Question

Stocks A and B each have an expected return of 12%, a beta of 1.2, and a standard deviation of 25%. The returns on the two stocks have a correlation of 0.6. Portfolio P has 50% in Stock A and 50% in Stock B. Which of the following statements is CORRECT? *Explain*

a. Portfolio P has a beta that is greater than 1.2.

b. Portfolio P has a standard deviation that is greater than 25%.

c. Portfolio P has an expected return that is less than 12%.

d. Portfolio P has a standard deviation that is less than 25%.

e. Portfolio P has a beta that is less than 1.2.

Answer 1

Portfolio beta = weighted average beta of stocks = 1.2 {since both stocks have same beta}

Portfolio Returns = weighted average returns of stocks = 12% {since both stocks have same returns}

Standard deviation of Portfolio is always less than or equal to weighted average standard deviation of stocks.

If correlation = 1, Standard deviation of Portfolio is equal to weighted average standard deviation of stocks.

If correlation < 1, Standard deviation of portfolio is less than weighted average standard deviation.

In above case, correlation among stocks is 0.6, therefore portfolio standard deviation will be less than weighted average standard deviation of stocks which 25%.

Therefore, option d is correct

d. Portfolio P has a standard deviation that is less than 25%.