You work for a private wealth management firm that follows an external investment model, whereby it decides which outside managers it should recommend to clients. One mutual fund that is a candidate for inclusion on your Premier Recommended List of approved managers is Active Fund (AFNDX), an actively managed stock portfolio benchmarked to the Standard & Poors 500 (SPX) Index. You have been asked to perform an evaluation of AFNDXs past investment performance, using a sample of monthly returns on the following positions: (1) AFNDX portfolio, (2) SPX Index, (3) U.S. Treasury bills, and (4) the three primary FamaFrench risk factors (excess market, SMB, and HML). These data are listed below.

Month	AFNDX	SPX INDEX	T BILL (RF)	EXCESS	SMB	HML
1	9.259	2.761	0.430	0.960	-4.040	4.620
2	7.566	7.551	0.420	6.150	-3.450	0.080
3	-2.109	-1.985	0.470	-1.600	3.140	1.080
4	5.080	6.246	0.440	4.840	-1.570	-2.540
5	-1.748	0.792	0.380	-0.490	-2.530	4.820
6	-5.023	-4.105	0.420	-4.870	-0.310	3.840
7	4.054	5.975	0.430	3.830	-5.140	-1.190
8	8.061	6.087	0.500	6.640	4.610	-4.090
9	3.397	4.486	0.370	4.050	1.350	0.830
10	6.890	7.947	0.430	7.190	-2.360	-0.680
11	0.292	-5.604	0.420	-4.060	7.440	0.890
12	3.074	5.476	0.430	5.370	2.590	-0.390
13	-1.610	-3.334	0.430	-3.840	-0.930	2.520
14	-2.936	4.631	0.400	2.730	-5.050	1.040
15	0.454	1.721	0.480	1.310	-2.320	3.610
16	-1.061	1.102	0.420	0.010	-1.020	-1.670
17	8.562	7.210	0.400	6.900	0.290	-1.230
18	3.817	5.111	0.390	4.740	-1.440	1.910
19	0.729	1.003	0.440	0.660	0.400	0.220
20	-2.560	-1.725	0.390	-2.940	-3.610	4.280
21	4.644	4.055	0.420	2.870	-3.400	-1.550
22	-1.798	-1.071	0.390	-2.720	-4.510	-1.790
23	-17.071	-14.433	0.430	-16.110	-5.920	5.700
24	15.715	6.403	0.450	5.940	0.020	-3.760
25	-3.536	8.124	0.310	7.100	-3.360	-2.850
26	3.587	6.049	0.320	5.850	1.360	-3.690
27	10.011	5.750	0.380	5.940	-0.320	-4.960
28	6.639	4.173	0.350	3.480	1.160	-6.150
29	-4.212	-3.103	0.340	-4.150	-5.600	1.660
30	5.422	4.006	0.420	3.310	-3.820	-3.050
31	0.801	3.867	0.370	4.470	2.900	2.790
32	-3.521	-2.357	0.330	-2.400	3.460	3.080
33	4.735	5.544	0.410	4.730	3.410	-4.340
34	-0.755	-3.114	0.370	-3.460	2.000	0.690
35	-1.883	-0.497	0.390	-1.350	-1.160	-1.260
36	-1.196	-2.729	0.400	-2.670	3.230	-3.190
37	7.066	6.316	0.400	5.810	-6.530	-3.190
38	2.436	2.043	0.350	3.200	7.710	-8.100
39	10.069	5.892	0.430	7.820	6.980	-9.060
40	-3.845	-5.031	0.400	-4.440	4.080	-0.170
41	5.790	-1.896	0.430	2.540	21.500	-12.040

1. For both AFNDX and SPX, calculate the series of monthly risk premia (stated returns in excess of the risk-free rate) for the 41-month sample period. Use these excess return data to compute the Sharpe ratio for both AFNDX and SPX. Do not round intermediate calculations. Round your answers to three decimal places.

   Sharpe ratio for AFNDX:

   Sharpe ratio for SPX:

2. Based on a regression of the excess returns to AFNDX on the excess returns to SPX, use regression analysis to calculate the active managers (1) one-factor Jensens alpha coefficient, (2) beta coefficient, and (3) R-squared measure. Briefly explain what each of these statistics tells you about how AFNDX has been managed. Do not round intermediate calculations. Round your answers to four decimal places.
   1. Jensens alpha coefficient:

   2. Beta coefficient:

   3. R-squared measure:

3. Using your work in parts (a) and (b), calculate the Treynor ratio performance measures for both AFNDX and SPX, assuming a beta coefficient of 1.00 for the latter. Do not round intermediate calculations. Round your answers to three decimal places.

   Treynor ratio for AFNDX:

   Treynor ratio for SPX:

4. Calculate the tracking error (TE) for AFNDX relative to the SPX benchmark, on both a monthly and an annualized basis. What does this TE error measure suggests about the managers investment style? Do not round intermediate calculations. Round your answers to four decimal places.

   Tracking error on a monthly basis:

   Tracking error on an annualized basis:

   The value of tracking error indicates that the -Select-activestructuredpassiveItem 18 managers investment style is used because the annualized TE is -Select-less than 1.0between 1.0 and 3.0over 3.0Item 19 .

5. Using the excess returns from part (a), compute the information ratio (IR) for AFNDX relative to the SPX benchmark on both a monthly basis and an annualized basis. Briefly explain what this IR suggests about the managers investment prowess relative to the general equity market. Do not round intermediate calculations. Round your answers to four decimal places.

   Information ratio on a monthly basis:

   Information ratio on an annualized basis:

6. Estimate a regression of AFNDXs excess returns on the three FamaFrench risk factors. Interpret each of the following components of your regression output: (1) the intercept coefficient, (2) the beta coefficients for each of the three independent variables, and (3) the R-squared measure. Use a 5% level of significance. Do not round intermediate calculations. Round your answers to four decimal places. Use a minus sign to enter negative values, if any.
   1. Intercept coefficient:

   2. Beta coefficients:

      Excess market:

      SMB: ,

      HML: ,

   3. R-squared measure: