Question

Suppose Stock M has an expected return of 10%, a standard deviation of 15%, and a Beta of 0.6 while Stock N has an expected return of 20%, a standard deviation of 25% and a beta of 1.04 , and the correlation between the two stocks is 0.50 . What is the standard deviation for a portfolio with 70% invested in Stock M and 30% invested in Stock N? Please show your formula and steps

Answer 1

The standard deviation for a portfolio with 70% invested in Stock M and 30% invested in Stock N is approximately 14.06%.

Step-by-step explanation:

To find the standard deviation for a portfolio with 70% invested in Stock M and 30% invested in Stock N, we can use the formula for portfolio standard deviation:

Portfolio Standard Deviation = sqrt((w1^2 * sd1^2) + (w2^2 * sd2^2) + (2 * w1 * w2 * sd1 * sd2 * correlation))

Where:

• w1 = weight of Stock M = 0.7
• w2 = weight of Stock N = 0.3
• sd1 = standard deviation of Stock M = 15%
• sd2 = standard deviation of Stock N = 25%
• correlation = correlation between Stock M and Stock N = 0.50

Plugging in these values, we get:

Portfolio Standard Deviation = sqrt((0.7^2 * 0.15^2) + (0.3^2 * 0.25^2) + (2 * 0.7 * 0.3 * 0.15 * 0.25 * 0.50))

Simplifying this equation, we find that the standard deviation for the portfolio is approximately 14.06%.