Question

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 & Poor’s 500 (SPX) Index. You have been asked to perform an evaluation of AFNDX’s 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 Fama–French risk factors (excess market, SMB, and HML). These data are listed below.

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

% 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 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: ________

B. Based on a regression of the excess returns to AFNDX on the excess returns to SPX, use regression analysis to calculate the active manager’s (1) one-factor Jensen’s 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.

Jensen’s alpha coefficient: ________

The value indicates that the manager generated a [higher or lower] return than what was expected given the portfolio’s risk level.

Beta coefficient: _______

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

R-squared measure: ________

C.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:________

Answer 1

Part A) As in the Part A of the Question it has been asked to find sharp ratios using calculated Risk premium which is given on monthly basis therefore in order to arrive at a single sharp ratio the average of calculated risk premium has been taken otherwise there would have been monthly sharp ratios

Part C)