Question
Problem 18-10 You work for a private wealth management firm that follows an external investment model, whereby it decides which outside managers it should recommend
Problem 18-10
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.
Monthly Return Data for AFNDX, SPX, T-Bill, and FamaFrench Factors | ||||||||||||||
% RETURNS TO: | F-F FACTOR % RETURNS: | |||||||||||||
Month | AFNDX | SPX Index | T-Bill (RF) | Excess Mkt | SMB | HML | ||||||||
1 | 9.246 | 2.760 | 0.420 | 0.980 | -4.040 | 4.630 | ||||||||
2 | 7.585 | 7.547 | 0.420 | 6.160 | -3.450 | 0.100 | ||||||||
3 | -2.107 | -1.984 | 0.470 | -1.610 | 3.140 | 1.070 | ||||||||
4 | 5.076 | 6.254 | 0.450 | 4.860 | -1.570 | -2.540 | ||||||||
5 | -1.751 | 0.794 | 0.380 | -0.490 | -2.540 | 4.840 | ||||||||
6 | -5.028 | -4.103 | 0.430 | -4.860 | -0.320 | 3.840 | ||||||||
7 | 4.054 | 5.955 | 0.420 | 3.830 | -5.140 | -1.200 | ||||||||
8 | 8.052 | 6.077 | 0.480 | 6.650 | 4.630 | -4.090 | ||||||||
9 | 3.401 | 4.477 | 0.380 | 4.050 | 1.350 | 0.820 | ||||||||
10 | 6.898 | 7.955 | 0.430 | 7.200 | -2.360 | -0.680 | ||||||||
11 | 0.283 | -5.587 | 0.410 | -4.050 | 7.450 | 0.890 | ||||||||
12 | 3.067 | 5.475 | 0.430 | 5.370 | 2.590 | -0.390 | ||||||||
13 | -1.615 | -3.343 | 0.410 | -3.820 | -0.940 | 2.520 | ||||||||
14 | -2.939 | 4.615 | 0.380 | 2.710 | -5.050 | 1.050 | ||||||||
15 | 0.451 | 1.721 | 0.470 | 1.320 | -2.340 | 3.590 | ||||||||
16 | -1.054 | 1.109 | 0.430 | 0.020 | -1.000 | -1.670 | ||||||||
17 | 8.575 | 7.212 | 0.390 | 6.880 | 0.280 | -1.240 | ||||||||
18 | 3.808 | 5.112 | 0.400 | 4.760 | -1.450 | 1.930 | ||||||||
19 | 0.742 | 1.013 | 0.430 | 0.670 | 0.410 | 0.230 | ||||||||
20 | -2.550 | -1.714 | 0.390 | -2.960 | -3.610 | 4.300 | ||||||||
21 | 4.638 | 4.049 | 0.400 | 2.870 | -3.400 | -1.530 | ||||||||
22 | -1.784 | -1.056 | 0.390 | -2.730 | -4.520 | -1.780 | ||||||||
23 | -17.070 | -14.448 | 0.440 | -16.120 | -5.930 | 5.700 | ||||||||
24 | 15.714 | 6.406 | 0.450 | 5.960 | 0.030 | -3.770 | ||||||||
25 | -3.536 | 8.128 | 0.320 | 7.100 | -3.370 | -2.860 | ||||||||
26 | 3.590 | 6.052 | 0.310 | 5.850 | 1.370 | -3.670 | ||||||||
27 | 10.014 | 5.767 | 0.370 | 5.950 | -0.300 | -4.940 | ||||||||
28 | 6.620 | 4.185 | 0.340 | 3.470 | 1.150 | -6.150 | ||||||||
29 | -4.205 | -3.110 | 0.360 | -4.150 | -5.590 | 1.660 | ||||||||
30 | 5.432 | 4.005 | 0.430 | 3.330 | -3.830 | -3.050 | ||||||||
31 | 0.812 | 3.871 | 0.370 | 4.460 | 2.880 | 2.790 | ||||||||
32 | -3.518 | -2.360 | 0.340 | -2.390 | 3.470 | 3.090 | ||||||||
33 | 4.735 | 5.544 | 0.410 | 4.710 | 3.420 | -4.330 | ||||||||
34 | -0.749 | -3.109 | 0.380 | -3.460 | 2.000 | 0.710 | ||||||||
35 | -1.875 | -0.500 | 0.390 | -1.340 | -1.170 | -1.260 | ||||||||
36 | -1.178 | -2.740 | 0.390 | -2.670 | 3.240 | -3.180 | ||||||||
37 | 7.067 | 6.331 | 0.380 | 5.810 | -6.530 | -3.180 | ||||||||
38 | 2.424 | 2.023 | 0.350 | 3.190 | 7.700 | -8.090 | ||||||||
39 | 10.067 | 5.884 | 0.430 | 7.830 | 6.990 | -9.050 | ||||||||
40 | -3.840 | -5.029 | 0.410 | -4.430 | 4.080 | -0.160 | ||||||||
41 | 5.783 | -1.901 | 0.440 | 2.540 | 21.490 | -12.030 |
- 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:
- 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.
- Jensens alpha coefficient:
The value indicates that the manager generated a -Select-higherlowerItem 4 return than what was expected given the portfolios risk level.
- Beta coefficient:
The fund is only slightly -Select-morelessItem 6 volatile than the market.
- R-squared measure:
It is -Select-higherlowerItem 8 than 0.50, which means that the funds performance -Select-isis notItem 9 statistically related to the benchmark.
- Jensens alpha coefficient:
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