Of two risky asssets, which one will always lie on the efficient frontier and will one of them always be inefficient if held alone?
One of the risky assets offers a higher return than the other, but it also has a higher standard deviation.
Just using the information given here, there is no way to know which of these assets will be on the efficient frontier and which will lie below it.
The efficient frontier is a representation of the idea that the most efficient investment is one that has the optimal balance of risk and return. There are many combinations of risk and return that can be efficient.
If we were given two investments with equal risk (equal standard deviation) we would know that the one with higher return would be more efficient. If we were given two investments with equal returns, we would know the one with less risk (lower standard deviation) would be more efficient. But here, both variables are different and we do not know what the actual value of any of the variables is.
Therefore, we cannot know which investment is on the frontier. It could be either of them because the one with the higher risk also has a higher return.