## What Is the Mutual Fund Theorem?

The mutual fund theorem is an investing strategy whereby mutual funds are used exclusively in a portfolio for diversification and mean-variance optimization. The latter term can be defined as the weighing of risk against the expected return from an investment.

#### An Introduction To Mutual Funds

## Understanding the Mutual Fund Theorem

The mutual fund theorem is the use of mutual fund investments in the building of a comprehensive portfolio. The mutual fund theorem was introduced by James Tobin, who worked alongside Harry Markowitz from 1955 to 1956 at the Cowles Foundation at Yale University. The mutual fund theorem follows the principles of modern portfolio theory, which Markowitz studied at the Cowles Foundation. Markowitz received the Nobel Memorial Prize in Economic Sciences in 1990 for his work on modern portfolio theory.

A portfolio of mutual funds provides risk mitigation from diversification while giving investors exposure to various investments.

## Modern Portfolio Theory

The mutual fund theorem explains the importance of diversification in a portfolio and portrays how including mutual funds in a portfolio can limit its risk. The concept of mean-variance optimization presented by Harry Markowitz—weighing the risk against the expected return— forms the basis for the theorem. Given mean-variance optimization from modern portfolio theory techniques, an investor can identify the optimal allocations in a portfolio.

### Key Takeaways

- Mutual fund theorem is a strategy used to construct a diversified portfolio with just mutual funds.
- The theorem subscribes to the modern portfolio theory, where diversification can limit portfolio risk.
- The mutual fund theorem allows investors to chart an efficient frontier to identify an optimal allocation.

Using a universe of investments, an investor can chart an efficient frontier and identify optimal allocations directed by the capital market line for investing. The capital market line is a guide in the form of a graphed line along which investors can choose their risk tolerance and invest optimally according to designated allocations at each interval.

Modern portfolio theory shows substantial latitude in the investments that can be used to build an efficient frontier. The assets used in the development of the efficient frontier form the basis for the capital market line. Thus, investors can generally shift the capital market line higher by using a universe of higher-performing investments at various risk levels.

## Mutual Fund Portfolio Construction

Given modern portfolio theory technical analysis, an investor can use modern portfolio theory to create the same graphical representations and coordinates using a universe of mutual funds. An efficient frontier is constructed using mutual funds, and a capital market line is created that provides the allocations for diversification.

Similar to modern portfolio theory, investments in risk-free assets are represented by Treasury bills. Farther up the capital market line an investor can include greater amounts of higher risk assets such as emerging market equity mutual funds. At the lower end of the spectrum, an investor may invest in short-term, high-quality-debt mutual funds.

Overall, the mutual fund theorem suggests that investors can build an optimal portfolio using mutual funds. This type of portfolio can increase diversification. It may also have other advantages, such as operational trading efficiencies.

## Scoring Mutual Funds

Investors seeking the best mutual funds, or the best funds for them, should focus on a few key criteria. A standard measure used to score mutual funds is the fund investment-quality scorecard (FIQS). This measure helps investors collect key data in an organized way in order to make informed judgments as to the quality of a mutual fund. A FIQS does not include all quantitative data and may include qualitative information, but all information should be quantifiable, for example, the risk-return profile and return and expense information.

The key criteria for the FIQS include the investment style of the fund, such as what the mutual fund invests in and the manager’s ability to manage the assets according to the investments' objectives. Other criteria to consider concerning the mutual fund quality are the risk-return profile, fund size and compatibility, manager tenure and structure, portfolio turnover, mutual fund expenses, total returns, and research analyst reports.