# MODERN PORTFOLIO THEORY AS A FOUNDATION FOR EFFICIENT FRONTIER ANALYSIS

Modern portfolio theory (MPT) is a mathematical method developed in the early 1950s and built out through the mid-1970s as a theory of finance that focuses on the maximization of portfolio return while minimizing the risk for a given amount or level of expected return, by specifically choosing the proportions of various assets contained in the portfolio. For the most part, MPT consists of a number of mathematical formulations that simulate and identify the impact of a risk-adjusted strategy investment diversification where the portfolio risk profile is collectively lower in value or volatility than any one asset.

In general, MPT models asset returns as a normally distributed function and recognizes risk as the standard deviation of return where the portfolio is viewed as the weighted combination of assets. Thus, the return of a given portfolio is considered the weighted combination of the asset return streams (Markowitz 1952). Expected return is characterized as:

where *R*p, is the return on the portfolio, *R*i is the return on the asset *i,* and is the weighting of the asset *i,* which represents the asset *i* in the overall portfolio.

The operational concept behind MPT is that the assets in an investment portfolio should not be selected individually but should consider how their relative prices and values change across the portfolio. For many, this speaks to the relative trade-offs between calculated risk and expected return. Therefore, MPT would argue that assets and investments with higher expected returns attract higher measurable levels of risk. If the objective is to maximize the highest possible return on a portfolio of performing assets, MPT provides a way to describe and select those assets and investments that fit the return demand.

From an SRM perspective, within any operating organization there exists a series of hazard, operational, market, human capital, and reputational risks. These risks, while generally identified and mitigated separately, in fact exist in an integrated operational space – a risk portfolio. The essential questions that MPT can attempt to answer are:

• What is the economic value of an organization's material risk profile when characterized as a financial portfolio?

• How can the economic and operational volatility of an organization's risk profile be characterized dynamically and intertemporally?

• Are an organization's risk mitigation strategies and methods efficiently matching an organization's risk profile?

• If an organization changes its operations in a material way, what impact can be visualized across the organization's risk portfolio?

• Given the financial and operational activities of an organization, can an efficient^{[1]} risk profile be determined? What trade-offs might be required to achieve an efficient risk profile? Efficiency could be defined as maximizing the contractual financial return relative to the expected utility of risk transferred to a third party. If the trade is equal – in other words, the price of the transference effectively matches the economic dynamics of the risk – then the trade may be considered efficient for both parties.

• If risk retention and risk transfer are considered two independent variables in an organization's risk profile distribution, how can the value of risk retention and risk transfer be maximized throughout an organization's insurance purchasing approach?

The approach to answering these questions is found with a number of mathematical techniques within MPT, notably efficient frontier analysis (EFA), dynamic financial analysis (DFA), capital asset pricing modeling (CAPM), or some other behavioral economic analysis of choice under conditions of information uncertainty. For the purpose of this chapter and its case study, we focus on the use of EFA within an insurance purchasing context.

It is important, however, to point out that some assumptions contained within the original MPT framework have been controversial and have generated a lively even-sided debate within the academic and practitioner literature base.^{[2]}

The key assumptions include:

• The owners of portfolios are exclusively interested in the optimization problem.

• Asset returns are jointly normally distributed and random.

• Expected correlations between assets are fixed and constant without a time frame – in effect, forever.

• All parties to the use or exploitation of the portfolio always maximize economic utility regardless of other information, expectations, or considerations.

• All parties to the portfolio are considered rational and risk-averse.

• All parties to the portfolio performance have consistent, timely, and the same information at all points in time.

• All parties have the ability to accurately conceptualize and calculate the possible distribution of returns to the portfolio, and these calculations, in fact, match the actual returns of the portfolio.

• The performance of the portfolio is free of tax or transaction costs, and there is no transactional or postreturn friction.

• All parties to the portfolio are considered price takers, and their behaviors and choices do not influence the price market for the portfolio.

• Like the transactional or postreturn friction assumption, capital to invest in the portfolio is free and without an encumbering interest rate.

• A priori risk volatility can be conceptualized, calculated, and known in advance of the portfolio's construction, including asset/investment selection. Also, the portfolio's risk volatility is constant except when significant or material changes to the asset/investment distribution are made.

For many, the primary criticism of the MPT model and many of its derivative subanalytics is that the assumptions are overly restrictive and do not adequately model real-world markets. Critics view MPT output and/or results as mathematical predictions about the future because many of the risk distributions, return calculations, and hypothesized correlations contained in the MPT approach are found in expected values. Since expected values are themselves statistical distributions, they may be inaccurate due to misspecification or may be subject to the influences of mitigating market information or circumstances.

Nonetheless, MPT and the use of EFA represent powerful ways to generate insight into portfolio performance and the prospective individual portfolio component efficiencies, which is a key step in implementing a strategic risk management philosophy.