Question

Ollie is considering two portfolios: 1) Portfolio A with a return of 12% and a standard deviation of 16%, and 2) Portfolio B with a return of 5% and a standard deviation of 7%. Assuming the correlation between A and B is -1 and he invests 30% in A and 70% in B, what is the portfolio standard deviation?

a) Between 0% and 3%.
b) Between 3% and 6%.
c) Between 6% and 9%.
d) Between 9% and 14%.

Answer 1

Ollie's portfolio standard deviation, with a -1 correlation between the two portfolios and given weightings, is roughly 0.1%, which places it in the range of 0% to 3%. The correct answer is option (a).

Step-by-step explanation:

When considering portfolio standard deviation, especially with portfolios that have a correlation of -1, it simplifies the calculation because the portfolios offset each other's risk perfectly. Since Ollie invests 30% in Portfolio A (with a standard deviation of 16%) and 70% in Portfolio B (with a standard deviation of 7%), and given that the correlation between A and B is -1, we can use the formula for the standard deviation of the combined portfolio:

σportfolio = √((wAσA)² + (wBσB)² + 2wAwBσAσBρAB)

Since ρAB is -1, the formula simplifies to:

σportfolio = √((wAσA - wBσB)²)

Substituting the values we get:

σportfolio = √((0.3*0.16 - 0.7*0.07)²)

σportfolio = √((0.048 - 0.049)²) = √(0.000001)

σportfolio is therefore roughly 0.1%, which falls within the range of between 0% and 3%. Thus, the correct answer is option (a) Between 0% and 3%.