Portfolio Optimization: A Technical Perspective - GAMS

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16 16 Trading Restrictions "Zero or Range"- Constraint: • Revision of existing (not optimized) portfolio • "Zero or Range“ - Constraint: Either no trade or the trade must stay between pre-defined ranges both for purchase and selling • <strong>Portfolio</strong> turnover: The total purchase of investments xi may not exceed some threshold τ e.g. cn: either no trade (20%) or new share between 23-31% (u) or between 0-18% (l)
17 17 <strong>GAMS</strong> Formulation Variables xi(i) fraction of portfolio increase, xd(i) fraction of portfolio decrease, y(i) binary switch for increasing current holdings of i, z(i) binary switch for decreasing current holdings of i; Binary Variables y, z; Positive Variables xi, xd; Equations xdef(i) final portfolio definition, maxinc(i) bound of maximum lot increase of fraction of i, mininc(i) bound of minimum lot increase of fraction of i, maxdec(i) bound of maximum lot decrease of fraction of i, mindec(i) bound of minimum lot decrease of fraction of i, binsum(i) restricts use of binary variables, turnover restricts maximum turnover of portfolio; xdef(i).. x(i) =e= bdata(i,'old') -xd(i) + xi(i); maxinc(i).. xi(i) =l= bdata(i,'umax')* y(i); mininc(i).. xi(i) =g= bdata(i,'umin')* y(i); maxdec(i).. xd(i) =l= bdata(i,'lmax')* z(i); mindec(i).. xd(i) =g= bdata(i,'lmin')* z(i); binsum(i).. y(i) + z(i) =l= 1; turnover.. sum(i, xi(i)) =l= tau; Model Type: MIQCP
Page 1 and 2: 1 1 Portfolio Optimization: A Techn
Page 3 and 4: 3 3 Agenda Introduction Mathematica
Page 5 and 6: 5 5 Agenda Introduction Mathematica
Page 7 and 8: 7 7 Portfolio Optimization Models -
Page 9 and 10: 9 9 Modeling Approaches - Programmi
Page 11 and 12: 11 11 MV Model Algebra Variance of
Page 13 and 14: 13 13 Modeling Issues Basic MV-Mode
Page 15: 15 15 More Complex Business Rules R
Page 19 and 20: 19 19 Efficient Frontier and Portfo
Page 21 and 22: 21 21 Stochastic Programming (SP) S
Page 23 and 24: 23 23 Challenges Deterministic equi
Page 25 and 26: 25 25 More Theory and Templates The
Page 27 and 28: 27 27 Grid Computing loop(pp, #calc
Page 29 and 30: 29 29 Advantages of Grid Computing
Page 31 and 32: 31 31 Simple Serial Solve Loop Loop
Page 33 and 34: 33 33 Results for 4096 MIPS on Cond
Page 35 and 36: 35 35 The End Thank you! … Questi

Portfolio Optimization: A Technical Perspective - GAMS

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