Using the data in the following table, and the fact that the correlation of A an

Question

Using the data in the following table, and the fact that the correlation of A and B is 0.56, calculate the volatility (standard deviation) of a portfolio that is 70% invested in stock A and 30% invested in stock B.

Using the data in the following table, and the fact that the correlation of A and B is 0.56, calculate the volatility (standard deviation) of a portfolio that is 70% invested in stock A and 30% invested in stock B Realized Returns Year 2008 2009 2010 2011 2012 2013 Stock A -8% 19% 2% -2% 3% 11% Stock B 24% 201 5% -9% -14% 24% The standard deviation of the portfolio is | %. (Round to two decimal places.)

Explanation / Answer

The first step is to find the standard deviations of the two stock returns. STOCK A: Year Return % [r] d = r-m d^2 2008 -4.00 -8.83 77.97 2009 19.00 14.17 200.79 2010 2.00 -2.83 8.01 2011 -2.00 -6.83 46.65 2012 3.00 -1.83 3.35 2013 11.00 6.17 38.07 29.00 374.83 Mean = 29/6 = 4.83% SD = (374.83/6)^0.5 = 7.90% STOCK B: Year Return % [r] d = r-m d^2 2008 24.00 13.00 169.00 2009 33.00 22.00 484.00 2010 8.00 -3.00 9.00 2011 -9.00 -20.00 400.00 2012 -14.00 -25.00 625.00 2013 24.00 13.00 169.00 66.00 1856.00 Mean = 66/6 = 11% SD = (1856/6)^0.5 = 17.59% Formula for Portfolio SD of two assets = [Wa^2*Sda^2+Wb^2*SDb^2+2*Waq*Wb*Sda*SDb*Cor(a,b)]^0.5 Where Wa and Wb are the weights of the two assets. SDa,SDb their standard deviations and Cor(a,b), their correlation. Substituting values in the above equation, we have SD of the portfolio = (0.7^2*7.9^2+0.3^2*17.59^2+2*0.7*0.3*7.9*17.59*0.56)^0.5= 9.55% Answer: Standard deviation of the portfolio = 9.55%

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