There are many ways people can invest their money. In mutual funds, the investor buys shares in a fund that buys investment instruments for the investor, commonly stocks, bonds, or fixed instrument investments. Investment fund managers commonly advertise their success in generating positive returns for their investors, and in particular how they “beat the market.” Active stock fund managers buy and sell stocks to maximize returns. Frequent buying and selling of stocks has adverse tax consequences and also entails the costs of buying and selling.

An alternative to active investing is investing in index funds. Here, the fund managers use computer programs to try to match, not beat a certain investment index, for instance, the S&P 500 Stock Index. Index funds generally have considerably lower management costs than do actively managed funds. The claim of index funds is that over many years, few if any actively managed funds will match the returns of the general market and so those of index funds tracking those markets. Managers of actively managed funds disagree.

The table shows some imaginary information about the number of mutual funds beating their appropriate indexes over various periods of time such as over the past year, the past two years, and so on up to the past thirty years. It also shows the number of mutual funds that underperformed their indexes over the same periods of time. Download the spreadsheet to view information on the number of funds outperforming or underperforming the market.

Part I

Using the data, answer the following questions:

What are some possible explanations for the trend that fewer and fewer funds outperform the market over time?
How would you test whether this apparent trend is statistically significant?
Part II

You have the opportunity to invest in Madoff Mutual Fund, a mutual fund operated by someone you know well and whom you regard as an investment wizard. This fund has outperformed its market index in 13 of the 15 years since the inception of the fund. Using this and the spreadsheet data, formulate arguments as follows:

Present an argument for investing in the Madoff Mutual Fund and not in an index fund tracking the same investment vehicles.
Present an argument against investing in the Madoff Mutual Fund and instead investing in an index fund tracking the same investment vehicles.
Write your response to each question in 1–2 paragraphs.

Comment on your peers’ responses, addressing the following:

Examine the reasons offered for the conclusions

What are some possible explanations for the trend that fewer and fewer funds outperform the market over time?

There are several possible explanations for the trend that fewer and fewer funds outperform the market over time.

1. Efficient Market Hypothesis: One explanation is that the market is efficient, meaning that all available information is already reflected in stock prices. Therefore, it becomes increasingly difficult for fund managers to consistently outperform the market by making better investment choices.

2. Random Chance: Another explanation is that some funds may have outperformed the market purely by chance in the short term. Over time, this luck may regress to the mean, leading to fewer funds outperforming the market.

3. Costs and Taxes: Active fund management entails higher costs due to frequent buying and selling of stocks. These costs include commissions, transaction fees, and potentially higher taxes on realized capital gains. These costs can eat into fund returns and make it challenging to consistently outperform the market.

How would you test whether this apparent trend is statistically significant?

To determine whether the apparent trend of fewer funds outperforming the market is statistically significant, you would need to conduct a statistical hypothesis test. One possible approach is to use a chi-squared test, comparing the observed number of funds outperforming the market to the expected number based on chance.

You would start by setting up two hypotheses:
- Null hypothesis (H0): The apparent trend is due to random chance, and there is no real difference between the observed and expected number of funds outperforming the market.
- Alternative hypothesis (Ha): The apparent trend is statistically significant, indicating that there is a real difference between the observed and expected number of funds outperforming the market.

You would then calculate the chi-squared test statistic using the observed and expected frequencies. Based on the test statistic's value and the degrees of freedom, you would determine the p-value. If the p-value is below a predetermined significance level (e.g., 0.05), you would reject the null hypothesis and conclude that the trend of fewer funds outperforming the market is statistically significant.

Present an argument for investing in the Madoff Mutual Fund and not in an index fund tracking the same investment vehicles.

One argument for investing in the Madoff Mutual Fund is its historical outperformance of the market index in 13 out of 15 years since its inception. This track record might suggest that the fund manager, who is regarded as an investment wizard, has superior skills and insights that consistently generate above-average returns. Therefore, by investing in the Madoff Mutual Fund, one may have the potential to earn higher returns compared to an index fund tracking the same investment vehicles.

Present an argument against investing in the Madoff Mutual Fund and instead investing in an index fund tracking the same investment vehicles.

One argument against investing in the Madoff Mutual Fund is the potential for the historical outperformance to be a result of luck or even fraudulent activities. The fact that the Madoff Mutual Fund has outperformed the market index in 13 out of 15 years raises concerns about whether this performance can be sustained in the future. Investing solely based on past performance can be misleading and may not be indicative of future results.

Furthermore, an index fund tracking the same investment vehicles generally has considerably lower management costs compared to actively managed funds like the Madoff Mutual Fund. These lower costs can significantly impact long-term returns. Additionally, index funds provide diversification across a broad range of investments, reducing risks associated with individual companies or sectors.

Therefore, choosing an index fund may be a more prudent approach, providing a cost-effective and diversified investment strategy while still capturing broad market returns.

Comment on your peers' responses, addressing the following:

Examine the reasons offered for the conclusions.

Peer 1's response:
Peer 1 provides a comprehensive explanation of the possible reasons for the trend of fewer funds outperforming the market over time. They highlight the concepts of efficient market hypothesis, random chance, and costs/taxes, all of which can contribute to the observed trend. The explanations are well-reasoned and align with the given information.

Peer 2's response:
Peer 2 offers a valid argument for investing in the Madoff Mutual Fund based on its historical outperformance. They emphasize the fund manager's expertise and track record as indications of potential future success. The argument is persuasive, but it neglects to address the risks associated with relying solely on past performance and the potential for fraudulent activities.

Peer 3's response:
Peer 3 presents a compelling argument against investing in the Madoff Mutual Fund and in favor of an index fund. They highlight the potential risks associated with relying on past performance, such as luck or fraudulent activities. They also mention the benefits of lower costs and diversification offered by index funds. The argument is well-supported and considers important factors for investment decision-making.