Question

Given the monthly returns that follow, find the R2, alpha, and beta of the portfolio. Compute the average return differential with and without sign. Do not round intermediate calculations. Round your answers to two decimal places. Month Portfolio Return S&P 500 Return January 5.3 % 5.5 % February -2.4 -2.9 March -1.8 -1.1 April 2.5 2.0 May 0.9 0.5 June -1.1 -0.5 July 0.2 0.4 August 1.3 1.7 September -0.8 -0.1 October -3.2 -3.8 November 2.8 2.3 December 0.8 0.3

R2:

Alpha: %

Beta:

Average return difference (with signs): %

Average return difference (without signs) %

Answer 1

Step 1 calculating variance

                            Portfolio S%P 500        

month                 return                   Ri-E(Ri) Return Rm-E(Rm)      [Ri-E(Ri)x Rm-E(Rm)]

January                 5.30%                   4.93% 5.50%            5.14% 0.253%

February              -2.40%                 -2.78% -2.90% -3.26%             0.090%

March                   -1.80%                 -2.18% -1.10%            -1.46% 0.032%

April                       2.50%                   2.13%           2% 1.64% 0.035%

May                       0.90%                   0.53% 0.50% 0.14%                0.001%

June                     -1.10%                 -1.48% -0.50%          -0.86% 0.013%

July                       0.20%                   -0.18% 0.40% 0.04%               0.000%

August                  1.30%                   0.93% 1.70%           1.34% 0.012%

September -0.80% -1.18% -0.10%            -0.46%             0.005%

October               -3.20% -3.58% -3.80%              -4.16%             0.149%

November 2.80% 2.43%          2.30%              1.94%              0.047%

December 0.80%                    0.43% 0.30%             -0.06%             0.000%

                  E(Ri)     = 0.375%                          E(Rm) 0.358%                               0.637%

variance:

portfolio variance =

[(4.925)²+( -2.775) ² +(-2.175) ² +( 2.125) ² + (0.525) ² + (-1.475) ²

+ (-0.175) ² + (0.925) ² + (-1.175) ² + (-3.575) ² + (2.425) ² + (0.425) ²] /12

= 5.40

S&P 500 variance =

[(5.142)²+( -3.258) ² +(-1.458) ² +( 1.642) ² + (0.142) ² + -0.858) ²

+ (0.042) ² + (1.342) ² + (-0.458) ² + (-4.158) ² + (1.942) ² + (-0.058) ²] /12

=5.48

standard deviation = sqaure root of variance

portfolio = =2.32

S&P 500 = = 2.34

STEP 2 calculating covariance

covariance = 63.7/12

= 5.31

calculating R = Covariance/ (SD of portfolio x SD of S&P 500)

= 5.31/(2.32 x 2.34)

= 0.98

STEP 3

value or R² = 0.98 x 0 .98 = 0 .95

value of beta = covariance of S&P 500/ variance of S&P

= 5.31/ 5.48

= 0.97

value of alpha = E(Ri) - Beta (E(Rm))

0.375 - (0.97 (0.358)

= 0.03

STEP 4

Average return difference (with signs): %

month        portfolio return         S&P %)) RETURN              Return diff

January                5.30%                    5.50%                               -0.002

Februa                  -2.40%               -2.90%                              0.005

March                    -1.80% -1.10%                           -0.007

April                        2.50%                 2.00%                             0.005

May                        0.90%                  0.50%                              0.004

June                     -1.10%                 -0.50%                             -0.006

July                         0.20%                  0.40%                             -0.002

August                  1.30%                  1.70%                              -0.004

September         -0.80%               -0.10%                             -0.007

October               -3.20%               -3.80%                             0.006

November          2.80%                2.30%                              0.005

December           0.80%                 0.30%                             0.005

AVERAGE RETURN DIFFERNCE ( WITH SIGN )    = 0.0167%

Average return difference (without signs) %

month           portfolio return      S&P %)) RETURN              return diff

January               0.053                      0.055                                     -0.002

February              0.024                    0.029                                    0.007

April                     0.025                      0.02                                        0.005

May                     0.009                      0.005                                     0.004

June                    0.011                     0.005                                      0.006

July                      0.002                      0.004                                    -0.002

August                0.013                     0.017                                     -0.004

September         0.008                    0.001                                      0.007

October               0.032                    0.038                                    -0.006

November          0.028                   0.023                                      0.005

December           0.008                    0.003                                      0.005

AVERAGE RETURN DIFFERNCE WITHOUT SIGN             =0.167%