Portfolio theory

Portfolio theory deals with the value and risk of portfolios rather than individual theories. It is often called modern portfolio theory or Markowitz portfolio theory.

The key result in portfolio theory is that the volatility of a portfolio is less than the weighted average of the volatilities of the securities it contains. The standard deviation of the expected return on a portfolio is:

√(ΣW_i²σ_i² + ΣΣW_iW_jCov_ij)

where the sums are over all the securities in the portfolio
W_i is the proportion of the portfolio in security i
σ_i is the standard deviation of expected returns of security i
and Cov_ij is the covariance of expected returns of securities of i and j.

Assuming that the covariance is less than one (invariably true), this will be less than the weighted average of the standard deviation of the expected returns of the securities. This is why diversification reduces risk.

The other important results in the financial economics of portfolios are those dealing with the construction of efficient portfolios.