Question

Given the monthly returns that follow:

Month	Portfolio Return	S&P 500 Return
Jan.	5.5.%	5.8%
Feb.	-2.4	-3.3
March	-1.8	-1.5
April	2.7	2.0
May	0.7	-0.1
June	-0.9	-0.4
July	0.1	0.5
August	1.5	2.0
September	-0.8	-0.6
October	-3.2	-3.7
November	2.4	1.6
December	0.6	0.1

Calculate R²:   

Alpha:   %

Beta:   

Average return difference (with signs):   %

Average return difference (without signs)   %

Answer 1

Putting the values in the MS Excel

Using Excel's Data Analysis, Regression was done where Y is S&P 500 Returns and X is Portfolio Return

Below is the output of the Regression:

As per the above results, R-squared = 94.9% and Adjusted R-squared = 94.4%

Average Portifolio Monthly Return = (Sum of all the monthly returns) / (Number of Observations) = 4.40% / 12 = 0.37%

Average S&P 500 Monthly Return = (Sum of all the monthly returns) / (Number of Observations) = 2.40% / 12 = 0.20%

Alpha is the Excess Return that Portfolio has yielded over S&P 500 = 0.37% - 0.20% = 0.17% (monthly)

Alpha is also the intercept of the regression results

Beta for the question is 1.017 which means if Portfolio Return changes by 1 unit, then S&P Index return changes by 1.017 unit.

Average Return difference with signs = Avg Portfolio Return monthly - Avg S&P Return monthly = 0.17%

If we annualize the average return of Portfolio and S&P 500 using (1+r)^12 -1 formula then

Annualized Portfolio Return = 4.49%

Annualized S&P 500 Return = 2.43%

Hence, Annualized return difference = 2.06%

Since Average return difference is positive, hence, both with signs and without signs, it remains same.