Different combinations of securities produce different levels of return. The efficient frontier represents the best combination of these assets i.e. those that produce the maximum expected return for a given level of risk. The efficient frontier is the basis for modern portfolio theory.

Modern portfolio theory was introduced by Harry Markowitz in 1952. Markowitz is a professor of finance at the Rady School of Management at the University of California, San Diego (UCSD). He later was awarded the Nobel Prize in economics for his work in the field of modern portfolio theory.

The core of Markowitzâ€™s MPT is the observation that investments should not be seen as isolated assets but observed in the context of the whole portfolio. He found that there are three parameters that describe the contribution of each individual asset to the overall portfolios:

- the expected return of each asset
- the degree of variation of each asset i.e. the volatility
- the correlation of the assets

Modern portfolio theory assumes that investors are risk averse, meaning that given two portfolios that offer the same expected return, investors will always choose the less risky one. Consequently, an investor is only willing to take on more risk if he gets compensated with higher expected returns. Equally, an investor who wants higher expected returns must be willing to accept more risk. The exact trade-off will be the same for all investors, but different investors will evaluate the trade-off differently based on their individual risk preferences. The implication is that a rational investor will not invest in a portfolio if a second portfolio exists with a more favorable risk/return profile, or to put it in other words, if for that level of risk an alternative portfolio exists that has better expected returns.

To construct an efficient portfolio, assets need to be combined to not only generate high expected returns, but to also ensure a steady return development of the overall portfolio. The relationship that assets have with each other is an important part of the efficient frontier. Some assets move in the same direction under similar circumstances, while others move in opposite directions. The more out of sync the assets in the portfolio are (i.e. the smaller their correlation), the smaller the risk of the portfolio that combines them. In other words, the individual assets should not be correlated to each other i.e. have a correlation of 0.

Diversification always leads to better investment results when there is uncertainty. And since markets are always uncertain, diversification is the way to go.

### Limitations

The efficient frontier and modern portfolio theory have many assumptions that may not properly represent reality. One of the assumptions is that asset returns follow a normal distribution. In reality however, asset returns are said to follow a leptokurtic distribution, or heavy tailed distribution.

Additionally, Markowitz’s theory assumes investors are rational, avoid risk when possible, not large enough to influence market prices, and have unlimited access to borrowing and lending money at the risk-free interest rate. However, in reality, the market includes irrational and risk-seeking investors, large market participants who influence market prices, and also investors do not have unlimited access to borrowing and lending money.