Portfolio managers focus their efforts on achieving the best possible trade-off between risk and return. For portfolios constructed from a fixed set of assets, the risk/return profile differs with the portfolio composition. Portfolios that maximize the return, given the risk, or, on the other hand, minimize the risk for the given return, are called optimal. Optimal portfolios define a line in the risk/return plane called the efficient frontier.
A portfolio could also have to meet additional requirements to be considered. Different investors have dissimilar levels of risk tolerance. Selecting the adequate portfolio for a particular investor is a difficult task. The portfolio manager can evade the risk related to a particular portfolio along the efficient frontier with partial investment in risk-free assets. The definition of the capital allocation line, and finding where the final portfolio falls on this line, if at all, is a function of :
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