Question

You have a two-stock portfolio. One stock has an expected return of 12% and a standard deviation of 24%. The other has an expected return of 8% and a standard deviation of 20%. You invested in these stocks equally (50% of your investment went toward each of the two stocks). If the two stocks are negatively correlated, which one of the following is the most feasible standard deviation of the portfolio?
A) 23%
B) 22%
C) 21%
D) not enough information to determine

Answer 1

Answer:

None of the options are correct.

The correct answer lies between 2 percent through to 15.6 percent.

Explanation:

We have been given enough data or parameters or information which is going to help in solving the problem effectively and efficiently;

So, we have the following main points from the question/problem given above:

=> " One stock has an expected return

= 12% and a standard deviation of 24%."

=> The other has an expected return of 8% and a standard deviation of 20%."

=> "50% of your investment went toward each of the two stocks."

=> "If the two stocks are negatively correlated"

Hence, the most feasible standard deviation of the portfolio can be calculated as below:

(1). For stock portfolio One , we have

(0.5 × 20/100 )

(2). For stock polio two, we have;

( 0.5 × 24/100)

(3). 2 × 0 5 × (20/100) × 0.5 × (24/100) × correlation.

Now, take the square of (1) and (2) above and then the square root of (1), (2) and (3); and add (1), (2) and (3) together to give the standard deviation;

√[0.0244 + 0.024 × b]. ---------------------------(****).

Where b = correlation.

NOTE : "We are to assume that stocks are negatively correlated, thus, the correlation, bvalue between -1 and 0.

Thus, slotting in the correlation values into equation (****).

=> So, between 2 percent through to 15.6 percent.