Question

Explain in detail how to design an optimal portfolio with N risky assets. What is an efficient frontier?

Answer 1

Designing an optimal portfolio with N risky assets

An optimal portfolio is the one that maximizes your returns for a given level of risk, or minimizes the risk for a given return(expected).

It implies that both the risk and return cannot be seen in isolation. Both of them are positively co-related, higher the risk, higher would be the returns associated.

Firstly, diversify into more asset classes having low correlations to stocks and bonds. Also, diversification into active strategies can be done.

An investor is interested in investing capital in number of available assets(n) so that the expected return is maximized.

With a set of n assets, with asset j ∈ {1 . . . n} having a return of Rj at the end of the investment period.

Let xj be the percentage of capital invested in asset j

Let x = (x1, . . . , xn) denote the portfolio choice

The portfolio’s return is given as

Rx = x1R1 + . . . + xnRn (Rj - Random variable)

Efficient Frontier

An efficient frontier is a set of optimal portfolios that offer the highest returns(expected) with a defined level of lowest risk.

Portfolios that lie below the efficient frontier are considered sub-optimal, as for the given risk, they offer lower returns. Refer to the graph above.