A model for selecting an optimum investment portfolio,devised by H. M. markowitz. It uses a discrete-time, continuous-outcome approach for modeling investment problems, often called the mean-variance paradigm. See Efficient frontier.
Harry Max Markowitz (born August 24, 1927) is an American economist and a recipient of the John von Neumann Theory Prize and the Nobel Memorial Prize in Economic Sciences.
Modern Portfolio Theory
A theory on how risk-averse investors can construct portfolios to optimize or maximize expected return based on a given level of market risk, emphasizing that risk is an inherent part of higher reward.
Portfolio theory deals with the value and risk of portfolios rather than individual securities. 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:
√(ΣWi2σi2 + ΣΣWiWjCovij)
where the sums are over all the securities in the portfolio,
Wi is the proportion of the portfolio in security i,
σi is the standard deviation of expected returns of security i, and,
Covij is the covariance of expected returns of securities of i and j.
Two Kinds of Risk
Modern portfolio theory states that the risk for individual stock returns has two components:
Systematic Risk – These are market risks that cannot be diversified away. Interest rates, recessions and wars are examples of systematic risks.
Unsystematic Risk – Also known as “specific risk”, this risk is specific to individual stocks and can be diversified away as you increase the number of stocks in your portfolio (see Figure 1). It represents the component of a stock’s return that is not correlated with general market moves.
For a well-diversified portfolio, the risk – or average deviation from the mean – of each stock contributes little to portfolio risk. Instead, it is the difference – or covariance – between individual stock’s levels of risk that determines overall portfolio risk. As a result, investors benefit from holding diversified portfolios instead of individual stocks.

Figure 1 |