General Education Statistics | MAT112

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

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