# Portfolio Diversification Theory Explained | CFA Level I Portfolio Management

Welcome back! Today, we’ll explore the theory of portfolio diversification, with a focus on understanding how to apply the formula for portfolio standard deviation. Let’s dive in!

## Theory of Portfolio Diversification

We learned in our last lesson that the standard deviation of returns can be an estimate of an asset or portfolio’s risk level. We’ll now dive deeper into the formula for calculating the portfolio variance of returns for a 2-asset portfolio. Remember, taking the square root of the variance gives us the standard deviation of returns.

## Understanding the Role of Correlation in Diversification

When two assets are perfectly positively correlated, there is no diversification benefit. The risk is simply a linear function of the weights of the 2 assets. However, when two assets are perfectly negatively correlated, you can create a portfolio with zero risk! The key takeaway is that the lower the correlation between the assets in a portfolio, the lower the risk of the portfolio. This illustrates the benefit of diversification.

### Portfolio Diversification in Practice

Most portfolios in practice consist of several different assets to improve diversification benefits. By plotting the expected return and standard deviation for different combinations of asset weights, we can identify the minimum-variance frontier and the efficient frontier.

#### Minimum-Variance Frontier

At each level of expected return, there is a portfolio with the minimum standard deviation. These portfolios are called the minimum-variance portfolios, and together, they make up the minimum-variance frontier.

#### Efficient Frontier

Assuming investors are risk-averse, they prefer the portfolio with the greatest expected return amongst portfolios with the same level of risk. The portfolios at the top half of the minimum-variance frontier that have the greatest expected return for each level of risk make up the efficient frontier. Risk-averse investors would only choose portfolios on the efficient frontier.

## Conclusion

And that’s it! In this lesson, we’ve covered the theory of diversification, the role of correlation in diversification, and the concepts of the minimum-variance and efficient frontiers.

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