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# - Interpret the two estimated slope coecients of your regression. Hint: Keep in mind that this is a multivariate regression. Here is the given Excel...

Mutual Fund Performance Evaluation

On Blackboard, you will find 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 di↵erent 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 file 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:

1. (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)
2. (b) Plot the rolling-window beta estimates for the four factors. Put all four series in one plot.

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 for 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 5⇥1 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 t59 to t. Denote this variable by r ̄M,t. Similarly, denote the average excess return on the Magellan Fund in months t 59 to t (computed in part 2a) by r ̄F,t. Regress the variable 'flow' (in column I) in month t on r ̄M,t and r ̄F,t using the available dates ,i.e. 1991-2016.

• What does the variable 'flow' measure? Hint: The spreadsheet contains a formula that computes flow. 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. ee different excel sheets!

- Interpret the two estimated slope coecients of your regression. Hint: Keep in mind that this is a
multivariate regression. Here is the given Excel Sheet Fidelity Magellan Fund (CRSP FUNDNO 11943) year month Mgr_Name expenses turnover return net_assets Flow 1968 1 1/1/68 0.00% -5.46% 1968 2 2/1/68 0.00% -8.85% 1968 3 3/1/68 0.00% 0.44% 1968 4 4/1/68 0.00% 15.73% 1968 5 5/1/68 0.00% 17.05% 1968 6 6/1/68 0.00% -2.23% 1968 7 7/1/68 0.00% —3.25% 1968 8 8/1/68 0.00% 5.46% 1968 9 9/1/68 0.00% 7.16% 1968 10 10/1/68 0.00% 1.65% 1968 11 11/1/68 0.00% 12.45% 1968 12 12/1/68 0.00% -1.67% 7.1
1969 1 1/1/69 0.00% -0.76% 7.1
1969 2 2/1/69 0.00% -11.11% 7.1
1969 3 3/1/69 0.00% 3.77% 7.1
1969 4 4/1/69 0.00% 4.08% 7.1
1969 5 5/1/69 0.00% 3.50% 7.1
1969 6 6/1/69 0.00% 42.25% 7.1
1969 7 7/1/69 0.00% -10.77% 7.1
1969 8 8/1/69 0.00% 7.11% 7.1
1969 9 9/1/69 0.00% -0.60% 7.1
1969 10 10/1/69 0.00% 6.38% 7.1
1969 11 11/1/69 0.00% -4.74% 7.1
1969 12 12/1/69 0.00% 0.77% 8.2
1970 1 1/1/70 0.79% -7.97% 8.2
1970 2 2/1/70 0.79% -0.05% 8.2
1970 3 3/1/70 0.79% -8.85% 8.2
1970 4 4/1/70 0.79% -12.22% 8.2
1970 5 5/1/70 0.79% 4.56% 8.2
1970 6 6/1/70 0.79% -7.06% 8.2
1970 7 7/1/70 0.79% 3.63% 8.2
1970 8 8/1/70 0.79% 4.27% 8.2
1970 9 9/1/70 0.79% 12.58% 8.2
1970 10 10/1/70 0.79% —2.71% 8.2
1970 11 11/1/70 0.79% 2.68% 8.2
1970 12 12/1/70 0.79% 6.25% 6.9
1971 1 1/1/71 0.00% 8.54% 6.9
1971 2 2/1/71 0.00% 6.45% 6.9
1971 3 3/1/71 0.00% 7.83% 6.9
1971 4 4/1/71 0.00% 4.02% 6.9

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6.21%
3.07%
-0.38% 11589.5
11589.5
11589.5
7800.1
7800.1
7800.1
8434.3
8434.3
8434.3
9257.4
9257.4
9257.4
9016
9016
9016
8971.1
8971.1
8971.1
9622.2
9622.2
9622.2
10756.6
10756.6
10756.6
12427.9
12427.9
12427.9
12699.6
12699.6
12699.6
13176.9
13176.9
13176.9
14038.9
14038.9
14038.9
11318.9
11318.9
11318.9
12325.7
13122.3
14292.5
14805.3
14990
16004.6
15251.8
16384.4
17227.3
17276.5 -0.53%
0.23%
0.19%
0.38%
1 .07%
1 .17%
1.22%
2.07%
0.66%

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