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 apply the well$-$known multifactor model proposed by Eugene Fama and Ken French to determine the risk of each mutual fund. The regression equation for the multifactor model she proposes to use is:

Rit $$ RFt $=\backslash$alpha i $+\backslash$beta $1($RMt $$ RFt$)+\backslash$beta $2($SMBt$)+\backslash$beta $3($HMLt$)+\backslash$epsi t

In the regression equation, Rit is the return on Asset i at Time t$,$ RFt is the risk$-$free rate at Time t$,$ and RMt is the return on the market at Time t$.$ The first risk factor in the Fama$-$French regression is the market factor often used with the CAPM.

The second risk factor, SMB$,$ or $$small minus big,$$ is calculated by taking the difference in the returns on a portfolio of small$-$cap stocks and a portfolio of large cap stocks. This factor is intended to pick up the so$-$called small$-$firm effect. Similarly, the third factor, HML$,$ or $$high minus low,$$ is calculated by taking the difference in the returns between a portfolio of $$value$$ stocks and a portfolio of $$growth$$ stocks. Stocks with low market$-$to$-$book ratios are classified as value stocks and vice versa for growth stocks. This factor is included because of the historical tendency for value stocks to earn a higher return.

Q$1$:The Fama$-$French factors and risk$-$free rates are available at Ken French$$s website: www$.$dartmouth.edu$/$~kfrench. 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 Fama$-$French factors and calculate the returns for each month. Be sure to include dividends. For each mutual fund, estimate the multifactor regression equation using the Fama$-$French factors. How well do the regression estimates explain the variation in the return of each mutual fund?