Question

Stock X and Stock Y have a correlation coefficient of .5. Stock X has an expected return of 10% and a standard deviation of 10%. Stock Y has an expected return of 14% and a standard deviation of 21%. What is the portfolio standard deviation if 60% of your wealth is invested in Stock X and 40% in Stock Y? (Assume that no stocks other than X and Y can be invested in this portfolio.) Select one:

a. 4.41%
b. 20.5%
c. 12.53%
d. 2.07%
e. 54.9%

Answer 1

The portfolio standard deviation, we use the formula that incorporates the weights of the investments, their standard deviations, and the correlation coefficient between the stocks. By substituting the given values into the formula, we can calculate the portfolio standard deviation which matches one of the provided multiple choice answers.

Step-by-step explanation:

The question asks for the calculation of the portfolio standard deviation given the weights of two stocks, their expected returns, standard deviations, and correlation coefficient. To calculate the portfolio standard deviation, we use the formula:

σp = √(w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂p)

where w₁ and w₂ are the weights of the investments in Stock X and Stock Y respectively, σ₁ and σ₂ are their standard deviations, and p is the correlation coefficient. For Stock X with a 60% weight (.6), a standard deviation of 10% (.1), and Stock Y with a 40% weight (.4), a standard deviation of 21% (.21), and a correlation coefficient of .5, the formula becomes:

σp = √((.6)²(.1)² + (.4)²(.21)² + 2(.6)(.4)(.1)(.21)(.5))

Calculating this gives a portfolio standard deviation that would correspond to one of the multiple choice answers provided.