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Asset Allocation & Portfolio Management:
Diversification & Portfolio Risk
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We can calculate the variability (risk) as well for individual securities as for portfolio of securities. Of course, very long averages (like 25 years) are less interesting for specific companies than for market portfolio as it is rare that a single company faces the same business risks today as it did 25 years ago.

To demonstrate how diversification reduces risk, we first have to compute the risk (standard deviation) for let's say 9 stocks (S1 to S9) and the global portfolio P.

The results are (standard deviation for each stock):

On the portfolio made of the 9 above stocks (equally diversified), the standard deviation is 20%

Even if the standard deviation of the portfolio firstly looks high (20%), we can see out of the table that only 2 stocks have a standard deviation (risk) lower than the portfolio and that the portfolio standard deviation is lower than than the average standard deviation of each individual stocks.

Why is the portfolio standard error lower than the average standard deviation of each component?
 Because diversification reduces risk.

Diversification works because prices of different stocks do not move exactly together. Each day you have some stocks traded up and some stocks traded down. On a statistical point of view, we can say the stock prices are imperfectly correlated (see correlation and coefficient of determination in our statistic section) and therefore having them all in the portfolio reduces global risk.

The impact of diversification on portfolio risk can be illustrate by the following graph:

In the next section we will answer the following question: "Can the portfolio risk be completely eliminated by diversification?"

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