Abstract
The , a new appearing financial risk-manage tool, have been applied widely. Many financial setups have accustomed to measure the risk of a portfolio with the . So it is very necessary to discuss the portfolio choice problem under the constraint. In this paper, by setting and solving the portfolio choice model under the constraint, we illustrate that the use of the constraint reduces the array of choice to a more manageable range. The probability of target , therefore, can be thought of as a risk tolerance assessment tool (when coupled with another measure of risk).
Highlights
In the path-breaking work on Portfolio Selection, Markowitz (1952) developed the concept of an efficient portfolio in terms of the expected return and standard deviation of return (i.e.(E, σ) criteria)
Baumel (1963) replaced the (E, σ) criteria with the (E, E−kσ) criteria, where k stands for the investor’s attitude toward risk. Baumol demonstrated that his (E, E−kσ) criteria yield a smaller efficient set, which is a subset of the Markowitz efficient set, and reduces the range of alternatives from which the investor has to select his portfolio
Our emphasis here is on algorithms because, unlike classical optimal mean-variance portfolios, optimal mean-variance portfolios in Value at Risk (VaR) constraint generally defy analysis with simple analytical tools
Summary
In the path-breaking work on Portfolio Selection, Markowitz (1952) developed the concept of an efficient portfolio in terms of the expected return and standard deviation of return (i.e.(E, σ) criteria). Baumel (1963) replaced the (E, σ) criteria with the (E, E−kσ) criteria, where k stands for the investor’s attitude toward risk Baumol demonstrated that his (E, E−kσ) criteria yield a smaller efficient set, which is a subset of the Markowitz efficient set, and reduces the range of alternatives from which the investor has to select his portfolio. Considerable amount of research was dedicated recently to development of methods of risk manage-ment based on Value at Risk. This literature is dedicated mainly to efficient techniques for computing VaR of a given portfolio. Our aim is to develop a theory that is the Markovitz theory for optimal mean-variance portfolios in VaR constraint and provide algorithmic tools for computing such portfolios. Our emphasis here is on algorithms because, unlike classical optimal mean-variance portfolios, optimal mean-variance portfolios in VaR constraint generally defy analysis with simple analytical tools
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