, as shown in chart 'Flat gradient in the coverage universe', after the first 10-20 stocks have meaningfully improved the risk-reward, there is no deterioration in the risk-reward of the portfolio due to the increase in the stock list to beyond 20 stocks. This is because there is no reduction in expected portfolio returns as the number of stocks increases, whilst there is a continued marginal reduction in risk due to portfolio diversification. For instance, the concentration risk of a 30-stock portfolio is slightly lower than that of a 20-stock portfolio, despite the expected performance of a 30-stock portfolio being the same as that of a 20-stock portfolio. For such a coverage universe, it is prudent to increase the number of stocks in the portfolio to the extent that the gradient of stock characteristics remains flat in the coverage universe.

Investment implications
Marcellus invests in a portfolio of companies where our research team is convinced about their (a) ability to generate strong free cash flows (hence high ROCEs) through deep-rooted competitive advantages and (b) ability to consistently reinvest the free cash flows back into the business to generate growth without any dilution in ROCEs over long periods of time.

There are not too many firms in India which fit this 'gradient' and hence our CCP (Consistent Compounders Portfolio) philosophy's coverage universe is very small. In fact, this characteristic is so rare in India that the top 20 profit generators in India ('the Leviathans') now account for 90 per cent of the country's corporate profits. Beyond dominating the country's profit pool, the Leviathans also reinvest these profits far more efficiently back into their businesses. By doing this over the last 25 years, the Leviathans have also widened the ROE gap between them and India Inc.

Since only a handful of companies in India possess the characteristics that we seek, the coverage universe of Marcellus' portfolio has a steep gradient, similar to what is highlighted in chart 'Steep gradient in the coverage universe'. Hence, we manage tightly concentrated portfolios containing 12-15 stocks.

Saurabh Mukherjea is the author of 'The Unusual Billionaires' and 'Coffee Can Investing: The Low-Risk Route to Stupendous Wealth'. He's part of the Investments team at Marcellus Investment Managers, a SEBI regulated provider of Portfolio Management Services.