Charlie and Lucinda each have $50, 000 invested in stock portfolios.Charlie's has a beta of 1.2, an expected return of 10.8%, and a standard deviation of 25%.Lucinda's has a beta of 0.8, an expected return of 9.2%, and a standard deviation that is also 25%.The correlation coefficient, r, between Charlie's and Lucinda's portfolios is zero.If Charlie and Lucinda marry and combine their portfolios, which of the following best describes their combined $100, 000 portfolio?

Question

Quizplus · Accepted Answer

The combined portfolio's beta will be equal to a simple weighted average of the betas of the two individual portfolios, which is:

(0.8 * $50,000 / $100,000) + (1.2 * $50,000 / $100,000) = 1.0

The combined portfolio's expected return will be equal to a simple weighted average of the expected returns of the two individual portfolios, which is:

(0.092 * $50,000 / $100,000) + (0.108 * $50,000 / $100,000) = 0.1 or 10.0%

Since the correlation coefficient between the two portfolios is zero, there is no diversification benefit, and the combined portfolio's standard deviation will be:

[(0.8^2 * 0.25^2 * $50,000^2 / $100,000^2) + (1.2^2 * 0.25^2 * $50,000^2 / $100,000^2) + 2 * 0.8 * 1.2 * 0.25^2 * $50,000^2 / $100,000^2]^0.5 = 0.2236 or 22.36%

This is less than the simple average of the two portfolios' standard deviations, which is:

(0.25 + 0.25) / 2 = 0.25 or 25%

Charlie and Lucinda Each Have $50, 000 Invested in Stock