[[Start here]] → [[diversify for resilience|diversity]] → effective position count --- It’s easy to fall into the trap of counting the number of positions you hold and considering that your portfolio breadth. But you may hold far less stocks than you can think if your position sizes vary. One of the most useful tools to measure this is the Herfindahl Index (or HHI for short). The Herfindahl Index has been used by Anti-Trust authorities to measure the concentration of a markets. It helps them identify monopolies, and uncompetitive markets that may be in need of reform. But quants have found it just as valuable for evaluating portfolios. You can calculate it by summing the squares of the weights of the position in your portfolio. You’ll end up with a number between 0 and 1. Lower values indicate broad diversification and higher values concentration. More usefully though, you can calculate your “effective number of positions” by calculating the inverse (i.e. 1/HHI). This gives you the number of *equally weighted* positions that would provide the same level of concentration as your actual portfolio. ## **Why It Matters** An example is useful here. If your portfolio has 10 equally weighted stocks, it would have an HHI of 0.1, yielding an effective number of positions of 10. However, as soon as you deviate from equal weighting, the effective number of positions (or ENP) drops, often dramatically. Even if you hold 20 stocks, if a few positions dominate the portfolio, your ENP - and therefore your true portfolio breadth - is significantly less than the number of stocks you own. This could expose you to much higher risks than you realise. For instance, if 60% of your portfolio is concentrated in your top few holdings, the ENP might be as low as 6 - far less effective positions than the 10 stock portfolio! Compare the calculations below: ![[herfingdahl.png]] This is important as you could easily be deceiving yourself about how diversified you are. Holding a large number of positions provides little benefit if most of your capital is allocated to just a few of them. The ENP provides a clearer picture, allowing you to adjust your portfolio if you find that your effective diversification is lacking. ## How to use it 1. **To calculate the HHI**: Sum the squares of the weights of each position in your portfolio. 2. **Determine Your ENP**: Calculate 1/HHI to find the equivalent number of positions if they equally weighted positions. 3. **Adjust/Rebalance if necessary**: If your ENP is lower than you'd like, consider making changes to your portfolio position sizing, and selling any redundant positions. In summary, while the count of your positions is a starting point, the Herfindahl Index provides a more accurate assessment of your actual portfolio breadth (diversity). ## For the geeks… The formula looks like this: \[ HHI = \sum_{i=1}^{N} w_i^2 \] Where \( w_i \) represents the weight of each position in the portfolio.