@article{MAKHILLJEAS2017121914852,
    title = {Quadratic Investment Portfolio Without a Risk-Free Asset Based on Value-at-Risk},
    journal = {Journal of Engineering and Applied Sciences},
    volume = {12},
    number = {19},
    pages = {4846-4850},
    year = {2017},
    issn = {1816-949x},
    doi = {jeasci.2017.4846.4850},
    url = {https://makhillpublications.co/view-article.php?issn=1816-949x&doi=jeasci.2017.4846.4850},
    author = {Sudradjat,Sukono,Pramono and},
    keywords = {Investment portfolio,value-at-risk,short-selling,maximization,minimization,discussions},
    abstract = {This study will discuss the problems of quadratic investment portfolio without a risk-free asset based
on value-at-risk. It is assumed that the risk of an investment portfolio measured by value-at-risk. The resolution
of problems that do include: first, formulate models the trade-off problem. Secondly, formulate expectation
maximization model of the problem. Third, formulate model minimization of value-at-risk problem. Based on the
results of the discussions can be concluded that the trade-off between risk and expected return does not only
depend on the type of investor but also on the size of the investment. In a realistic investment situation, it is
likely that more constraints, e.g., restriction on short-selling, need to be considered.}
    }