Diversification can be viewed by many as an attractive tool for risk limitation for a given portfolio currently held by investor. Dealing with numbers one can show that if one holds $N$ securities that are uncorrelated completely, the volatility of such portfolio $Vol(P)$ will decrease with an increasing number of securities $N$ as follows:

$$

Vol(P) = \left[\sum_{i=1}^{N} \left(\frac{1}{N}\right)^2 Var(y_i)^2 \right] = \frac{Var(y)}{\sqrt{N}} .

$$

What remains unspoken but important to keep in mind is that all securities $i$ where $i=1,…,N$ have the same volatility and the same expected return. Therefore, by holding uncorrelated securities, one can eliminate portfolio volatility if one holds sufficiently many of these securities.

That is a theory. The investor’s reality is usually far from this ideal situation as portfolios usually contain a number of investments mutually connected or dependable upon themselves as the feedback to the market movements or sentiments. Thus, the reminder of *diversifiable risk* which cannot be eliminated by the diversification process becomes a *systematic risk*.