Question

The stock of a technology company has an expected return of 15% and a standard deviation of 20% The stock of a pharmaceutical company has an expected return of 13% and a standard deviation of 18%. A portfolio consisting of 50% invested in each stock will have an expected

return of 14 % and a standard deviation
A) greater than the average of 20% and 18%.
B) the answer cannot be determined with the information given.
C) the average of 20% and 18%.
D) less than the average of 20% and 18%.

Answer 1

The correct answer is: D) less than the average of 20% and 18%.

The weighted average of the projected returns of each individual asset in the portfolio is used to determine the expected return of the entire portfolio.

For the technology company stock with an expected return of 15% and the pharmaceutical company stock with an expected return of 13%, where the portfolio consists of 50% invested in each stock:

`\[ \text{Expected Return of Portfolio} = (0.5 * 15\%) + (0.5 * 13\%) = 14\% \]`

This indicates that the portfolio's predicted return is 14%.

The standard deviation of a portfolio of two assets is calculated using a formula that takes into account the weights of each asset and their individual standard deviations, as well as their correlation coefficient:

`\[ \text{Portfolio Standard Deviation} = \sqrt{(w_1^2 * \sigma_1^2) + (w_2^2 * \sigma_2^2) + (2 * w_1 * w_2 * \sigma_1 * \sigma_2 * \rho_(12))} \]`

Given that there's no information about the correlation between the technology and pharmaceutical company stocks, let's assume they have no correlation (which would result in a higher portfolio standard deviation). The portfolio standard deviation in this instance is:

`\text{Portfolio Standard Deviation} = √((0.5^2 * 20\%^2) + (0.5^2 * 18\%^2))`

`= √((0.25 * 400) + (0.25 * 324))`

`= √(100 + 81)`

`= √(181) \approx 13.45\%`

So, the portfolio standard deviation is approximately 13.45%.

Comparing this with the average of the individual standard deviations (20% and 18%), which is (20% + 18%) / 2 = 19%, the portfolio's standard deviation (13.45%) is less than the average of 20% and 18%.

Answer 2

A portfolio consisting of 50% invested in each stock will have an expected return of 14 % and a standard deviation A portfolio consisting of 50% invested in each stock will have an expected return of 14 % and a standard deviation.

What is the standard deviation?

The standard deviation of the portfolio measures the portfolio's volatility. It is calculated using this formula:

The standard deviation of the portfolio =
`√((w1^2 * sd1^2 + w2^2 * sd2^2 + 2 * w1 * w2 * correlation * sd1 * sd2))`

The expected return of a portfolio measures the weighted average of the expected returns of its individual components.

So, the standard deviation from the values would be;

Standard deviation of portfolio =
`√((0.5)^2 * (0.20^2 + (0.5)^2 * (0.18)^2 + 2 * (0.5) * (0.5) * 0.5 * (0.20) * (0.18))`

= 16.4%

This value is less than the average of 20% and 18%.