Diversification is a confusing topic for some investors. More often than not, it simply acts as a media buzz word to sell investors more securities into their portfolio than they need. However, there can be no argument against the effectiveness of diversification as a means of improving the stability of a portfolio.

The trick comes down to being able to understand the basic mathematical reasoning behind diversification, and how it applies to a personal investment portfolio. Don’t worry, I’m not going to overwhelm you with numbers in this article. I’m instead going to do all the math for you, and return with the simplest explanation of why it is you should have at least 32 holdings in your portfolio.

The simplest reason as to why you want 32 holdings in a portfolio is “because the math told you so”. From a basic mathematical standpoint, a portfolio of 32 equal holdings will result in you having a maximum position size of 3.125% your entire wealth. Think about that for a minute, it means that the complete bankruptcy of a company in your portfolio will only result in an acute loss of 3% of your holdings.

Given that stock indexes alone tend to increase as a whole by as much as 3-7% in a year, a 3% loss caused by a dramatic loss in value seems to have a fairly inconsequential impact. However, having an equal distribution of stocks in our portfolio assumes that there is an equal risk and reward for each of the holdings.

In order to accommodate for varying risks and rewards within our portfolios, we need to begin shifting the weightings of our positions. Ideally, we want this shift to reflect a desire for consistency. This means that we should weight our most volatile holdings as lightly as possible, and weight our least volatile as heavily as possible. Ideally, this will create a bell-curve of returns. The smallest, and most volatile positions will create the greatest percentage returns by themselves, and therefore create similar positional returns as the larger, and more stable positions.

However, because we are spending less money on the more volatile returns, we are getting a more efficient return overall, while maintaining the stability of the core holdings. So how do the pros handle this situation?

A professionally managed fund will generally allocate its holdings in a way that allow it to best take advantage of volatility. If you look on the marketing materials of a fund, you’ll notice that it will usually be advertising its top ten holdings as being between 3-6% of their total position. These are the positions that are expected to perform with the greatest respect for the goal of the fund. Assuming the fund holds at least 32 positions, it means that all of the other positions must be diluted to reflect their contributions to the fund.

In funds with upwards of 50 holdings, you may see that there are positions that are less than half a percent of the holdings of the entire fund, but may make up a full couple percentage points worth of returns in a given year because of a massive surge in the stock. Through careful evaluation, a fund manager is able to evaluate how to allocate resources towards creating stable cash flows over the long term, without exposing investors to the volatility of systemic risk.

So with that information in mind, lets come back to the initial question of the article: Why 32 positions? Rather than boggle you down with math, I think the best way to describe the tests over time that have decided this basic minimum is through the ‘coin-toss’ thought experiment. Assuming you flip a coin a number of times, at what point do you become reasonably sure that the future outcomes will be 50%? For our purposes, the general answer is about 32.