All such optimal portfolios, i.e., one for each level of return, comprise the efficient frontier.

Thus buyers and sellers must adjust the prices of assets to make them attractive enough to fit into someone's "optimal" portfolio.

Suggested optimal portfolios are created from either user-controlled model portfolios or from predefined investing themes.

Robert Merton used stochastic control to study optimal portfolios of safe and risky assets.

The optimal portfolio at arbitrary can then be written as a weighted average of and as follows:

For selection of the optimal portfolio or the best portfolio, the risk-return preferences are analyzed.

The investor's optimal portfolio is found at the point of tangency of the efficient frontier with the indifference curve.

Any other portfolio, say X, isn't the optimal portfolio even though it lies on the same indifference curve as it is outside the efficient frontier.

Constructing the optimal portfolio in terms of both performance and volatility is easy, too.

An investor may not even be able to assemble the theoretically optimal portfolio if the market moves too much while they are buying the required securities.