Stocks A, B, and C all have an expected return of 10% and a standard deviation o

Question

Stocks A, B, and C all have an expected return of 10% and a standard deviation of 25%. returns that are independent of one another, i.e., their correlation coefficient, r, equals zero. returns that are negatively correlated with one another, i.e,r is less than 0. Portfolio AB is a portfolio with half of 26) Stocks A and B have Stocks A and C have 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 greater than 25%. 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 less than 10%.

Explanation / Answer

Expected Return of both AB and AC = 50% x 10% + 50% x 10% = 10%

Hence, Options B and E are incorrect.

Standard Deviation = [(w1 x SD1)^2 + (w2 x SD2)^2 + (2 x w1 x w2 x SD1 x SD2 x corr12)]^(1/2)

Now for AB, corrAB = 0 and for AC, corrAC < 0.

Hence, the standard deviation of AB and AC would be less than 25%, but due to negative correlation, the standard deviation of AC would be lower than that of AB.

Hence, C is correct.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.