Ryan Giannotto, CFA
- Square root of market cap weighting diversifies portfolios and counteracts high concentration issues.
- This method automatically targets high weight holdings most aggressively, and does not rely on arbitrary hard caps.
- Application in US large cap and digital asset markets effectively enhances investability and risk management.
Market concentration is proving a pain point for investors and allocators across many assets. Not only do risk contributions become defined by an ever more select cohort of the largest companies and assets, but the benefits of cross-asset diversification are diminished as well. Put bluntly, market concentration forces us to be bad portfolio managers, where even going passive entails making the big bets that were formerly the domain of active investors.
Defining asset exposures by the square root of market caps, rather than raw market cap weighting, is a clever approach to dampen the ill-effects of hyper concentration. This strategy is both simple and demonstrably effective; it reduces the extreme weights of top holdings while preserving the relative proportion of assets across the portfolio. After exploring the basic operation of a square rooted cap methodology, we will examine how this strategy performs in the highly concentrated US large cap and digital asset markets, in both cases enhancing investability.
The Roots of a Solution
The Concentration Cheat Sheet
| Top 5 Weight | Bottom 50% Wgt | Effective N | ||||
|---|---|---|---|---|---|---|
| M Cap | Sq Root | M Cap | Sq Root | M Cap | Sq Root | |
| Russell 1000 Index | 21.50% | 4.70% | 7.10% | 25.00% | 76 | 543 |
| Smart Contract Platform Index | 86.30% | 44.60% | 2.80% | 20.60% | 1.76 | 11.83 |
| Digital Currency Index | 99.10% | 86.10% | 0.40% | 9.80% | 1.18 | 2.78 |
Source: FTSE Russell Data, September 2023.
As an example of this naturally corrective approach, consider Companies A, B and C with market caps of $1,000,000, $10,000 and $100 respectively (obviously this is from before the inflation cycle), where each company is 100 times larger than the next. If we take the square roots of these market caps however, we get values of $1,000, $100 and $10; notice how Company A is reduced by a factor of 1,000 while Company C is scaled down only by 10. This effect follows as square roots naturally reduce larger numbers to a larger extent than they do small numbers. Moreover, the proportional weighting between each company is now only 10 to 1 compared to 100 to 1 as was previously the case under market cap weighting—when concentration become more extreme, rooting enacts a greater intervention for restorative balance.
Large Cap, Large Concentration
Beginning with the familiar before progressing to the novel, the square root methodology can vigorously reapportion the outsized weights of the U.S. large cap ecosystem. The chart below depicts this dramatic reconfiguration, where the top 25 holdings are scaled down from 40.3% of the index weight to only 12.7% under the square root method. This dynamic also helps remediate the valuation risk arising from portfolio concentration—why allocate so heavily to names after aggressive run-ups in price?
Russell 1000 Index Recapped
Source: FTSE Russell Data, as of 9/30/23. Past performance is no guarantee to future results. Please see the end for important disclosures.
Moreover, the non-linear adjustment mechanism is clearly at play. The top holding Apple undergoes a staggering 83% reduction in weight, while META is downsized only by two thirds, and by the time we reach the 25th holding, PepsiCo receives only a 44% haircut. Hence disproportionate outliers are earmarked for disproportionate redress. The crossover to when companies increase in weight occurs fairly high in the portfolio, beginning with 108th holding of CME Group with its $72 billion market cap.
Market Cap Portfolio
Source: FTSE Russell Data, as of 9/30/23. Past performance is no guarantee to future results. Please see the end for important disclosures.
The impacts of the square root methodology reverberate throughout the whole portfolio, and are not isolated to the top holdings. The pie charts above illustrate the cascading effects in each tranche of the large cap universe, where the pesky MAG 7 see a whopping 19 percentage point decrease and the remaining top 100 names are cut by 14 points. In effect, this freed up portfolio weight is redistributed though the bottom 89% of the index. While market cap squeezes all but the top 120 names into a 25% share of the portfolio by weight, square rooting gives the bottom half of holdings a near one quarter allocation, a 3.5 factor increase. The effective number of companies in the index rises markedly as well, progressing from a paltry 76 to a much more robust 543.
Leveling the Digital Playing Field
If market cap weighting can prove challenging for large cap investors, it can be prohibitive entirely with respect to digital crypto assets. The upstart ecosystem is characterized by the two break-out assets of Bitcoin and Ethereum against a backdrop of nascent, yet significant, universe of digital holdings. This emerging environment is the ideal use case for the square rooting methodology, creating indices designed for investability and meaningful diversification. Two pioneering indices will be used to bear out this thesis, first the FTSE Grayscale Smart Contract Platform Index (SCP), and second the FTSE Grayscale Currency Index—anchored by Ethereum and Bitcoin respectively.
A Tale of Two Cappinings: Smart Contract Platforms
Concentration no more—rooting creates a balanced portfolio. Source: FTSE Russell Data, as of 9/15/23. Past performance is no guarantee to future results. Please see the end for important disclosures.
Square rooting literally flips the script with the SCP index, as while Ethereum garners a 75.0% weight under a conventional market cap regimen, rooting gives the other 38 holdings a 74.8% allocation. In either scenario, Ethereum with its roughly $200 billion market cap remains the primary risk contributor, but the square root method creates ample space for the smart contract ecosystem on a holistic level. Whereas raw cap weighting yields an effective-N of 1.76—essentially a single stock exposure with a few token positions—rooting market cap broadens this figure to 11.83.
Digital Assets Currencies Ecosystem
Square rooting confronts the $500 billion gorilla of the digital assets market. Source: FTSE Russell Data, as of 9/15/23. Past performance is no guarantee to future results. Please see the end for important disclosures.
While smart contracts feature a great diversity of offerings, the digital assets currency market is a much more circumspect sector—and yet square rooting can once more help tame the concentration. By raising market caps to the power of one half, the allocation to Bitcoin is reduced from 92.3% to 57.6%, and effective-N increased from 1.18 to 2.78. The downscaling is not as intense as is the case with the smart contract portfolio, as the square rooting methodology benefits from a greater number of constituents. As it stands, some of the smaller currencies such as Zcash and Ravencoin have seen their weights bolstered by a factor of over 30.
Creating Balance from Concentration
Lamenting concentration has emerged as every investor’s most frustrating pastime. By taking the square root of constituent market caps, indexes can be aggressively recalibrated to create a more level distribution of risks, demonstrated in U.S. large cap and cryptocurrencies alike. We cannot change the market we are dealt, but we can adapt new strategies to better manage the dilemma of concentration. We’re rooting for you!
For more information about the FTSE Grayscale Crypto Sectors Index Series, please visit FTSE Grayscale Crypto Sector Index Series.
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