TY - JOUR
T1 - An algorithmic approach to deriving the minimum-variance zero-beta portfolio
AU - Alexander, Gordon J
PY - 1977/3
Y1 - 1977/3
N2 - This paper examines the problem of deriving Black's (1972) minimum-variance zero-beta portfolio. Long's (1971) methods, used by Morgan (1975), are briefly mentioned. Then the complementary pivot algorithm of Lemke (1965), which has been shown to be capable of deriving the optimal solution to certain quadratic programming problems that are subject to a non-negativity constraint, is described. Finally, Lemke's algorithm is shown to be capable of deriving the minimum-variance zero-beta portfolio efficiently from samples of risky assets where both long and short positions are allowed by reformulating the problem so as to avoid the difficulties encountered by having a non-negatively constraint.
AB - This paper examines the problem of deriving Black's (1972) minimum-variance zero-beta portfolio. Long's (1971) methods, used by Morgan (1975), are briefly mentioned. Then the complementary pivot algorithm of Lemke (1965), which has been shown to be capable of deriving the optimal solution to certain quadratic programming problems that are subject to a non-negativity constraint, is described. Finally, Lemke's algorithm is shown to be capable of deriving the minimum-variance zero-beta portfolio efficiently from samples of risky assets where both long and short positions are allowed by reformulating the problem so as to avoid the difficulties encountered by having a non-negatively constraint.
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U2 - 10.1016/0304-405X(77)90012-5
DO - 10.1016/0304-405X(77)90012-5
M3 - Article
AN - SCOPUS:49449120344
SN - 0304-405X
VL - 4
SP - 231
EP - 236
JO - Journal of Financial Economics
JF - Journal of Financial Economics
IS - 2
ER -