# Efficient portfolio frontier

The efficient portfolio frontier is the set of most efficient portfolios in a market, that is, those that offer the highest expected return according to the different levels of risk that can be assumed (or the lowest risk for an expected return).

It is represented graphically as a curve, where any portfolio that is not above the border line will not be efficient, and therefore it will be running unnecessary risks or receiving a lower return than it could obtain, with respect to the risk that is assuming.

Therefore, the efficient portfolio frontier represents the optimal relationship that we find in an investment portfolio between volatility and profitability, that is, between the benefits that the investor will be able to obtain and the risks that they will have to face to do so.

## Graphical representation of the efficient portfolio frontier

In the financial world there is usually a positive relationship between risks and profitability, the higher the profitability, the greater the risk, since if in a project the possibility of suffering losses is greater, the debtor will have to offer greater benefits to creditors, and otherwise it will be very difficult to obtain financing. At the frontier of efficient portfolios, the risk-free assets are the portfolios with minimum variance and are located to the left of the frontier. As risk increases, so does profitability.

This relationship between risk (whose measurement in finance is usually volatility, represented by the standard deviation) and profitability (as a percentage of the nominal amount invested) can be represented graphically with a curve that represents the efficient portfolio frontier (the blue line in the chart above). This curve is also called the "Markowitz frontier" and serves as a reference for making rational decisions about investment projects.

Markowitz modelThere is no common Markowitz frontier for all portfolios and situations, since in each case the values will change according to the market situation. If assets with less risk offer returns close to zero, this will push the curve down and force investors to take more risks to obtain the same returns as before.

Finally, it is important to point out that the market situation (that is, the relationship between profitability and risk to which all agents are subjected) is what defines the shape of the curve, but from then on it is each investor who decides. about which point on the Markowitz border you should position yourself. Thus, while the most conservative will seek positions in the left zone of the curve (where volatility is closer to zero), those with less aversion to risk will do so in the right zone, in search of a higher profitability even under the possibility of suffering greater losses.

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