You work for a private wealth

You work for a private wealth management firm that follows an“external investment” model, whereby it decides which outsidemanagers it should recommend to clients. One mutual fund that is acandidate for inclusion on your Premier Recommended List ofapproved managers is Active Fund (AFNDX), an actively managed stockportfolio benchmarked to the Standard & Poor’s 500 (SPX) Index.You have been asked to perform an evaluation of AFNDX’s pastinvestment performance, using a sample of monthly returns on thefollowing positions: (1) AFNDX portfolio, (2) SPX Index, (3) U.S.Treasury bills, and (4) the three primary Fama–French risk factors(excess market, SMB, and HML). These data are listed below.

Monthly Return Data for AFNDX, SPX, T-Bill, and Fama–FrenchFactors

% RETURNS TO: F-F FACTOR % RETURNS:

Month AFNDX SPX Index T-Bill (RF) Excess Mkt SMB HML

1 9.257 2.765 0.410 0.960 -4.020 4.620

2 7.586 7.549 0.410 6.170 -3.460 0.080

3 -2.113 -1.981 0.450 -1.600 3.140 1.080

4 5.082 6.250 0.450 4.860 -1.590 -2.530

5 -1.751 0.778 0.380 -0.490 -2.540 4.820

6 -5.034 -4.097 0.440 -4.880 -0.320 3.850

7 4.064 5.955 0.430 3.810 -5.130 -1.210

8 8.069 6.087 0.490 6.640 4.630 -4.090

9 3.395 4.479 0.360 4.060 1.370 0.830

10 6.896 7.958 0.430 7.210 -2.370 -0.700

11 0.302 -5.596 0.410 -4.050 7.450 0.910

12 3.075 5.482 0.440 5.360 2.590 -0.390

13 -1.625 -3.337 0.410 -3.820 -0.940 2.520

14 -2.922 4.621 0.380 2.730 -5.050 1.050

15 0.449 1.721 0.470 1.310 -2.330 3.590

16 -1.054 1.107 0.430 0.020 -1.010 -1.670

17 8.564 7.214 0.380 6.880 0.290 -1.220

18 3.804 5.118 0.390 4.740 -1.460 1.910

19 0.723 1.014 0.420 0.660 0.420 0.220

20 -2.563 -1.713 0.400 -2.960 -3.620 4.290

21 4.647 4.066 0.410 2.860 -3.400 -1.530

22 -1.800 -1.057 0.410 -2.710 -4.500 -1.800

23 -17.074 -14.444 0.420 -16.110 -5.920 5.690

24 15.720 6.403 0.470 5.950 0.030 -3.770

25 -3.536 8.134 0.320 7.100 -3.360 -2.860

26 3.587 6.052 0.320 5.870 1.360 -3.690

27 10.020 5.764 0.390 5.940 -0.310 -4.950

28 6.638 4.171 0.340 3.480 1.160 -6.150

29 -4.197 -3.098 0.350 -4.140 -5.580 1.660

30 5.422 4.001 0.430 3.320 -3.820 -3.030

31 0.811 3.879 0.380 4.480 2.890 2.810

32 -3.514 -2.352 0.330 -2.400 3.470 3.080

33 4.736 5.554 0.390 4.710 3.430 -4.340

34 -0.750 -3.119 0.390 -3.440 2.010 0.690

35 -1.879 -0.505 0.380 -1.360 -1.170 -1.270

36 -1.193 -2.746 0.400 -2.690 3.230 -3.170

37 7.071 6.318 0.380 5.800 -6.520 -3.190

38 2.437 2.032 0.360 3.200 7.700 -8.100

39 10.064 5.889 0.430 7.820 6.990 -9.040

40 -3.853 -5.025 0.410 -4.420 4.070 -0.150

41 5.788 -1.890 0.440 2.540 21.500 -12.020

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

Sharpe ratio for AFNDX: ______

Sharpe ratio for SPX: ________

B. Based on a regression of the excess returns to AFNDX on theexcess returns to SPX, use regression analysis to calculate theactive manager’s (1) one-factor Jensen’s alpha coefficient, (2)beta coefficient, and (3) R-squared measure. Briefly explain whateach of these statistics tells you about how AFNDX has beenmanaged. Do not round intermediate calculations. Round your answersto four decimal places.

Jensen’s alpha coefficient: ________

The value indicates that the manager generated a [higher orlower] return than what was expected given the portfolio’s risklevel.

Beta coefficient: _______

The fund is only slightly [more or less] volatile than themarket.

R-squared measure: ________

C.Using your work in parts (a) and (b), calculate the Treynorratio performance measures for both AFNDX and SPX, assuming a betacoefficient of 1.00 for the latter. Do not round intermediatecalculations. Round your answers to three decimal places.

Treynor ratio for AFNDX:_________

Treynor ratio for SPX:________