Sudradjat  Supian, Sukono  , Pramono  Sidi, Dwi  Susanti, 
    Quadratic Investment Portfolio Without a Risk-Free Asset Based on Value-at-Risk,
    Journal of Engineering and Applied Sciences,
    Volume 12,Issue 19,
    2017,
    Pages 4846-4850,
    ISSN 1816-949x,
    jeasci.2017.4846.4850,
    (https://makhillpublications.co/view-article.php?doi=jeasci.2017.4846.4850)
    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.
    Keywords: Investment portfolio;value-at-risk;short-selling;maximization;minimization;discussions