Performance analysis for a large U.S. mutual fund

Conduct a performance analysis for a large U.S. mutual fund and
attempt to relate fund performance to characteristics of the fund.
Mutual Fund Performance Evaluation
On Blackboard, you will nd a spreadsheet containing historical returns as well as other in-
formation on the Fidelity Magellan Fund for the period 1968-2016. To conduct a performance
analysis on this fund, you will also need data on dierent systematic risk factors. Go to Ken
French’s website and download monthly returns for the three Fama-French factors, the risk-free
rate, and the momentum factor over the same sample period and add them to your spreadsheet.
Note that the risk-free rate is included in the same le as the three Fama-French factors.

1. Estimate the Carhart 4-factor model for the Magellan fund by regressing its’ excess returns
on the four factors (note that the fund returns in the spreadsheet are NOT in excess of
the risk-free rate). Use the entire 1968-2016 sample period for this regressions.
What does the regression suggest about the investment strategy of this fund?
Based on the results from the 4-factor model, is this a good fund to invest in?

2. Perform rolling window 4-factor model regressions: In each month t (starting with the
60est month of the sample), estimate the regression using data for months t ? 59 to t.1
Produce two plots:
(a) Plot the time series of rolling-window alpha estimates, along with a rolling window
average of the excess return (not adjusted for risk; also using data for months t?59
to t)
(b) Plot the rolling-window beta estimates for the four factors. Put all four series in one

3. Interpret the development of the coecients with respect to the data provided about the
fund (changes of the manager, expenses,…). Do you see any connection to the facts about
the fund? Comment on the alphas. Hint: This is an open-ended question, i.e. there isn’t
one correct answer. It is sucient to discuss a few things you notice about the relationship
between the fund’s betas and the other information you know about the fund.
1The easiest way to do this in Excel is the ‘=linest()’ function. You can use linest as an array function and
have it return all slope coecients (betas) and the intercept (alpha) simultaneously. For estimating the 4-factor
model, select a 51 block of cells, type =linest() with the appropriate inputs, then press SHIFT-CTRL-ENTER.
Consulting the help page for LINEST may help.

4. In each month t, compute the average excess return on the market using data for months
t?59 to t. Denote this variable by rM;t. Similarly, denote the average excess return on the
Magellan Fund in months t ? 59 to t (computed in part 2a) by rF;t. Regress the variable
‘ ow’ (in column I) in month t on rM;t and rF;t using the available dates ,i.e. 1991-2016.
What does the variable ‘ ow’ measure? Hint: The spreadsheet contains a formula
that computes ow. Looking at this formula is helpful for the interpretation.
Interpret the two estimated slope coecients of your regression. Hint: Keep in mind
that this is a multivariate regression.

Sample Solution