Question

1A) Nicholas has built a 16,000 dollar stock portfolio with a beta of 1.2, an expected return of 10.8 percent, and a standard deviation of 25%. Melinda also has a 16,000 dollar portfolio, but it has a beta of 0.8, an expected return of 9.2 percent, and a standard deviation that is also 25%. The correlation coefficient between Nicholas' and Melinda's portfolios is zero. If Nicholas and Melinda marry and combine their portfolios, which of the following best describes their combined $32,000 portfolio?

- The combined portfolio's expected return will be greater than the simple weighted average of the expected returns of the two individual portfolios, 10.0%.

- The combined portfolio's standard deviation will be equal to a simple average of the two portfolios' standard deviations, 25%.

- The combined portfolio's beta will be equal to a simple weighted average of the betas of the two individual portfolios, 1.0; its expected return will be equal to a simple weighted average of the expected returns of the two individual portfolios, 10.0%; and its standard deviation will be less than the simple average of the two portfolios' standard deviations, 25%.

- The combined portfolio's standard deviation will be greater than the simple average of the two portfolios' standard deviations, 25%.

1B) Stock A has an expected return of 11 percent, a beta of 0.9, and a standard deviation of 15 percent. Stock B also has a beta of 0.9, but its expected return is 9 percent and its standard deviation is 13 percent. Portfolio AB has $900,000 invested in Stock A and $300,000 invested in Stock B. The correlation between the two stocks' returns is zero. Which of the following statements is CORRECT?

- The stocks are not in equilibrium based on the CAPM; if A is valued correctly, then B is overvalued.

- Portfolio AB's expected return is 11.0%.

- The stocks are not in equilibrium based on the CAPM; if A is valued correctly, then B is undervalued.

- Portfolio AB's beta is less than 1.2.

1C) Suppose you obtain the following information regarding Companies Facebook and Uber:

• Company Facebook has a higher expected return than Company Uber.
• Company Facebook has a lower standard deviation of returns than Company Uber.
• Company Facebook has a higher beta than Company Uber.

Given this information, which of the following statements is CORRECT?

- Company Facebook's stock is a better buy than Company Uber's stock.

- Company Facebook has more diversifiable risk than Company Uber.

- Company Facebook's returns will be negative when Uber's returns are positive.

- Company Facebook has a lower coefficient of variation than Company Uber.

Answer 1

1A) Expected Return of combined portfolio = Weighted Average of 2 portfolios

Expected Return = (10.8+9.2)/2 = 10%

Beta of combined portfolio = Weighted Average of 2 portfolios = (1.2+0.8)/2 = 1

Standard Deviation of combined portfolio = Square root of (weight1²*sd1² + weight2²*sd2²​​​​​​​ + 2*correlation * weight1*weight2)

Standard Deviation of portfolio = Square root of (0.5² * 25² + 0.5² * 25² + 2 * 0 * 0.5 * 0.5) = 17.68

So, 3 option is best and correct.

1B) weight of A​​​​​​​ = 900,000/(900,000+300,000) = 0.75

weight of B​​​​​​​ = 300,000/(900,000+300,000) = 0.25

Expected Return of portfolio =​​​​​​​ weight of A * Expected Return of A + weight of B * Expected Return of B

Expected Return of portfolio = 0.75 * 11 + 0.25 * 9 = 10.5

Beta of portfolio =  weight of A * Beta A + weight of B * Beta B = .75 * 0.9 + 0.25 * 0.9 = 0.9

Standard Deviation of portfolio = Square root of (weight1²*sd1² + weight2²*sd2²​​​​​​​​​​​​​​ + 2*correlation * weight1*weight2)

Standard Deviation of portfolio = Square root of (0.75² * 15² + 0.25² * 13² +0) = 11.71

So, 4 option is best and correct.

1C) Since, Company Facebook has a lower standard deviation of returns than Company Uber.

I think So, 4 option is best and correct.