# Diversification Can Be Achieved From Fewer Stocks

In an earlier article, I discussed about the importance of quality of stocks in a portfolio rather than number of stocks for risk manage

I am using a stock being positive or negative as

Here, my interest is to break it down to the best possible scenario, and that is, stocks being +ve or stocks being –ve. I am calculating the probability of 1 stock being +ve in 1 stock portfolio, in a 2 stock portfolio, in a 5 stock portfolio, in a 10 stock portfolio, and in a 20 stock portfolio. Furthermore, this probability can the extended to 2 stocks being positive or 3 stocks being positive. The results are then plotted for graphical presentation and discussion.

The chart below shows the plot of probability of stock being positive vs. number of stocks in a portfolio. This chart is read as follows:

- The curve 1 +ve stock is the curve (topmost curve) for probability of one stock being positive for a portfolio with 5 stocks, 10 stocks, 15 stocks, and 20 stocks.
- If a portfolio consists of only one stock, then probability that it will be positive is 0.5 (i.e. 50% chance that it will be positive).
- If a portfolio has 5 stocks, then the probability that at least one will be positive is 0.9.
- If a portfolio has 10 stocks, then the probability that at least one will be positive is 0.95.
- If a portfolio has 20 stocks, then the probability that at least one will be positive is 0.98.
- The chart shows similar curves for probability of 2 positive stocks, three stocks, 4 positive stocks, and 5 positive stocks.

In general, it can be observed that there is a significant increase in probability of stocks being positive until 5 or 10 stocks in the portfolio. Beyond that the change in probability of stocks being positive is very very small.

We want to have higher probability for stock to be positive. Let us say we want to have 0.8 probability, so we look at this chart horizontally at 0.8. We can have that with 5 stocks, 8 stocks, 10 stocks, and 12 stocks (intersection points between curve and full digit stock). As an individual investor what would you do? If the odds are sa

These simple probability curves show that there is an optimum point beyond which more stocks will not have any diversification benefits.

**A Customary Caveat**: The results from these plots are good for understanding the relationship among different variables (in this case number of stocks vs. diversification). These may not be used for making portfolio decision. While it correctly explains the funda