TL;DR
This paper derives analytical formulas for the efficient frontier in portfolio optimization, including cases with risk-free assets, and provides an R implementation with a numerical example involving stocks.
Contribution
It introduces explicit analytical expressions for the efficient frontier in portfolio optimization and offers an R implementation with practical examples.
Findings
Derived analytical expressions for the efficient frontier.
Provided an R implementation for portfolio optimization.
Demonstrated the approach with a numerical example.
Abstract
We consider the problem of finding the efficient frontier associated with the risk-return portfolio optimization model. We derive the analytical expression of the efficient frontier for a portfolio of N risky assets, and for the case when a risk-free asset is added to the model. Also, we provide an R implementation, and we discuss in detail a numerical example of a portfolio of several risky common stocks.
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Taxonomy
TopicsRisk and Portfolio Optimization · Stochastic processes and financial applications · Insurance, Mortality, Demography, Risk Management