Question

Stocks A and B each have an expected return of 15%, a standard deviation of 17%, and a beta of 1.2. The returns on the two stocks have a correlation coefficient of <1.0. You have a portfolio that consists A) The portfolio's beta is less than 12. B) The portfolio's standard deviation is greater than 17%. C) The portfolio's standard deviation is less than 17%. D) The portfolio's expected return is 15%.

Answer 1

If both assets have a beta of 1.2 and it is only a two asset portfolio, then the portfolio will also have a beta of 1.2. Beta is the sensitivity of the market portfolio. This rules out option A

$\beta_{portfolio} = Weight_{A} \times \beta_{A}+Weight_{B} \times \beta_{B}$

$\Rightarrow \beta_{portfolio} = Weight_{A} \times \beta_{A}+ (1-Weight_{A}) \times \beta_{B}$

$\Rightarrow \beta_{portfolio} = Weight_{A} \times 1.2 + (1-Weight_{A}) \times 1.2 = 1.2$

Standard deviation is calculated using the following formula and value of portfolio standard deviation comletely depends on the weights of the two assets. Having a correlation less than 1 is not sufficient to say whether it will be greather than 17 or less than 17

$\sigma_ {Portfolio} = \sqrt{(W_{A} \times \sigma_{A})^{2}+(W_{B} \times \sigma_{B})^{2} +2 \times W_{A} \times \sigma_{A} \times W_{B} \times \sigma_{B} \times \rho_{AB}}$

So options B & C cant be determined with conclusivity with the given information

Expected return completely depends on the weights of the portfolio it will change values if we change weights, but if both assets have the same expected return then no matter what are the weights the portfolio return will alway be the same. Which in this case is 15% so option D is true

$ER_{portfolio} = Weight_{A} \times ER_{A}+Weight_{B} \times ER_{B}$

$\Rightarrow ER_{portfolio} = Weight_{A} \times ER_{A}+ (1-Weight_{A}) \times ER_{B}$

$\Rightarrow \beta_{portfolio} = Weight_{A} \times 15 + (1-Weight_{A}) \times 15 = 15$

Therefore the correctoption is D