Question

The expected return on VZ next year is 12% with a standard deviation of 20%. The expected return on ANT next year is 24% with a standard deviation of 30%. The correlation between the two stocks is 1.0. If Emily makes equal investments in VZ and ANT, what is the standard deviation of her portfolio? Selected answer will be automatically saved. For keyboard navigation, press up/down arrow keys to select an answer. a 22.47% b 25.00% c 5.05% d 15.00%

Answer 1

The standard deviation of Emily's portfolio with equal investments in stocks VZ and ANT, which have a correlation of 1.0, is 25.00%.

Step-by-step explanation:

To compute the standard deviation of Emily's portfolio consisting of equal investments in stocks VZ and ANT, which exhibit a correlation of 1.0, we can use the formula for the combined standard deviation of two assets in a portfolio:

The formula for two assets, A and B, with standard deviations σA and σB, and correlation coefficient ρ (rho), is:

σp = √[wA^2 σA^2 + wB^2 σB^2 + 2wAwBσAσBρ]

Since the correlation coefficient is 1.0:

• σVZ = 20%
• σANT = 30%
• ρ = 1.0

With equal investments, the weights wVZ and wANT are 0.5.

Plugging these values into the formula gives:

σp = √[(0.5^2)(0.2^2) + (0.5^2)(0.3^2) + 2(0.5)(0.5)(0.2)(0.3)(1.0)]

σp = √[(0.25)(0.04) + (0.25)(0.09) + (0.5)(0.2)(0.3)]

σp = √[(0.01) + (0.0225) + (0.03)]

σp = √[0.0625]

σp = 0.25 or 25%

Therefore, the correct answer is b 25.00%.

Answer 2

The standard deviation of Emily's portfolio, which consists of equal investments in VZ and ANT, is a. 22.47%.

Step-by-step explanation:

To find the standard deviation of a portfolio, you need to consider the individual standard deviations of the stocks and their correlation. In this case, the standard deviation of VZ is 20% and the standard deviation of ANT is 30%. The correlation between the two stocks is 1.0.

The formula to calculate the standard deviation of a portfolio is:

Standard Deviation of Portfolio

`= \sqrt(Standard Deviation of Stock 1)^2 * Weight of Stock 1 + (Standard Deviation of Stock 2)^2 * Weight of Stock 2 + 2 * Correlation Coefficient * Standard Deviation of Stock 1 * Standard Deviation of Stock 2)`

Since Emily is making equal investments in VZ and ANT, both stocks have a weight of 0.5. Plugging in the values, the standard deviation of her portfolio is:

Standard Deviation of Portfolio
`= \sqrt{((20^2 * (0.5)^2 + 30^2 * (0.5)^2 + 2 * 1.0 * 20 * 30%))`

= 22.47%