(!****************************************************** Mosel Example Problems ====================== file folioqp_py.mos ``````````````````` Modeling a small QP problem to perform portfolio optimization. -- 1. QP: minimize variance 2. MIQP: limited number of assets -- -- Using Python to calculate covariance matrix -- (c) 2018 Fair Isaac Corporation author: S. Lannez, J. Müller, April 2018 *******************************************************!) model "Portfolio optimization with QP/MIQP" uses "mmxprs", "mmnl" uses "python3" ! Use Python functions parameters MAXVAL = 0,3 ! Max. investment per share MINAM = 0,5 ! Min. investment into N.-American values MAXNUM = 4 ! Max. number of different assets TARGET = 9 ! Minimum target yield end-parameters ! procedure get_cov() ! end-procedure declarations SHARES = 1..10 ! Set of shares RISK: set of integer ! Set of high-risk values among shares NA: set of integer ! Set of shares issued in N.-America DATES: set of string ! Historical dates RET: array(SHARES) of real ! Estimated return in investment VAR: array(SHARES,SHARES) of real ! Variance/covariance matrix of ! estimated returns OPEN: array(SHARES,DATES) of real ! Historical share value at market opening CLOSE: array(SHARES,DATES) of real ! Historical share value at market closing end-declarations initializations from "folioqp.dat" RISK RET NA end-initializations ! Load historical values to compute the covariance initializations from "folioqphist.dat" OPEN CLOSE end-initializations ! **** Perform some statistics using Python **** ! Copy array to Python environment initialisations to PY_IO_GLOBAL_VAR SHARES as 'shares' DATES as 'dates' OPEN as 'open' CLOSE as 'close' end-initialisations ! Import functions from Python scripts pyrun('mosel_numpy.py') pyrun('folioqp_py.py') ! Print covariance of share value at market openings writeln("Covariances at market openings:") pyexec('covariance(open, shares, dates)') ! Calculate and retrieve covariance of mean value writeln("Covariances of mean value of openings and closings:") pyexec('var = covariance_of_mean(open, close, shares, dates)') initialisations from PY_IO_GLOBAL_VAR VAR as 'var' end-initialisations declarations frac: array(SHARES) of mpvar ! Fraction of capital used per share end-declarations ! **** First problem: unlimited number of assets **** ! Objective: mean variance Variance:= sum(s,t in SHARES) VAR(s,t)*frac(s)*frac(t) ! Minimum amount of North-American values sum(s in NA) frac(s) >= MINAM ! Spend all the capital sum(s in SHARES) frac(s) = 1 ! Target yield sum(s in SHARES) RET(s)*frac(s) >= TARGET ! Upper bounds on the investment per share forall(s in SHARES) frac(s) <= MAXVAL ! Solve the problem minimize(Variance) ! Solution printing writeln("With a target of ", TARGET, " minimum variance is ", getobjval) forall(s in SHARES) writeln(s, ": ", getsol(frac(s))*100, "%") ! **** Second problem: limit total number of assets **** declarations buy: array(SHARES) of mpvar ! 1 if asset is in portfolio, 0 otherwise end-declarations ! Limit the total number of assets sum(s in SHARES) buy(s) <= MAXNUM forall(s in SHARES) do buy(s) is_binary frac(s) <= buy(s) end-do ! Solve the problem minimize(Variance) writeln("With a target of ", TARGET," and at most ", MAXNUM, " assets,\n minimum variance is ", getobjval) forall(s in SHARES) writeln(s, ": ", getsol(frac(s))*100, "%") ! Round integer values and resolve fixglobal(true) minimize(Variance) writeln("With all binary variables rounded to the nearest integer:") forall(s in SHARES) writeln(s, ": ", getsol(frac(s))*100, "%") end-model