Question

Problem 4-07 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 5.3% -2.7 -1.6 S&P 500 Return 5.6% -3.2 -1.0 1.7 0.1 -0.6 0.9 January February March April May June July August September October November December 2.3 1.8 0.7 -1.2 0.5 1.5 -0.3 -3.2 2.8 0.3 -0.1 -3.7 2.0 0.0 R2: Alpha: % Beta: Average return difference (with signs): Average return difference (without signs) %

Answer 1

4 AB Month Portfolio Reti S&P500 Ret Return diff (without si Return diff (with signs) Jan 5.30% 5.60% 0.30% -0.30% Feb -2.70% -3.20% 0.50% 0.50% Mar -1.60% -1.007 0.60% -0.60% Apr 2.30% 1.70% 0.60% 0.602 May 0.70% 0.107 0.60% 0.60% Jun -1.20% -0.60% 0.60% -0.60%. 0.50% 0.90% 0.40% -0.40% Aug 1.50% 1.80% 0.30% -0.302 Sep -0.307. -0.10%. 0.20%. -0.20% Oct -3.20% -3.70% 0.50% 0.50% Nov 2.802 2.00% 0.80% 0.80% Dec 0.302 0.00% 0.30% 0.30% Average 0.37% 0.29% 0.482 0.08% Return diff (without si Return diff (with signs) Jul Correlatic 0.97736331 Formula =CORREL(Portfolio Return array, S&P500 Return array) R2 is the square of correlation SoR2 95.52% We can also calculate R2 using 'RSQ'excel function Formula =RSQ[Portfolio Return array, S&P500 Return array) Variance of portfolio return = 0.05846% Formula =VAR.S(D3:014) Covariance 0.058142 Formula COVARIANCE, S(Portfolio Return array, S&P500 Return array) Beta = covariance between asset and benchmark return/Variance of asset return Beta =0.058467/0.05814% 1.0055 Alpha=Rp - RF-beta (Rm-RF) Rp is portfolio return Rt is risk free rate Rm is the market portfolio return Since beta is roughly 1 Alpha = Rp-Rm Alpha= 0.37%-0.29% Alpha = 0.08%