1a) In your portfolio you have invested 30% and 70% in Stock X and Stock Z,...

1a) In your portfolio you have invested 30% and 70% in Stock X and Stock Z, respectively. The standard deviation of X is 12%. The standard deviation of Z is 9%. The correlation between X and Z is 0.50. Calculate the portfolio standard deviation.

1b) For the same problem before, now calculate the portfolio standard deviation if the correlation between X and Z is -0.50.

Solutions

Expert Solution

Weight of stock X in the portfolio = wX = 30%

Weight of stock Z in the portfolio = wZ = 70%

Standard deviation of stock X = σX = 12%

Standard deviation of stock Z = σZ = 9%

Part 1a

Correlation between X and Z = ρ = 0.5

Variance of the portfolio is calculated using the formula:

Variance of portfolio = σP2 = wX2*σX2 + wZ2*σZ2 + 2*ρ*wX*wZ*σX*σZ

Portoflio variance = σP2 = (30%)2*(12%)2 + (70%)2*(9%)2 + 2*0.5*30%*70%*12%*9% = 0.001296+0.003969+0.002268 = 0.007533

Standard deviation of the portfolio is square-root of variance

Standard deviation of portfolio = (0.007533)1/2 = 8.67928568489366% ~ 8.68% (Rounded to two decimals)

Answer 1a -> 8.68%

Part 1b

Correlation between X and Z = ρ = -0.5

Variance of the portfolio is calculated using the formula:

Variance of portfolio = σP2 = wX2*σX2 + wZ2*σZ2 + 2*ρ*wX*wZ*σX*σZ

Portoflio variance = σP2 = (30%)2*(12%)2 + (70%)2*(9%)2 + 2*(-0.5)*30%*70%*12%*9% = 0.001296+0.003969-0.002268 = 0.002997

Standard deviation of the portfolio is square-root of variance

Standard deviation of portfolio = (0.002997)1/2 = 5.4744862772684% ~ 5.47% (Rounded to two decimals)

Answer 1b -> 5.47%

jeff jeffy answered 1 year ago

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