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

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:

      The value indicates that the manager generated a -Select-higherlowerItem 4 return than what was expected given the portfolios risk level.

   2. Beta coefficient:

      The fund is only slightly -Select-morelessItem 6 volatile than the market.

   3. 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.

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. Compare what the Sharpe and Treynor measures indicate about the ability of AFNFXs manager to beat the market on a risk-adjusted basis. If the two measures give contradictory indications, reconcile that discrepancy.

   The portfolio has a -Select-higherlowerItem 12 risk premium per unit of risk than the market portfolio as indicated by the Sharpe ratio. The portfolio plots -Select-abovebelowItem 13 the SML, indicating -Select-superiorinferiorItem 14 risk-adjusted performance, as its T value is -Select-higherlowerItem 15 than the market portfolios.