Global Minimum-Variance Portfolio
When selecting the optimal portfolio you want to select a portfolio on the __minimum-variance frontier__ as such a portfolio maximizes return for any given risk.
However, not all portions of the minimum-variance frontier meet this goal.
Look at the graph below of the minimum-variance frontier. What is the significance of point C on the graph?
Incorrect.
Point C is not inherently the optimal portfolio for all investors. The optimal portfolio depends on the risk preferences of the investor and will vary from individual to individual.
Point C on the graph is the __global minimum-variance portfolio__, which is the point of lowest risk on the minimum-variance frontier.
Well done!
Point C on the graph is the lowest possible risk given this set of risky assets.
The __global minimum-variance portfolio__ is the point of lowest risk on the minimum-variance frontier.
Notice that point C divides two sections of the minimum-variance portfolio, shaded red and yellow.
If an investor were to choose between the portfolios denoted as points A and B, which should he or she prefer?
Correct, you're doing well!
Risk for the two portfolios is identical, but the expected return is higher for Portfolio A.
The rational investor will always seek to optimize the expected return at a given level of risk.
Incorrect.
Notice that risk is the same for the two portfolios, but the expected return is much higher for Portfolio A.
The rational investor will always seek to optimize the expected return at a given level of risk and should thus select Portfolio A over B.
To summarize:
[[summary]]
The global minimum-variance portfolio separates the efficient and inefficient portions of the minimum-variance frontier.
Notice that for every portfolio on the red portion of the frontier there is a portfolio on the yellow region with the same risk but a higher expected return.
A portfolio is considered efficient in this context if it provides the highest expected return at a given level of risk.
It is the point of lowest possible risk given the set of assets
It is the optimal portfolio for the investor to hold
Portfolio A
Portfolio B
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