Previously, we've discovered several methods for estimating portfolio, including return, risk, and their combination known as risk-adjusted return.

However, we still needed to determine how to select weights for portfolio which satisfy our requirements.

The answer on this question is given by Modern Portfolio Theory (MPT).

What is MPT?

First of all, let's define what Modern Portfolio Theory is.

Practically, this theory introduces an important concept known as the efficient frontier, which is a key element of MPT.

What is Efficient Frontier?

Now, let's define the efficient frontier:

We can visualize this as follows.

Imagine we have a set of different portfolios, each with a specific values of risk and expected return.

In this context, each point represents a portfolio, determined by its risk and expected return:

Practically, the efficient frontier would be a line where each point represents an optimal portfolio, which approximately would look like this:

In this context, points that are closer to the efficient frontier represent better portfolios.

The efficient frontier is positioned above all the plotted points, indicating that for the same level of risk, points of efficient frontier offer higher expected return. This aligns with the definition of optimality in terms of MPT.

Additionally there are two special cases of optimal portfolios which we will discuss in detail in the next chapter.