Question

The expected return on Big Time Toys is 9% and its standard deviation is 21.9%. The expected return on Chemical Industries is 10% and its standard deviation is 29%.

             

a.	Suppose the correlation coefficient for the two stocks' returns is 0.2. What are the expected return and standard deviation of a portfolio with 34% invested in Big Time Toys 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 0.7, 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 0.2 and when it was 0.7?

Answer 1

(a) Big Time toys

E₁ = 9%

σ₁ = 21.9%

w₁ = 0.34

Chemical Industries

E₂ = 10%

σ₂ = 29%

w₂ = 0.66

Portfolio Expected Return = E₁w₁ + E₂w₂ = 0.34*9% + 0.66*10% = 9.66%

Corr = 0.2

Portfolio Standard deviation = (w²₁*σ²₁ + w²₂*σ²₂ + 2*(w₁)*(w₂)*(σ₁)*(σ₂)*Corr(1,2))^1/2 = (0.34²*0.219² + 0.66²*0.29² + 2*(0.34)*(0.66)*(0.219)*(0.29)*0.2)^1/2 = 0.2188 or 21.88%

(b)

Big Time toys

E₁ = 9%

σ₁ = 21.9%

w₁ = 0.34

Chemical Industries

E₂ = 10%

σ₂ = 29%

w₂ = 0.66

Portfolio Expected Return = E₁w₁ + E₂w₂ = 0.34*9% + 0.66*10% = 9.66%

Corr = 0.7

Portfolio Standard deviation = (w²₁*σ²₁ + w²₂*σ²₂ + 2*(w₁)*(w₂)*(σ₁)*(σ₂)*Corr(1,2))^1/2 = (0.34²*0.219² + 0.66²*0.29² + 2*(0.34)*(0.66)*(0.219)*(0.29)*0.7)^1/2 = 0.2493 or 24.93%

(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