In early 2010, Morningstar, a Chicago-based financial services company, announced the Morningstar Fund Managers of the Decade. The award was based on the performance of mutual funds from January 2000 to December 2009. The award was not just about returns, though. Morningstar also considered the risks assumed to achieve those results and took into account the strength of the manager, strategy, and firm's stewardship. They also thought it's a greater feat to make a lot of money for a lot of people than to earn sky-high returns on a tiny pool of assets, so asset size factored in.^[1] The winner for the domestic equity category was Bruce Berkowitz, the manager of the Fairhome (FAIRX) mutual fund. The two runner-up managers were Charlie Dreifus of Royce Special Equity Investment (RYSEX) and Don Yacktman of the Yackman Fund (YACKX).

You want to investigate whether these award-winning managers continued to perform well since then. The Excel file Mutual Fund Data includes monthly data for these three award-winning funds, as well as for the Vanguard 500 Index Fund (VFINX) from January 2000 to September 2021. The first tab of the Excel spreadsheet includes the dates (expressed as YYYYMMDD) and the monthly total returns of these funds. The second tab includes the dates (expressed as YYYYMM), the monthly Treasury bill rate, RF (i.e., a monthly rate of return that is not annualized), and the return of the market portfolio, Mkt, which includes all publicly-traded firms in the U.S. For example, a risk-free rate of 0.0041 means that during the corresponding month, you receive a monthly return of 0.41% by investing in Treasury bills.

Briefly describe the investment strategies and styles of the four mutual funds. What are the current expense ratios, the current turnover ratios, and the current assets under management of the funds? Check any financial websites (Morningstar, Yahoo, Google, Fund Families) that has information on mutual funds.

See morningstar.articles/321713/announcing-the-morningstar-fund-managers-of-the-decade

1. Compute the following statistics for each of the four funds, for the market, and for Treasury bills over the period from January 2000 to December 2009: (3 Points)

1. Average arithmetic means of monthly total returns
2. Average geometric means of monthly total returns
3. Standard deviations of monthly total returns
4. Monthly Sharpe ratio

Briefly comment on the performance of the different assets.

2. Compute the following statistics for each of the four funds, for the market, and for Treasury bills over the period from January 2010 to September 2021:

1. Average arithmetic means of monthly total returns
2. Average geometric means of monthly total returns
3. Standard deviations of monthly total returns
4. Monthly Sharpe ratio

Briefly comment on the performance of the different assets.

c. Estimate the monthly alphas, the market betas, and the R-squared of the regression for each of the four funds using the CAPM model over the period from January 2010 to September 2021. Which fund takes more systematic risk? Which fund has a higher alpha (abnormal return)? What does the R-Squared tell us? What is your conclusion on the persistence of performance for these award-winning funds?