# Mutual Fund Theorem

Mutual Fund Theorem is an investing strategy that uses mutual funds exclusively in a portfolio for diversification and mean-variance optimization.
Mutual fund theorem
3 min
05-July-2024

Mutual fund theorem is an investing strategy for constructing a portfolio solely using mutual funds to achieve diversification and optimize risk and expected return through mean-variance analysis. The latter term can be defined as the weighing of risk against the expected return from an investment.

One of the most popular theories that guide the investment decisions of both individual and institutional investors is the mutual fund theorem. The mutual fund theorem essentially states that investors can construct a portfolio with an optimal risk-return profile by including mutual funds.

By following this theory, investors can simplify their investment decisions without compromising their wealth-creation ability or resorting to complicated asset-selection methods. In this article, we are going to explore the mutual fund theorem, examine how it works, and look into the various advantages it offers.

## What is the mutual fund theorem?

First introduced in the late 1950s, the mutual fund theorem is the brainchild of James Tobin. The theorem, also known as the mutual fund separation theorem, states that an investor can optimize diversification and the risk-return profile of their portfolio simply by including mutual funds.

One of the key requirements of this particular theory is that the number of mutual funds must be lower than the number of individual securities in the portfolio for effective diversification and risk-return profile.

The primary basis of the mutual fund separation theorem can be traced back to the concept of mean-variance optimisation and the modern portfolio theory of Harry Markowitz. The modern portfolio theory states that portfolio diversification can limit risk and protect it from fluctuations and volatility. Mean-variance optimisation, on the other hand, involves constructing a portfolio in such a way that it delivers the highest expected return for a given level of risk or has the lowest risk for a given level of expected return.

The mutual fund theorem builds on these two theories and states that an investor can achieve mean-variance optimisation and effective diversification by including mutual funds in their portfolio.

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## How does the mutual fund separation theorem work?

Now that you are aware of the meaning of the mutual fund theorem, let us look at a hypothetical example to understand how it works.

Assume you are an investor with a moderate tolerance for risk. Your portfolio consists of a risk-free asset in the form of a long-term government bond, a fixed deposit with a bank, and the debentures of a company with a 10-year tenure.

According to the mutual fund separation theorem, your investment portfolio is not properly diversified or optimised for mean-variance until you include mutual funds. Therefore, you decide to invest in two well-diversified mutual fund schemes, with one focusing on the equity market and the other focusing on the debt market.

Since the number of mutual fund investments (two) is lower than the number of individual securities in your portfolio (3), as per the mutual fund theorem, you have successfully created a portfolio with optimal diversification and mean-variance. Your portfolio should now have less risk and stay protected from market fluctuations to a large extent.

## Mutual fund portfolio construction

Constructing a mutual fund portfolio in accordance with the mutual fund theorem is simple. All you need to do is first invest in a risk-free asset. Risk-free assets typically comprise short-term government securities, such as Treasury bills (T-bills), which are often considered free of default risk due to the sovereign guarantee.

The next step is to invest your risk capital—capital you can afford to risk to get high returns—in mutual funds. Mutual funds are considered to be high-risk assets, and investing in them alongside risk-free assets balances out the portfolio’s risk-return profile and helps you achieve an effective level of diversification.

One of the many advantages of creating a portfolio, according to the mutual fund theorem, is that you get the freedom to choose the type of mutual funds to invest in based on your risk tolerance level. For example, if you are a moderately conservative investor, you could consider investing in mutual funds that provide exposure to high-quality debt instruments. On the other hand, if you are a risk-aggressive investor, you could invest in equity mutual funds along with a risk-free asset.

## Advantages of using mutual fund theorem

The mutual fund theorem has several advantages. Understanding what they are is crucial for making effective investment decisions.

### Simplifies the investment process

The mutual fund theorem simplifies the investment process by focusing on just two components: a risk-free asset and a well-diversified mutual fund.

### Helps achieve optimum diversification

By encouraging investors to create a portfolio consisting of risk-free assets and diversified mutual funds, the theorem helps them achieve effective diversification and reduces unsystematic risk.

### Can be customised according to the investor’s risk profile

The mutual fund theorem gives investors the freedom to tailor their portfolios to match their risk tolerance by adjusting the proportions of the risk-free asset and the mutual fund.

### Increases efficiency of the portfolio

By helping investors achieve ideal mean-variance, the mutual fund theorem ensures that their portfolios produce the best possible returns for their chosen level of risk.

### Scoring mutual funds

Selecting the right mutual fund is crucial for implementing the mutual fund theorem effectively. Here are some key factors to consider when evaluating and scoring mutual funds:

### Performance metrics

Examining performance metrics is a good way to evaluate mutual funds. When looking into the historical performance of the fund, focus on metrics like the Sharpe ratio, alpha, and beta. This will help you understand the fund’s risk-adjusted returns and market sensitivity.

### Expense ratios

Expense ratios are another major factor to consider when scoring mutual funds since they have a direct effect on the returns. Mutual funds with lower expense ratios can enhance returns in the long run.

### Management’s track record

The track record and expertise of the fund managers are key evaluating factors. A fund that has performed consistently over different market cycles potentially indicates the presence of skilled management.

### Diversification

For the mutual fund theorem to work as intended, the mutual fund must be diversified enough across different asset classes, sectors, and geographies.

### Fund size and stability

Large mutual funds tend to be more stable with less turnover compared to smaller funds. However, smaller funds may have higher growth potential than larger funds. It is important to analyse these factors and select the fund that aligns with your needs.

## Key Takeaways

The mutual fund theorem states that any investor, irrespective of their risk profile, can construct an optimum portfolio by including well-diversified mutual funds.

• The theorem is based on modern portfolio theory, which states that diversification can reduce risk.
• One of the major requirements of the theorem is that the number of mutual funds in the portfolio must be less than the number of individual assets.
• The mutual fund theorem gives investors the freedom to choose mutual funds based on their risk profile.

## Conclusion

The mutual fund theorem is a revolutionary way to construct a portfolio. It provides investors with a straightforward and effective way to achieve optimal returns. By understanding and applying the principles of the theorem, investors can make well-informed and efficient investment decisions that can help create long-term wealth.

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## Essential tools for mutual fund investors

What is the two-mutual fund theorem?
The two-mutual fund theorem states that investors can construct an efficient portfolio even if there are no risk-free assets, as long as they invest in two efficient mutual funds.
What is the one fund theorem?
The one-fund theorem states that investors can achieve an efficient portfolio using a single mutual fund consisting of assets with risk along with a risk-free asset.
How does the Mutual Fund Separation Theorem apply to modern investment strategies?
The mutual fund separation theorem enables investors to achieve optimal diversification and risk-return profiles by simplifying modern investment strategies. It reduces the need for complex asset selection and eliminates the requirement of assessing the merits of each investment individually before investing.
Is the mutual fund separation theorem applicable to all kinds of investors?
Yes. All investors, irrespective of their risk profile and investment amount, can apply the mutual fund separation theorem when constructing their portfolio. The theorem is also applicable to institutional investors.
What are some shortcomings of the mutual fund separation theorem?
The mutual fund separation theorem has a few limitations. For instance, it presumes that the markets are always efficient and that all investors get the same risk-free rate. Also, it does not consider the behavioural biases of investors and the various expenses associated with investing, such as transaction charges and taxes.
What are the criticisms associated with the mutual fund theorem?
Some of the criticisms surrounding the mutual fund theorem are the lack of control over mutual funds and their performance, high mutual fund fees reducing returns, and no guarantee of returns.
How are the mutual fund theorem and covariance pricing theorem related?
The mutual fund theorem emphasises the importance of diversification and how including mutual funds in an investment portfolio can reduce risk. The covariance pricing theorem, on the other hand, establishes a relationship between the prices of two assets. Both of these theorems have the same core principle, which is risk reduction.

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Bajaj Finance Limited (“BFL”) is an NBFC offering loans, deposits and third-party wealth management products.

The information contained in this article is for general informational purposes only and does not constitute any financial advice. The content herein has been prepared by BFL on the basis of publicly available information, internal sources and other third-party sources believed to be reliable. However, BFL cannot guarantee the accuracy of such information, assure its completeness, or warrant such information will not be changed.

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