Dawn Browne, an investment broker, has been approached by client Jack Thomas about the risk of his

Question:

Dawn Browne, an investment broker, has been approached by client Jack Thomas about the risk of his investments. Dawn has recently read several articles concerning the risk factors that can potentially affect asset returns, and she has decided to examine Jack’s mutual fund holdings. Jack is currently invested in the Fidelity Magellan Fund (FMAGX), the Fidelity Low-Priced Stock Fund (FLPSX), and the Baron Small Cap Fund (BSCFX).
Dawn would like to estimate the well-known multifactor model proposed by Mark Carhart in 1997 to determine the risk of each mutual fund.

In other words, if the alpha is positive, the asset earned a return greater than it should have given its level of risk; if the alpha is negative, the asset earned a return lower than it should have given its level of risk. This measure is called ‘Jensen’s alpha’, and it is a very widely used tool for mutual fund evaluation.
1. For a large-company equity mutual fund, would you expect the betas to be positive or negative for each of the factors in a Carhart multifactor model?
2. The SMB, HML, MOM factors, and risk-free rates for the US are available at Ken French’s website: mba.tuck.dartmouth.edu/pages/faculty/ken.french/. Download the monthly factors and save the most recent 60 months for each factor. The historical prices for each of the mutual funds can be found on various websites, including finance.yahoo.com. Find the prices of each mutual fund for the same time as the Carhart factors and calculate the returns for each month. Be sure to include dividends. For each mutual fund, estimate the multifactor regression equation using the Carhart factors. How well do the regression estimates explain the variation in the return of each mutual fund?
3. What do you observe about the beta coefficients for the different mutual funds?
Comment on any similarities or differences.
4. If the market is efficient, what value would you expect for alpha? Do your estimates support market efficiency?
5. Which fund has performed best considering its risk? Why?