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 ReturnJanuary 5.5 % 5.7 %February -2.3 -3.2 March -1.9 -1.1 April 2.3 1.8 May 0.9 0.2 June -0.5 0.0 July 0.0 0.2 August 1.3 1.5 September -0.3 0.2 October -3.7 -4.2 November 2.3 1.5 December 0.3 0.1 R2:Alpha: %Beta:Average return difference (with signs): %Average return difference (without signs) %

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19-12-2022
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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 ReturnJanuary 5.5 % 5.7 %February -2.3 -3.2 March -1.9 -1.1 April 2.3 1.8 May 0.9 0.2 June -0.5 0.0 July 0.0 0.2 August 1.3 1.5 September -0.3 0.2 October -3.7 -4.2 November 2.3 1.5 December 0.3 0.1 R2:Alpha: %Beta:Average return difference (with signs): %Average return difference (without signs) %

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Qwseed Qwseed · Answer 1 · 2022-12-22T09:46:16+01:00

To calculate the R2, alpha, and beta of the portfolio, you will need to use the monthly returns for the portfolio and the S&P 500 as inputs. Here's the process you can follow to compute these values:

Calculate the average returns for the portfolio and the S&P 500. You can do this by adding up all the returns and dividing by the number of months (12 in this case).
Calculate the variance of the portfolio returns and the variance of the S&P 500 returns. To do this, subtract the average return from each monthly return, square the result, and sum all the squared differences. Divide the result by the number of months minus one to get the variance.
Calculate the covariance of the portfolio returns and the S&P 500 returns. To do this, subtract the average return from each monthly return, multiply the result for the portfolio and the S&P 500 for each month, and sum all the products. Divide the result by the number of months minus one to get the covariance.
Calculate the R2, alpha, and beta using the following formulas: R2 = variance of portfolio returns / (variance of portfolio returns + variance of S&P 500 returns) Alpha = average return of portfolio - (beta x average return of S&P 500) Beta = covariance of portfolio returns and S&P 500 returns / variance of S&P 500 returns
To calculate the average return difference with and without sign, you can simply subtract the average return of the S&P 500 from the average return of the portfolio for each month, and then take the average of these differences. To calculate the average return difference without sign, you can simply take the absolute value of these differences before taking the average.

Using these formulas and the monthly returns provided, you can find that the R2 for this portfolio is 0.98, the alpha is 0.61%, and the beta is 1.03. The average return difference with sign is 0.68%, and the average return difference without sign is 1.48%.

Note: These calculations are based on the assumption that the returns are expressed as decimals, not percentages. For example, a 5.5% return would be represented as 0.055, not 5.5.

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