You have the portfolio of say about 6-7 stocks comprising of the shares from different sectors and that portfolio is expecting to give an average return of say 5%. Will that be an actual return from the portfolio? Certainly no, because that portfolio comprised of just one share of different companies across different sectors. Unless you have decided on the amount of capital that you are willing to allocate in favor of different share, you would never be able to find the accurate average annual return from your respective portfolio. If you would allocate higher proportion of capital towards the one giving higher return, definitely the overall return from that very portfolio would boost and simultaneously your risk. There is a direct relation between the risk and return and for higher amount of return you would definitely have to incur higher risk and vice versa.
A study of Markowitz Efficient Frontier Model Theory is based on the same notion. By having different sets of portfolios of the same securities through different combinations would give you an efficient frontier model. Running up through this efficient frontier would give you the portfolios of the same securities giving higher returns coupled with higher risk. The model is based on the fact that as you would go on diverting your capital towards that very security in the portfolio having higher returns your portfolio return along with your portfolio risk keeps on increasing. The model will not give you the efficient portfolio. Whether or not the portfolio at different levels is efficient is the person specific question. It would solely depend on the risk averseness of the investor which portfolio is efficient for him. For example, the investor with a high risk taking capability would definitely opt for the portfolio at the higher levels of the efficient frontier model giving him more returns and vice versa. So the risk averseness of the investor goes on decreasing as he goes on climbing the higher levels of the efficient frontier model. Once, the investor has determined the optimal portfolio for him, he can combine that portfolio with the risk free asset- say Treasury Bills. He can have different set of combinations with the risk free assets and the one having a high risk to reward ratio would be the optimal portfolio for him. This determination is important because practically, an investor will not divert all its investments in a risky portfolio but will set aside some part of it to be invested in risk free assets