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		9.253		2.754		0.410			0.980		-4.020		4.620
2		7.566		7.553		0.420			6.160		-3.470		0.090
3		-2.106		-1.972		0.470			-1.610		3.140		1.080
4		5.076		6.251		0.460			4.860		-1.580		-2.530
5		-1.736		0.776		0.390			-0.470		-2.530		4.840
6		-5.027		-4.105		0.420			-4.870		-0.310		3.840
7		4.074		5.965		0.430			3.830		-5.140		-1.210
8		8.072		6.086		0.500			6.650		4.630		-4.100
9		3.387		4.475		0.380			4.050		1.350		0.830
10		6.892		7.952		0.430			7.200		-2.360		-0.690
11		0.291		-5.587		0.400			-4.060		7.430		0.910
12		3.071		5.471		0.430			5.350		2.580		-0.380
13		-1.617		-3.345		0.410			-3.830		-0.930		2.530
14		-2.939		4.627		0.380			2.710		-5.060		1.050
15		0.442		1.711		0.480			1.310		-2.320		3.590
16		-1.066		1.109		0.440			0.020		-1.000		-1.660
17		8.577		7.198		0.390			6.880		0.280		-1.220
18		3.799		5.108		0.400			4.760		-1.450		1.930
19		0.740		0.997		0.430			0.670		0.400		0.210
20		-2.549		-1.717		0.410			-2.940		-3.610		4.290
21		4.642		4.055		0.400			2.850		-3.410		-1.540
22		-1.787		-1.052		0.390			-2.730		-4.520		-1.800
23		-17.069		-14.448		0.430			-16.110		-5.910		5.690
24		15.713		6.400		0.450			5.940		0.010		-3.760
25		-3.542		8.123		0.330			7.110		-3.370		-2.840
26		3.574		6.061		0.300			5.850		1.370		-3.670
27		10.012		5.755		0.390			5.930		-0.300		-4.940
28		6.621		4.171		0.340			3.460		1.140		-6.150
29		-4.199		-3.102		0.340			-4.150		-5.580		1.660
30		5.437		3.992		0.430			3.310		-3.830		-3.050
31		0.808		3.866		0.380			4.470		2.890		2.810
32		-3.510		-2.367		0.330			-2.380		3.460		3.090
33		4.732		5.537		0.390			4.730		3.410		-4.320
34		-0.759		-3.120		0.370			-3.440		2.000		0.700
35		-1.884		-0.496		0.390			-1.340		-1.150		-1.250
36		-1.185		-2.744		0.400			-2.680		3.240		-3.170
37		7.074		6.321		0.390			5.800		-6.530		-3.180
38		2.442		2.033		0.360			3.190		7.700		-8.080
39		10.051		5.892		0.450			7.830		6.970		-9.040
40		-3.850		-5.030		0.410			-4.420		4.070		-0.170
41		5.789		-1.900		0.430			2.550		21.500		-12.030

2. 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:

4. 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.
   2. Jensens alpha coefficient:

      The value indicates that the manager generated a -Select- (higher - lower) return than what was expected given the portfolios risk level.

   4. Beta coefficient:

      The fund is only slightly -Select- (more - less ) volatile than the market.

   6. R-squared measure:

      It is -Select- (higher - lower) than 0.50, which means that the funds performance -Select-(is - is not) statistically related to the benchmark.
7. 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:

9. 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.

11. 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 .

13. 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:

     

    The managers investment prowess relative to the general equity market is considered as -Select-badgoodexceptionalItem 22 because the annualized IR is -Select-less than 0.5greater than or equal to 0.5 and less than 1.0equal to 1.0Item 23