Questions

$1.$ Answer the Performance Evaluation Question from the Case Study. To evaluate the performance of each mutual fund, estimate the CAPM and Multifactor Models. Which funds do you recommend for investment?

Notes: Using the results of linear regressions formulate and test the null hypothesis whether each mutual fund $($GLCGX$,$ TRBCX$,$ DTMVX$,$ DVPEX$)$ performed as expected by the CAPM and Multifactor models.

Explain whether you reject or not reject the null hypothesis: alpha$=0$ at $5\%$ significance level. If a fund did not perform as expected explain whether it over$-$performed $($alpha$>0)$ or underperformed $($alpha$<0).$

$2.$ Test the null hypothesis that market beta is equal to $1$ in the CAPM model for TRBCX fund only. Explain whether you reject or not reject the null hypothesis at $5\%$ significance level.

Estimation Notes

All the data and code for this assignment are in multifactor.zip folder. Save the data $($multifactor$.$csv$)$ and R code $($linearreg$.$R$)$ in the same directory, open the linearreg.R code in R Studio and set working directory by Clicking:

Session$-->$Set Working Directory$-->$To Source File Location.

Run lines in the code to load the data and estimate linear regressions for GLCGX and TRBCX mutual funds. Add lines of code for the remaining mutual funds: DTMVX and DVPEX.

For each mutual fund estimate two models: CAPM and Multifactor.

CAPM Model:

r$\_$fund$=\backslash$alpha $+\backslash$beta $\_$market r$\_$mt$+\backslash$epsi

Multifactor Model:

r$\_$fund$=\backslash$alpha $+\backslash$beta $\_$market r$\_$mt$+\backslash$beta $\_$size SMB$+\backslash$beta $\_$Value HML$+\backslash$beta $\_$mom MOM$+\backslash$epsi

Here the risk$-$free rate equal to Treasury Bill rate is subtracted from funds$$ returns and market return before running linear regression. When you run regressions, you would find estimates of alpha $($the constant term or intercept$)$ and beta $($systematic risk$).$ Next, you would look at the t$-$statistics and test whether alpha is statistically significant. If it is significant and positive $($alpha$>0$ and p$-$value$<5\%)$ the fund over$-$performed the benchmark return based on particular risk model $($CAPM or Multifactor$).$ If it is significant and negative $($alpha$<0$ and p$-$value$<5\%)$ the fund underperformed. Finally, if it is not statistically significant $($p$-$value$>5\%)$ the fund performed as expected.

See examples of t$-$tests for linear regression in Module $2$ lecture, page $4.$