Create a portfolio using the two stocks and information below: (Do not round int

Question

Create a portfolio using the two stocks and information below:

(Do not round intermediate calculations. Record your answers in decimal form and round your answers to 4 decimal places. Ex. x.xxxx)

What is the variance of A?

What is the variance of B?

What is the Correlation (A,A)?

What is the Correlation (B,B)?

What is the Covariance (A,A)?

What is the Covariance (A,B)?

What is the Covariance (B,A)?

What is the Covariance (B,B)?

What is the expected return on the portfolio above?

What is the variance on the portfolio above?

What is the standard deviation on the portfolio above?

Expected Return Standard Deviation Weight in Portfolio Stock A 14.00% 14.00% 60.00% Stock B 5.00% 16.00% 40.00% ---------------------- ---------------------- ---------------------- ---------------------- Correlation (A,B) 0.6600 ---------------------- ----------------------

Explanation / Answer

i) Variance of A = (Standard DeviationA)2 = (0.14)2 = 0.0196

ii) Variance of B = (Standard DeviationB)2 = (0.16)2 = 0.0256

iii) Correlation is the relative movement of two stock returns. When they the stocks are the same (A, A) then correlation will always be 1.

Correlation (A, A) = 1.0000

iv) Correlation (B,B) = 1.0000

iv) Covariance (A, A) = Correlation (A, A) x Standard Deviation of A x Standard Deviation of B = 1 x 0.14 x 0.16 = 0.0224

v) Covariance (A, B) = Correlation (A, B) x Standard Deviation of A x Standard Deviation of B = 0.66 x 0.14 x 0.16 = 0.0148

vi) Covariance (B, A) = Correlation (B, A) x Standard Deviation of A x Standard Deviation of B = 0.66 x 0.14 x 0.16 = 0.0148

vii) Covariance (B, B) = Correlation (B, B) x Standard Deviation of A x Standard Deviation of B = 1 x 0.14 x 0.16 = 0.0224

viii) Expected return of Portfolio = Expected Return (A) x Weight (A) + Expected Return (A) x Weight (A) = 0.14 x 0.60 + 0.05 x 0.40 = 0.1040

ix) Variance of Portfolio = (WeightA x Standard DeviationA)2 + (WeightB x Standard DeviationB)2 + 2 x WeightA x Standard DeviationA x WeightB x Standard DeviationB x Correlation (A, B)

or, Variance of Portfolio = (0.60 x 0.14)2 + (0.40 x 0.16)2 + 2 x 0.60 x 0.14 x 0.40 x 0.16 x 0.66 = 0.01824832 or 0.0182

x) Standard deviation of portfolio = (Variance)1/2 = (0.01824832)1/2 = 0.1351

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