Modern Portfolio Theory (MPT)

Modern portfolio theory (MPT) is a theory in finance that aims to maximize the expected return of a portfolio for a given level of risk. It is based on the idea that risk and return are two sides of the same coin: the higher the expected return, the higher the risk.

MPT was developed by Harry Markowitz in the 1950s. Markowitz's key insight was that investors can reduce risk without sacrificing return by diversifying their portfolios. This is because the risk of a portfolio is not simply the sum of the risks of its individual assets. Rather, the risk of a portfolio is also affected by the way in which the assets are held together.

MPT provides a framework for investors to construct portfolios that are both efficient and diversified. An efficient portfolio is one that maximizes the expected return for a given level of risk. A diversified portfolio is one that is not too heavily invested in any one asset class or security.

MPT is based on a number of assumptions, including:

* Investors are risk-averse.
* Investors can choose from a large number of assets.
* Investors can borrow and lend at the risk-free rate.
* Investors have perfect information about the future returns of assets.

These assumptions are not always met in practice, but MPT can still be a useful tool for investors.

MPT has been used to justify a number of investment strategies, including:

* Passive investing, which involves investing in a diversified portfolio of index funds.
* Active investing, which involves selecting individual stocks or bonds based on fundamental analysis.
* Quantitative investing, which uses mathematical models to select investments.

MPT is a complex theory, and there is still debate about its validity. However, it remains one of the most important and influential theories in finance.