The Efficient Frontier

Efficient Frontier presents a set of optimal portfolios offering the highest expected return for a given level of risk or the lowest risk for a given level of expected return. The efficient portfolios have the optimal risk return balance and can be considered optimal for given risk-return ratio.

The theory of Efficient Frontier suggests that each combination of securities can be presented on a graph on its two axes defining the standard deviation (risk) of the securities and their expected returns. An area bordered on the risk-return space by an upward sloping line indicates the set of portfolios. This line is called the efficient frontier.

The portfolios that fall on the efficient frontier are considered efficient, meaning portfolios with the lowest level of risk for a given amount of return or with the highest level of return for a given level of risk.

The Two Mutual Fund Theorem

An essential point in the theory of the efficient frontier is the Two Mutual Fund Theorem. The idea of the theorem is the following: a combination of any two portfolios that are fallen on the efficient frontier and are accepted to be called mutual funds leads to the generation of an efficient portfolio.

As already mentioned, efficient portfolios give the maximum return for a given risk or the minimum risk for the given return.

Here is how to select portfolios:

  • From the portfolios having the same return choose the one with lower risk
  • From the portfolios having the same risk level, choose the one with higher level of return.
The Efficient Frontier
Efficient Frontier - Separation Theorem

The shaded area shows all the possible securities an investor can invest in. The efficient portfolios fall on the boundary of ABDE. It is obvious that at the same risk level (here it is x2), there are two portfolios C and F from which the portfolio C is considered efficient. This is because by the same risk level it has the highest return.

Choosing the Best Portfolio

Selecting the best portfolio is based on the analysis of risk-return preferences. The portfolios lying below the Efficient Frontier are not referred as good enough as in this case the return would be lower at the given risk level. Portfolios lying to the right of the Efficient Frontier are also regarded not so good, because there is higher risk for a given level of return.

It’s typical of an highly risk averse investor to choose a portfolio on the lower left side of the frontier and conversely, an investor who isn’t so risk averse is likely to choose the one on the upper side of the frontier. Therefore, choosing the optimal portfolio also depends on the investor’s risk tolerance. But the fact is that Efficient Frontier is the same for all investors since they all set the goal to get the highest return with the lowest possible risk.