On a standard risk-return plane where the vertical axis measures expected return and the horizontal axis measures standard deviation, a portfolio is strictly better than portfolios that lie to the _____________.

Question

BlackTom AI · Accepted Answer

Let's break down the geometry of the standard risk-return plane. The vertical axis represents expected return (higher is better), and the horizontal axis represents standard deviation (risk) (lower is better). 
Option 1: 'Right and above' — If a portfolio lies to the right (more risk) and above (higher return) of another portfolio, it does not necessarily dominate the other portfolio; in fact, it trades more risk for more return, so it isn’t strictly better in all respects. A portfolio that is strictly better would need to have higher return and lower risk, which is not described by 'right and above.'
Option 2: 'Left and below' — A portfolio left (less risk) and below (lower return) would be worse in both dimensions compared to a portfolio that is to the right and above; however, the phrasing asks about portfolios that a given portfolio is strictly better than, and being to the left and below would correspond to being worse, not better, than the other. This makes the option inconsistent with a strict dominance relation where the other portfolio would be worse if it is to the right and below. 
Option 3: 'Right and below' — This places the other portfolio at higher risk (to the right) and lower return (below) relative to the given portfolio. In that case, the given portfolio has both lower risk and higher return compared to that other portfolio, making it strictly better. That matches the idea of dominance: you beat portfolios that lie to the right (more risk) and below (less return). 
Option 4: 'Left and above' — A portfolio to the left (less risk) and above (higher return) would itself be superior in both dimensions, so calling the given portfolio strictly better than something that is actually already better in both dimensions would be inconsistent and suggests a misalignment with the dominance concept. This option describes the opposite relationship.
In summary, only the 'Right and below' option correctly captures the dominance idea: a portfolio is strictly better than those that lie to the right (more risk) and below (lower return).

On a standard risk-return plane where the vertical axis measures expected return and the horizontal axis measures standard deviation, a portfolio is strictly better than portfolios that lie to the _____________. 单项选择题

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