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In: Finance

The expected return on Tobiko is 13% and its standard deviation is 21.8%. The expected return...

The expected return on Tobiko is 13% and its standard deviation is 21.8%. The expected return on Chemical Industries is 10% and its standard deviation is 27.7%.

a.	Suppose the correlation coefficient for the two stocks' returns is 0.29. What are the expected return and standard deviation of a portfolio with 56% invested in Tobiko and the rest in Chemical Industries? (Round your answers to 2 decimal places.)

	Portfolio's expected return %

	Portfolio's standard deviation %

b.	If the correlation coefficient is 0.79, recalculate the portfolio expected return and standard deviation, assuming the portfolio weights are unchanged. (Round your answers to 2 decimal places.)

	Portfolio's expected return %

	Portfolio's standard deviation %

c.

Why is there a slight difference between the results, when the correlation coefficient was 0.29 and when it was 0.79?

The higher the correlation is between the two variables, the higher the potential is for diversification or the higher the correlation is between the two variables, the less the potential is for diversification.?

Expert Solution

(a) Tobiko

E₁ = 13%

σ₁ = 21.8%

w₁ = 0.56

Chemical Industries

E₂ = 10%

σ₂ = 27.7%

w₂ = 0.44

Portfolio Expected Return = E₁w₁ + E₂w₂ = 0.56*13% + 0.44*10% = 11.68%

Corr = 0.29

Portfolio Standard deviation = (w²₁*σ²₁ + w²₂*σ²₂ + 2*(w₁)*(w₂)*(σ₁)*(σ₂)*Corr(1,2))^1/2 = (0.56²*0.218² + 0.44²*0.277² + 2*(0.56)*(0.44)*(0.218)*(0.277)*0.2)^1/2 = 0.1959 or 19.59%

(b)

E₁ = 13%

σ₁ = 21.8%

w₁ = 0.56

Chemical Industries

E₂ = 10%

σ₂ = 27.7%

w₂ = 0.44

Portfolio Expected Return = E₁w₁ + E₂w₂ = 0.56*13% + 0.44*10% = 11.68%

Corr = 0.79

Portfolio Standard deviation = (w²₁*σ²₁ + w²₂*σ²₂ + 2*(w₁)*(w₂)*(σ₁)*(σ₂)*Corr(1,2))^1/2 = (0.56²*0.218² + 0.44²*0.277² + 2*(0.56)*(0.44)*(0.218)*(0.277)*0.79)^1/2 = 0.2307 or 23.08%

(c) As the correlation between stock increases, the diversification reduces, since the stocks start moving together. Hence, we see an increase in the portfolio standard deviation as correlation increases

jeff jeffy answered 1 year ago

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