Efficient Frontier Q !

In a two-asset portfolio, reducing the correlation between the two assets moves the efficient frontier in which direction? A) The efficient frontier is stable unless return expectations change. If expectations change, the efficient frontier will extend to the upper right with little or no change in risk. B) The efficient frontier tends to move down and to the left, representing increased risk from negative correlation. C) The efficient frontier is stable unless the asset’s expected volatility changes. This depends on each asset’s standard deviation. D) The frontier extends to the left, or northwest quadrant representing a reduction in risk while maintaining or enhancing portfolio returns.

I think A. Based on my light retention though.

My choice would be “D”. It helps to refer to a diagram not unlike the one on page 245 of Volume 4. I believe the idea here is that as you vary the correlation coefficient, you are enlarging your feasible set (for a fixed set of weights). As you change your feasible set, you are also changing your efficient frontier. To be more precise, let r_1 and r_2 denote correlation coefficients such that -1 < r_2 < r_1 < 1. The idea is that you start with a correlation coefficient of r_1 and move to a correlation coefficient of r_2. As you change from r_1 and r_2, it is assumed that you vary the weights so that you can trace out the “arc” border of a new (and larger) feasible set. The new feasible set will induce a new efficient frontier. As you enlarge you feasible set to the “west” you are also pushing your efficient set to the “west”. This would indicate that you are reducing standard deviation (i.e., risk) of your portfolio.

yes ans is D … and thanks for the good explanation. I agree reducing the correlation between two assets will decrease risk and moving efficient frontier towards left, but what I don’t want to agree with is the last part — “enhancing returns”. Returns are based on expected value and not on standard deviations/correlation. So all the points should move left or right along with decrease/increase in Correlation coefficient.

D it is

I know it is D, but why 'd change (or reduction) in corelaton between assests enhance returns (last part of the D). Returns are based on expectation rather than corelaion ??

D. would be my answer

More ideally, it would lead to a portfolio with lesser variance for every given expected return. Hence, for a user with a certain risk profile i.e std dev, it will lead to a portfolio with higher returns for that risk due to the lesser correlation. Did I get my point across well enough?

thunderanalyst Wrote: ------------------------------------------------------- > I know it is D, but why 'd change (or reduction) > in corelaton between assests enhance returns (last > part of the D). Returns are based on expectation > rather than corelaion ?? you are right, there is no enhancement of returns. only reduction of volatility.

here’s my thoughts: 1.from the fomula E(Rp)=W1E(R1)+w2E(R2) it is hardly to prove “enhancing portfolio returns” 2.Let’s draw a efficient frontier H of Cor(i,j)=0.3, and another efficient frontier L of Cor(i,j)=-0.3. i,j are 2 different assets. 3. you will find efficient frontier L is at the northwest of efficient frontier H, i.e. L above H in diagram. 4. draw a vertical line from X-axis (represent risk) to cross above 2 efficient frontier L & H. the intersection point w/L , E(L) is higher than intersection point w/H, E(H). 5. from Y-axis (represent return),you can find the E value of intersection points E(L) and E(H) . 6. E(L) is higher than E(H), i.e. return from efficient frontier L of Cor(i,j)=-0.3 higher than efficient frontier H of Cor(i,j)=0.3 at same same risk. thus “enhancing portfolio returns” with low correlation. If we can post image at this website, it is easy to explain and understand.

annexguy, it’s a matter of semantics. Efficient frontier - max return for a given level of standard deviation. Efficient frontier for assets with lower correlation has higher return for the same level of standard deviation as a frontier for assets with higher correlation. Or lower standard deviation for the same level of return (same weights to two assets).

I agree with maratikus. Reduction in co-relation will cause points to move left keeping them at the same level at Y-axis (which is expected return in this case). Real Enhancement will be only if the points move upward relative to their pre-corelation reduction positions.