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Stocks A, B, and C are similar in some respects: Each has an expected return of 10% and a standard deviation of 25%. Stocks A and B have returns that are independent of one another; i.e., their correlation coefficient, r, equals zero. Stocks A and C have returns that are negatively correlated with one another; i.e., r is less than 0. Portfolio AB is a portfolio with half of its money invested in Stock A and half in Stock B. Portfolio AC is a portfolio with half of its money invested in Stock A and half invested in Stock C. Which of the following statements is CORRECT?

a. Portfolio AB has a standard deviation that is greater than 25%.
b. Portfolio AC has an expected return that is less than 10%.
c. Portfolio AC has a standard deviation that is less than 25%.
d. Portfolio AB has a standard deviation that is equal to 25%.
e. Portfolio AC has an expected return that is greater than 25%.

Respuesta :

Answer:

The correct situation from the given statements is:

C.  Portfolio AC has a standard deviation that is less than 25%.

Explanation:

Given details of the question are:

There are three stocks A,B,C,

All of the three are similar in some or the other respects.

Expected return of each of them is 10% and standard deviation of each of them is calculated to be 25%.

The stocks which are independent of one another of having returns is Stock A and B

  i.e. their correlation coefficient, r, has a value equalling to zero.

Now, stocks A and C are negatively correlated to one another in terms of returns,

i.e.  the value of correlation coefficient r is less than zero.

Therefore, A portfolio which is having half of its money invested in stock A and the other half in stock B is portfolio AB.

On the other hand portfolio of which half of its money in stock A and other half in stock C is portfolio AC.

So, The correct situation from the given statements is:

C. A standard deviation that is less than 25% is of portfolio AC.

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