{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "![MOSEK ApS](https://www.mosek.com/static/images/branding/webgraphmoseklogocolor.png )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Data-driven distributionally robust optimization ([Mohajerin Esfahani and Kuhn, 2018](https://rdcu.be/cbBoC))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook illustrates parameterization in MOSEK's [Fusion API for python](https://docs.mosek.com/9.2/pythonfusion/intro_info.html), by implementing the numerical experiments presented in a paper titled \"Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations\" ([Mohajerin Esfahani and Kuhn](https://rdcu.be/cbBoC) hereafter), authored by [Peyman Mohajerin Esfahani](https://scholar.google.co.in/citations?user=ZTan-7YAAAAJ&hl=en) and [Daniel Kuhn](https://scholar.google.com/citations?user=RqnXytkAAAAJ&hl=en). \n", "\n", "#### Contents:\n", "1. [Data-driven stochastic programming (Paper summary)](#Data-driven-stochastic-programming-(Paper-summary)) \n", " - [Choice of the ambiguity set](#Choice-of-the-ambiguity-set-$\\widehat{\\mathcal{P}}_N$)\n", " - [Convex reduction of the worst-case expectation problem](#Convex-reduction-of-the-worst-case-expectation-problem)\n", "\n", "\n", "2. [Mean risk portfolio optimization with Fusion API](#Mean-risk-Portfolio-Optimization-(Section-7.1-in-paper)) \n", " - [Parameterized Fusion model](#Parameterized-Fusion-model)\n", " - [Market setup](#Market-setup)\n", "\n", "\n", "3. [Simulations and results](#Simulations-and-results)\n", "\n", " - [Impact of the Wasserstein radius](#Impact-of-the-Wasserstein-radius)\n", " - [Portflios driven by out-of-sample performance](#Portfolios-driven-by-out-of-sample-performance)\n", " - [Holdout method](#Holdout-method)\n", " - [k-fold cross validation method](#k-fold-cross-validation-method)\n", " - [Portfolios driven by reliability](#Portfolios-driven-by-reliability)\n", " - [Impact of sample size on Wasserstein radius](#Impact-of-sample-size-on-Wasserstein-radius)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Data-driven stochastic programming (Paper summary)\n", "\n", "Consider a loss function $h(x,\\xi)$ which depends on the decision variables $x$ and uncertain parameters $\\xi$. The goal is to minimize the expected value of $h(x,\\xi)$ for all $x\\in \\mathbb{X}$, where $\\mathbb{X} \\subset \\mathbb{R}^n$. The expected value is calculated over $\\mathbb{P}(\\xi)$, which is the probability distribution of the random vector $\\xi \\in \\mathbb{R}^m$. This distribution is supported on the uncertainty set $\\Xi$. The problem statement is written as in $\\ref{eq:main_prob}$.\n", "\n", "$$\n", "\\begin{equation}\n", "J^\\star := \\underset{x\\in \\mathbb{X}}{\\inf} \\bigg\\{ \\mathbb{E}^{\\mathbb{P}}\\big[ h(x,\\xi) \\big] = \\int_{\\Xi} h(x,\\xi)\\mathbb{P}(d\\xi)\\bigg\\}\n", "\\label{eq:main_prob} \\tag{1}\n", "\\end{equation}\n", "$$\n", "\n", "In practice, however, the probability distribution is often unknown. Instead, one usually has access to a set $\\widehat{\\Xi}_N := \\{\\widehat{\\xi}_i \\}_{i\\leq N}$, that contains $N$ historic realizations of the $\\xi$ vector. A data-driven solution $\\widehat{x}_N$ can be constructed by using some approximation of the true probability distribution. A natural choice for such an approximation is based on $\\widehat{\\Xi}_N$, and it is given by the discrete empirical probability distribution, as shown in $\\ref{eq:empirical_dist}$.\n", "\n", "$$\n", "\\begin{equation}\n", "\\mathbb{\\widehat{P}}_N := \\frac{1}{N}\\sum^{N}_{i = 1} \\delta_{\\widehat{\\xi}_i}\n", "\\label{eq:empirical_dist} \\tag{2}\n", "\\end{equation}\n", "$$\n", "\n", "The sample-average-approximation, which is obtained by replacing $\\mathbb{P}$ with $\\mathbb{\\widehat{P}}_N$ in $\\ref{eq:main_prob}$, is usually easier to solve but shows poor out-of-sample performance. Out-of-sample performance of a data-driven solution $\\widehat{x}_N$ is the expected loss for that decision under the true probability distribution. To obtain better out-of-sample performance, [Mohajerin Esfahani and Kuhn](https://rdcu.be/cbBoC) solve the robust optimization problem stated in $\\ref{eq:dist_rob}$.\n", "\n", "$$\n", "\\begin{equation}\n", "\\widehat{J}_N := \\underset{x\\in \\mathbb{X}}{\\inf} \\underset{\\mathbb{Q}\\in \\mathcal{\\widehat{P}}_N}\\sup \\mathbb{E}^\\mathbb{Q}\\big[ h(x, \\xi)\\big]\n", "\\label{eq:dist_rob} \\tag{3}\n", "\\end{equation}\n", "$$\n", "\n", "The distributionally robust problem stated in $\\ref{eq:dist_rob}$ is conceptually similar to $\\ref{eq:main_prob}$, but it compensates for the unknown $\\mathbb{P}$ by maximizing the expected value over all probability distributions $\\mathbb{Q}$ inside an ambiguity set $\\widehat{\\mathcal{P}}_N$. Maximization is done in order to obtain the worst-case estimate.\n", "\n", "If $\\widehat{x}_N$ is an optimal decision vector for the distributionally robust program, then the authors associate performance guarantees to $\\widehat{x}_N$ of the type shown in $\\ref{eq:perf_guarantee}$.\n", "\n", "$$\n", "\\begin{equation}\n", "\\mathbb{P}^N \\bigg\\{ \\widehat{\\Xi}_N : \\mathbb{E}^\\mathbb{P}\\big[ h(\\widehat{x}_N, \\xi) \\big] \\leq \\widehat{J}_N \\bigg \\} \\geq 1 - \\beta\n", "\\label{eq:perf_guarantee} \\tag{4}\n", "\\end{equation}\n", "$$\n", "\n", "Here, $\\mathbb{P}^N$ is a probability distribution that governs the realization of the set $\\widehat{\\Xi}_N$. The expression in $\\ref{eq:perf_guarantee}$ states that $\\widehat{J}_N$ provides an upper bound to the out-of-sample performance of $\\widehat{x}_N$ with at least $1-\\beta$ probability. Thus, $\\widehat{J}_N$ is a certificate of out-of-sample performance and the probability on the left side is the reliability of this certificate.\n", "\n", "### Choice of the ambiguity set $\\widehat{\\mathcal{P}}_N$\n", "\n", "The ambiguity set resides within a space of probability distributions and is chosen to be a ball of radius $\\epsilon$ centered at $\\widehat{\\mathbb{P}}_N$. The metric of choice is the [Wasserstein metric](http://nbviewer.jupyter.org/github/MOSEK/Tutorials/blob/master/wasserstein/wasserstein-bary.ipynb). Mathematically, the ambiguity set is defined as shown in $\\ref{eq:wass_ball}$.\n", "\n", "$$\n", "\\begin{equation}\n", "\\mathbb{B}_\\epsilon(\\mathbb{\\widehat{P}}_N) := \\big\\{ \\mathbb{Q} \\in \\mathcal{M}(\\Xi) : d_W (\\mathbb{\\widehat{P}}_N, \\mathbb{Q}) \\leq \\epsilon \\big\\}\n", "\\label{eq:wass_ball} \\tag{5}\n", "\\end{equation}\n", "$$\n", "\n", "As proved in section 3 of the paper, solving $\\ref{eq:dist_rob}$ with $\\mathcal{\\widehat{P}}_N$ set to $\\mathbb{B}_\\epsilon(\\mathbb{\\widehat{P}}_N)$ will provide finite sample performance guarantees of the type seen in $\\ref{eq:perf_guarantee}$. Furthermore, given certain assumptions (see paper), as $N\\to\\infty$, the certificate $\\widehat{J}_N$ approaches $J^\\star$ (optimal value of $\\ref{eq:main_prob}$) and the data-driven decision $\\widehat{x}_N$ approaches the true optimal decision $x^\\star$.\n", "\n", "### Convex reduction of the worst-case expectation problem\n", "\n", "The infinite dimensional maximization problem within $\\ref{eq:dist_rob}$ can be reduced to a computationally tractable finite-dimensional convex program, given the following requirements are met:\n", "\n", "1.) The uncertainty set $\\Xi$ is convex and closed.\n", "\n", "2.) The loss function is a point-wise maximum of more elementary functions, i.e. $l(\\xi) := \\underset{k\\leq K}{\\max} l_k(\\xi)$, where $-l_k(\\xi)$ are proper, convex, and lower semi-continuous for all $k\\leq K$. Note the suppression of the loss function's dependence on $x$.\n", "\n", "For problems that satisfy these requirements, the convex reduction is given in $\\ref{eq:convex_red}$.\n", "$$\n", "\\begin{align}\n", "& \\underset{\\lambda, s_i, z_{ik}, \\nu_{ik}}{\\inf} & & \\lambda \\epsilon + \\frac{1}{N}\\sum_{i=1}^{N}s_i & \\nonumber \\\\\n", "& \\text{s.t.} & &[-l_k]^*(z_{ik} - \\nu_{ik}) + \\sigma_{\\Xi}(\\nu_{ik}) - \\langle z_{ik},\\widehat{\\xi}_i\\rangle \\leq s_i & & \\forall i\\leq N , \\forall k\\leq K \\label{eq:convex_red} \\tag{6}\\ \\\\\n", "& & &\\|z_{ik}\\|_* \\leq \\lambda & & \\forall i\\leq N, \\forall k\\leq K \\nonumber \\\\\n", "\\end{align}\n", "$$\n", "\n", "where $[-l_k]^*$ denotes the conjugate of the negative $k^{\\text{th}}$ component of the loss function, $\\|z_{ik}\\|_*$ is the dual norm corresponding to the norm used in defining the Wasserstein ball and $\\sigma_\\Xi$ is the support function for the uncertainty set.\n", "\n", "# Mean risk Portfolio Optimization (Section 7.1 in paper)\n", "\n", "Consider a market that forbids short-selling and has $m$ assets. Yearly returns of these assets are given by the random vector $\\xi = [\\xi_1, ..., \\xi_m]^T$. The percentage weights (of the total capital) invested in each asset are given by the decision vector $x = [x_1, ..., x_m]^T$ where $x$ belongs to $\\mathbb{X} = \\{x \\in \\mathbb{R}_+^m : \\sum^{m}_{i=1}x_i = 1\\}$. We have to solve the problem stated in $\\ref{eq:mean_risk_port}$.\n", "\n", "$$\n", "\\begin{equation}\n", "J^\\star = \\underset{x\\in \\mathbb{X}}{\\inf} \\big\\{ \\mathbb{E}^{\\mathbb{P}}[-\\langle x, \\xi \\rangle] + \\rho \\mathbb{P}\\text{-CVaR}_\\alpha \\big(-\\langle x, \\xi\\rangle\\big)\\big\\}\n", "\\label{eq:mean_risk_port} \\tag{7}\n", "\\end{equation}\n", "$$\n", "\n", "which amounts to minimizing a weighted sum of the expected value and the conditional value-at-risk (see also: [Fusion notebook on stochastic risk measures](https://nbviewer.jupyter.org/github/MOSEK/Tutorials/blob/master/stochastic-risk/stochastic-risk-measures.ipynb)) of the portfolio loss, $- \\langle x, \\xi \\rangle$. Using the definition of conditional value-at-risk ([Optimization of conditional value-at-risk](https://www.ise.ufl.edu/uryasev/files/2011/11/CVaR1_JOR.pdf) by R. T. Rockafellar and S. Uryasev), $\\ref{eq:mean_risk_port}$ can be written as a maximum of $K=2$ affine loss functions ($\\ref{eq:cvar_prob}$).\n", "\n", "$$\n", "\\begin{equation}\n", "J^\\star = \\underset{x \\in \\mathbb{X}, \\tau \\in \\mathbb{R}}{\\inf} \\mathbb{E}^{\\mathbb{P}}\\big[\\underset{k\\leq K}{\\max} a_k \\langle x, \\xi \\rangle + b_k \\tau \\big]\n", "\\label{eq:cvar_prob} \\tag{8}\n", "\\end{equation}\n", "$$\n", "$$\n", "\\text{where}\\,\\, a =\\big(-1, -1-\\frac{\\rho}{\\alpha}\\big)\\, ,\\,\\, b =\\big(\\rho, \\rho-\\frac{\\rho}{\\alpha}\\big) \n", "$$\n", "\n", "If the uncertainty set is a polytope of the form $\\Xi = \\{ \\xi \\in \\mathbb{R}^m : C\\xi \\leq d \\}$, then the distributionally robust counterpart of the program in $\\ref{eq:cvar_prob}$ will have a convex reduction as shown in $\\ref{eq:convex_red_port}$. \n", "\n", "$$\n", "\\begin{align}\n", "& \\underset{x,\\tau,\\lambda,s_i, \\gamma_{ik}}{\\inf} & & \\lambda \\epsilon + \\frac{1}{N}\\sum^{N}_{i=1}s_i & \\nonumber \\\\\n", "&\\text{s.t.} & & b_k \\tau + a_k \\langle x, \\widehat{\\xi}_i \\rangle + \\langle \\gamma_{ik}, d - C\\widehat{\\xi}_i\\rangle \\leq s_i & \\forall i\\leq N, \\forall k\\leq K \\label{eq:convex_red_port} \\tag{9}\\\\\n", "& & &\\| C^T \\gamma_{ik} - a_k x\\|_* \\leq \\lambda & \\forall i\\leq N, \\forall k\\leq K &\\nonumber \\\\\n", "& & & \\gamma_{ik} \\geq 0 & \\forall i \\leq N, \\forall k \\leq K & \\nonumber \\\\\n", "& & & x \\in \\mathbb{X} & \\nonumber \\\\\n", "\\end{align}\n", "$$\n", "\n", "### Parameterized Fusion model\n", "\n", "Finally, we make a [Fusion](https://docs.mosek.com/9.2/pythonfusion/api-reference.html) model for the program in $\\ref{eq:convex_red_port}$. The following code cell defines `DistributionallyRobustPortfolio`, a wrapper class (around our fusion model) with some convenience methods. The key steps in the Fusion model implementation are (see `portfolio_model` method in class):\n", "\n", "- `M = Model('DistRobust_m{0}_N{1}'.format(m, N))`: instantiate a Fusion `Model` object.\n", "\n", "\n", "- `dat = M.parameter('TrainData', [N, m])` and `eps = M.parameter('WasRadius')`: declare a Fusion `parameter` object named \"TrainData\" and a parameter for the Wasserstein Radius, called \"WasRadius\". \"TrainData\" represents the past `N` realizations of the `m` sized random vector, $\\xi$. \n", "\n", "\n", "- `a_k = [-1, -51]` and `b_k = [10, -40]`: lists that are defined as in $\\ref{eq:cvar_prob}$. All experiments that follow have the same $a_k$ and $b_k$, therefore we use lists. However, with minor modifications these lists can be replaced with Fusion parameters. \n", "\n", "\n", "- `x = M.variable('Weights', m, Domain.greaterThan(0.0))`: declare Fusion variables for all the optimization variables involved in $\\ref{eq:convex_red_port}$, except $\\gamma$, which is excluded as $\\Xi \\in \\mathbb{R}^m$ ([see the market setup below](#Market-setup)).\n", "\n", "\n", "- `M.objective('J_N(e)', ObjectiveSense.Minimize, certificate)`: declare the objective sense and the expression of the objective. Here `certificate` is an `Expr` object that evaluates to the objective in $\\ref{eq:convex_red_port}$.\n", "\n", "\n", "- `self.M.constraint('C1',Expr.add([e1, e2, Expr.neg(Expr.repeat(s, 2, 1))]), Domain.lessThan(0.0))`: defining the constraints. Here `e1` and `e2` are `Expr` objects that evaluate to the relevant terms in the first constraint in $\\ref{eq:convex_red_port}$. Constraints \"C2_pos\" and \"C2_neg\" correspond to the second constraint and finally \"C3\" ensures that $x \\in \\mathbb{X}$.\n", "\n", "\n", "- `self.M.setSolverParam('optimizer','freeSimplex')`: use the [simplex optimizer](https://docs.mosek.com/9.2/pythonfusion/solving-linear.html#the-simplex-optimizer). By default, MOSEK will use its interior point optmizer. However, we plan to re-solve a linear model many times over and it is therefore imperative to exploit the warm-start capabilities of the simplex optimizer.\n", "\n", "Note: More details regarding the code can be found within comments." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "class DistributionallyRobustPortfolio:\n", "\n", " def __init__(self, m, N):\n", " self.m, self.N = m, N\n", " self.M = self.portfolio_model(m, N)\n", " self.x = self.M.getVariable('Weights')\n", " self.t = self.M.getVariable('Tau')\n", " self.dat = self.M.getParameter('TrainData')\n", " self.eps = self.M.getParameter('WasRadius')\n", " self.sol_time = []\n", "\n", " def portfolio_model(self, m, N):\n", " '''\n", " Parameterized Fusion model for program in 9.\n", " '''\n", " M = Model('DistRobust_m{0}_N{1}'.format(m, N))\n", " ##### PARAMETERS #####\n", " dat = M.parameter('TrainData', [N, m])\n", " eps = M.parameter('WasRadius')\n", " a_k = [-1, -51] # Alternative: Fusion parameters.\n", " b_k = [10, -40] # Alternative: Fusion parameters.\n", " ##### VARIABLES #####\n", " x = M.variable('Weights', m, Domain.greaterThan(0.0))\n", " s = M.variable('s_i', N)\n", " l = M.variable('Lambda')\n", " t = M.variable('Tau')\n", " ##### OBJECTIVE #####\n", " # certificate = lamda*epsilon + sum(s)/N\n", " certificate = Expr.add(Expr.mul(eps, l),\n", " Expr.mul(1/N, Expr.sum(s)))\n", " M.objective('J_N(e)', ObjectiveSense.Minimize, certificate)\n", " ##### CONSTRAINTS #####\n", " # b_k*t\n", " e1 = Expr.transpose(Expr.repeat(Expr.mul(t, b_k), N, 1))\n", " # a_k*\n", " e2 = Expr.hstack([Expr.mul(a_k[i], Expr.mul(dat, x))\n", " for i in range(2)])\n", " # b_k*t + a_k* <= s\n", " M.constraint('C1', Expr.add(\n", " [e1, e2, Expr.neg(Expr.repeat(s, 2, 1))]), Domain.lessThan(0.0))\n", " # a_k*x\n", " e3 = Expr.hstack([Expr.mul(a_k[i], x) for i in range(2)])\n", " e4 = Expr.repeat(Expr.repeat(l, m, 0), 2, 1)\n", " # ||a_k*x||_infty <= lambda\n", " M.constraint('C2_pos', Expr.sub(e3, e4), Domain.lessThan(0.0))\n", " M.constraint('C2_neg', Expr.add(e3, e4), Domain.greaterThan(0.0))\n", " # x \\in X\n", " M.constraint('C3', Expr.sum(x), Domain.equalsTo(1.0))\n", " # Use the simplex optimizer\n", " M.setSolverParam('optimizer', 'freeSimplex')\n", " return M\n", "\n", " def sample_average(self, x, t, data):\n", " '''\n", " Calculate the sample average approximation for given x and tau.\n", " '''\n", " l = np.matmul(data, x)\n", " return np.mean(np.maximum(-l + 10*t, -51*l - 40*t))\n", "\n", " def iter_data(self, data_sets):\n", " '''\n", " Generator method for iterating through values for the \n", " TrainData parameter.\n", " '''\n", " for data in data_sets:\n", " yield self.simulate(data)\n", "\n", " def iter_radius(self, epsilon_range):\n", " '''\n", " Generator for iterating through values for the WasRadius\n", " parameter.\n", " '''\n", " for epsilon in epsilon_range:\n", " yield self.solve(epsilon)\n", "\n", " def simulate(self, data):\n", " '''\n", " Tentative goal of this method is to set a value for the\n", " data parameter, and solve the model for the same.\n", " \n", " Define in child classes.\n", " '''\n", " pass\n", "\n", " def solve(self, epsilon):\n", " '''\n", " Tentative goal of this method is to set a value for the \n", " radius parameter, and solve the model for the same.\n", " \n", " Define in child classes.\n", " '''\n", " pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Market setup\n", "\n", "The simulation results presented in the paper are based on a market with $m = 10$ assets. Each asset's return is expressed as $\\xi_i = \\psi + \\zeta_i$, where $\\psi \\sim \\mathcal{N}(0, 0.02)$ is the systematic risk factor and $\\zeta_i \\sim \\mathcal{N}(0.03\\times i, 0.025\\times i)$ is the idiosyncratic risk factor. By construction, assets with higher indices have higher risk as well as higher returns. The uncertainty set is $\\Xi \\in \\mathbb{R}^m$, thus $C$ and $d$ are set to zero. $1$-norm is used to define the Wasserstein ball, therefore the dual norm will be the $\\infty$-norm. Lastly, $\\alpha = 20\\%$ and $\\rho = 10$ are used within the loss function. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Function to generate N samples of the m-shaped random vector xi.\n", "def normal_returns(m, N):\n", " R = np.vstack([np.random.normal(\n", " i*0.03, np.sqrt((0.02**2+(i*0.025)**2)), N) for i in range(1, m+1)])\n", " return (R.transpose())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Simulations and results\n", "\n", "The concluding section of this notebook reproduces the results provided in sections 7.2 of [Mohajerin Esfahani and Kuhn](https://rdcu.be/cbBoC). We do not pursue details of the design of these simulations, instead we focus primarily on implementing them with the models constructed above. The reader will find details/hints about the code within the in-code comments.\n", "\n", "## Impact of the Wasserstein radius" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from mosek.fusion import Model, Expr, Domain, ObjectiveSense\n", "import matplotlib.pyplot as plt\n", "from scipy.special import erfinv\n", "from sklearn.model_selection import train_test_split\n", "from sklearn.utils import resample" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Inherits from the portfolio class defined above.\n", "class SimSet1(DistributionallyRobustPortfolio):\n", " # Market setup\n", " m = 10\n", " mu = np.arange(1, 11)*0.03\n", " var = 0.02 + (np.arange(1, 11)*0.025)\n", "\n", " # Constants for CVaR calculation.\n", " beta, rho = 0.8, 10\n", " c2_beta = 1/(np.sqrt(2*np.pi)*(np.exp(erfinv(2*beta - 1))**2)*(1-beta))\n", "\n", " def __init__(self, N, eps_range):\n", " self.eps_range = eps_range\n", " # Fusion model instance\n", " super().__init__(SimSet1.m, N)\n", "\n", " def simulate(self, data):\n", " '''\n", " This method is called within the generator method called iter_data, which \n", " was defined in the parent class.\n", "\n", " Returns\n", " wts: optimal asset weights for each radius\n", " perf: analytic out-of-sample performance for each radius\n", " rel: reliability for each radius\n", " '''\n", " # Set TrainData parameter\n", " self.dat.setValue(data)\n", " # Iterate through range of Wasserstein radii (see solve method below)\n", " wts, perf, rel = zip(*[(_w, _p, _r)\n", " for _w, _p, _r in self.iter_radius(self.eps_range)])\n", " return wts, perf, rel\n", "\n", " def solve(self, epsilon):\n", " '''\n", " This method is used within the generator method called iter_radius, which\n", " was defined in the parent class.\n", "\n", " Returns:\n", " x_sol: asset weights\n", " out_perf: analytica out-of-sample performance\n", " rel: reliability for the certificate\n", " '''\n", " # Set WasRadius parameter (TrainData is already set)\n", " self.eps.setValue(epsilon)\n", " # Solve the Fusion model\n", " self.M.solve()\n", " self.sol_time.append(self.M.getSolverDoubleInfo('optimizerTime'))\n", " # Portfolio weights\n", " x_sol = self.x.level()\n", " # Analytical out-of-sample performance\n", " out_perf = self.analytic_out_perf(x_sol)\n", " return x_sol, out_perf, (out_perf <= self.M.primalObjValue())\n", "\n", " def analytic_out_perf(self, x_sol):\n", " '''\n", " Method to calculate the analytical value for the out-of-sample performance.\n", " [see Rockafellar and Uryasev]\n", " '''\n", " mean_loss = -np.dot(x_sol, SimSet1.mu)\n", " sd_loss = np.sqrt(np.dot(x_sol**2, SimSet1.var))\n", " cVaR = mean_loss + (sd_loss*SimSet1.c2_beta)\n", " return mean_loss + (SimSet1.rho*cVaR)\n", "\n", " def run_sim(self, data_sets):\n", " '''\n", " Method to iterate over several datasets and record the results.\n", " '''\n", " wts, perf, rel = zip(*self.iter_data(data_sets))\n", " self.weights = np.mean(wts, axis=0)\n", " self.perf_mu = np.mean(perf, axis=0)\n", " self.perf_20 = np.quantile(perf, 0.2, axis=0)\n", " self.perf_80 = np.quantile(perf, 0.8, axis=0)\n", " self.reliability = np.mean(rel, axis=0)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Time taken in initial solve of model with N=300: 0.0064 s\n", "Mean time to solve a model with N=300: 0.0018 s\n", "Total time to solve 200 models with N=300: 13.0416 s\n" ] } ], "source": [ "# Cardinality\n", "N = 300\n", "# Number of simulations\n", "num_sim = 200\n", "\n", "# Range of Wasserstein radii to consider\n", "epsilon_range = np.append(np.concatenate(\n", " [np.arange(1, 10)*10.0**(i) for i in range(-4, 0)]), 1.0)\n", "\n", "# Making 200 independent datasets\n", "sim_data = [normal_returns(10, N) for i in range(num_sim)]\n", "\n", "# Instantiate SimSet1 class\n", "sim1 = SimSet1(N, epsilon_range)\n", "\n", "# 200 simulations...\n", "sim1.run_sim(sim_data)\n", "\n", "print(\"Time taken in initial solve of model with N={0}: {1:.4f} s\".format(\n", " N, sim1.sol_time[0]))\n", "print(\"Mean time to solve a model with N={0}: {1:.4f} s\".format(\n", " N, np.mean(sim1.sol_time)))\n", "print(\"Total time to solve 200 models with N={0}: {1:.4f} s\".format(\n", " N, np.sum(sim1.sol_time)))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(ncols=2, figsize=(10, 4), dpi=150, gridspec_kw={'wspace': 0.3})\n", "fig.suptitle('N = {}'.format(N))\n", "\n", "# Portfolio weight vs Wasserstein radius\n", "for i in range(1, 11):\n", " ax[0].fill_between(epsilon_range, np.sum(sim1.weights[:, :i-1], axis=1), \n", " np.sum(sim1.weights[:, :i], axis=1),color=plt.cm.RdYlBu(1 - i/11))\n", " ax[0].plot(epsilon_range, np.sum(sim1.weights[:, :i], axis=1),\n", " color='black', linewidth=1.0)\n", "ax[0].set_xscale('log')\n", "ax[0].set_xlabel('$\\epsilon$')\n", "ax[0].set_xlim(10**-3, 1)\n", "ax[0].set_ylim(0, 1)\n", "ax[0].set_ylabel('Mean portfolio weights')\n", "\n", "# Evolution of certificate and reliability\n", "ax[1].plot(epsilon_range, sim1.perf_mu, color='blue')\n", "ax[1].fill_between(epsilon_range, sim1.perf_20, sim1.perf_80, color='blue', alpha=0.4)\n", "ax[1].set_xscale('log')\n", "ax[1].set_xlabel('$\\epsilon$')\n", "ax[1].set_xlim(10**-4, 1.0)\n", "ax[1].set_ylabel('Out-of-sample performance', color='blue')\n", "ax[1].set_yticks(np.arange(-1.4, -0.8, 0.1))\n", "ax[1].grid(which='major',alpha=0.4)\n", "ax[1].grid(which='minor',alpha=0.3)\n", "\n", "ax2 = ax[1].twinx()\n", "\n", "ax2.set_ylabel('Reliability', color='red')\n", "ax2.plot(epsilon_range, sim1.reliability, color='red')\n", "ax2.set_yticks(np.arange(0, 1.2, 0.2))\n", "ax2.set_ylim(0, 1)\n", "\n", "plt.savefig('sim1_N{}.jpg'.format(N), dpi = 150, bbox_inches='tight')\n", "plt.show()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Portfolios driven by out-of-sample performance\n", "\n", "### Holdout method" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "class SimSet2_Holdout(DistributionallyRobustPortfolio):\n", " # Market setup\n", " m = 10\n", "\n", " # Radius range (see page 156 in Mohajerin Esfahani and Kuhn)\n", " eps_range = np.concatenate([np.arange(1, 10)*10.0**(i)\n", " for i in range(-3, 0)])\n", "\n", " # Validation data set of 2*10**5 samples (page 158 in paper)\n", " valids = normal_returns(10, 2*10**5)\n", "\n", " def __init__(self, N, k=5):\n", " # 1/k sized split for the test data.\n", " self.k = k\n", " # Fusion model for (train) data size N*(k-1)/k (see holdout method)\n", " super().__init__(SimSet2_Holdout.m, np.rint(N*(k-1)/k).astype(np.int32))\n", "\n", " def validate(self, data_sets):\n", " '''\n", " Method to iterate over a list of independent datasets via the iter_data\n", " generator method so as to apply the holdout technique to each dataset \n", " and then save the results.\n", " '''\n", " self.perf, self.cert, radii = zip(*self.iter_data(data_sets))\n", " self.rel = np.mean(np.array(self.perf) <= np.array(self.cert), axis=0)\n", " self.radius = np.mean(radii, axis=0)\n", "\n", " def simulate(self, data):\n", " '''\n", " Method called within the iter_data generator.\n", "\n", " Returns\n", " out_perf: out-of-sample performance calculated with validation data\n", " cert: performance certificate (optimal objective for M)\n", " eps_holdout: radius selected from holdout method\n", " '''\n", " # Split data into test and train\n", " train, self.test = train_test_split(data, test_size=1/self.k)\n", " # Set the TrainData parameter to train data\n", " self.dat.setValue(train)\n", " # Iterate through a range of Wasserstein radii\n", " out_perf_test, x, t, J_N = zip(\n", " *self.iter_radius(SimSet2_Holdout.eps_range))\n", " # Index of eps_holdout in the eps_range.\n", " min_arg = np.argmin(out_perf_test)\n", " # Out-of-sample performance for x_N(eps_holdout)\n", " out_perf = self.sample_average(\n", " x[min_arg], t[min_arg], SimSet2_Holdout.valids)\n", " # J_N(eps_holdout)\n", " cert = J_N[min_arg]\n", " return out_perf, cert, SimSet2_Holdout.eps_range[min_arg]\n", "\n", " def solve(self, epsilon):\n", " '''\n", " Method called within the iter_radius generator.\n", "\n", " Returns\n", " out_perf: SA-approx of out-of-sample performance using test data\n", " x: Portfolio weights\n", " t: Tau\n", " self.M.primalObjValue(): performance certificate\n", " '''\n", " # Set the WasRadius parameter\n", " self.eps.setValue(epsilon)\n", " # Solve the Fusion model\n", " self.M.solve()\n", " self.sol_time.append(self.M.getSolverDoubleInfo('optimizerTime'))\n", " # Weights and Tau optimal values\n", " x, t = self.x.level(), self.t.level()\n", " # SAA of out-of-sample performance based on test data\n", " out_perf = self.sample_average(x, t, self.test)\n", " return out_perf, x, t, self.M.primalObjValue()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# Range of cardinality values to consider\n", "N_range = np.append(np.concatenate([np.arange(1,10)*10**(i) for i in range(1,3)]),1000)\n", "\n", "holdout_results = []\n", "for N in N_range:\n", " # List of 200 independent datasets of cardinality N\n", " n_data = [normal_returns(10, N) for i in range(200)]\n", " # Instance of SimSet2_Holdout class with cardinality N\n", " hld = SimSet2_Holdout(N)\n", " # Running the holdout method over each dataset\n", " hld.validate(n_data)\n", " # Save the object \n", " holdout_results.append(hld)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def N_plot(results, title, save_name, y_l = [[-1.5, 0.5], [-2.5, 10], [0, 1]]):\n", " N_range = np.append(np.concatenate(\n", " [np.arange(1, 10)*10**(i) for i in range(1, 3)]), 1000)\n", " \n", " fig, ax = plt.subplots(nrows=1, ncols=3, figsize=(13, 3), dpi=150)\n", " fig.suptitle(title)\n", " # Out-of-sample performance\n", " ax[0].fill_between(N_range, [np.quantile(r.perf, 0.2, axis=0) for r in results], [\n", " np.quantile(r.perf, 0.8, axis=0) for r in results], alpha=0.4)\n", " ax[0].plot(N_range, [np.mean(r.perf, axis=0) for r in results], marker='>')\n", " # Certificate\n", " ax[1].fill_between(N_range, [np.quantile(r.cert, 0.2, axis=0) for r in results], [\n", " np.quantile(r.cert, 0.8, axis=0) for r in results], alpha=0.4)\n", " ax[1].plot(N_range, [np.mean(r.cert, axis=0) for r in results], marker='>')\n", " # Reliability\n", " ax[2].plot(N_range, [r.rel for r in results], marker='>')\n", "\n", " y_n = [\"Out-of-sample performance\", \"Certificate\", \"Reliability\"]\n", " for i in range(3):\n", " ax[i].set_ylabel(y_n[i])\n", " ax[i].set_ylim(y_l[i])\n", " ax[i].grid(which='major',alpha=0.4)\n", " ax[i].grid(which='minor',alpha=0.3)\n", " ax[i].set_xscale('log')\n", " ax[i].set_xlabel('N')\n", " ax[i].set_xlim([10, 1000])\n", " ax[0].set_yticks([-1.5, -1, -0.5, 0, 0.5])\n", " plt.savefig(save_name, dpi = 150, bbox_inches='tight')\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "N_plot(holdout_results, 'Holdout Method', 'sim2_holdout.jpg')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### k-fold cross validation method" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "# IMPORTANT: sub-class of the SimSet2_Holdout class!\n", "class SimSet2_kFold(SimSet2_Holdout):\n", "\n", " def __init__(self, N, k=5):\n", " self.k = k\n", " # Object for holdout method (k-holdouts)\n", " super().__init__(N, k=k)\n", " # Fusion model for N-size dataset (results)\n", " self.M_N = self.portfolio_model(SimSet2_Holdout.m, N)\n", " self.dat_N = self.M_N.getParameter('TrainData')\n", " self.eps_N = self.M_N.getParameter('WasRadius')\n", " self.x_N = self.M_N.getVariable('Weights')\n", " self.t_N = self.M_N.getVariable('Tau')\n", "\n", " def simulate(self, data):\n", " '''\n", " Method called within the iter_data generator. This method overwrites\n", " the one defined in the SimSet2_Holdout class.\n", "\n", " Returns\n", " out_perf: out-of-sample performance calculated with validation data\n", " cert: performance certificate (optimal objective for M_N)\n", " eps_kFold: radius selected from k-Fold method\n", " '''\n", " # Set TrainData paremeter for M_N to data\n", " self.dat_N.setValue(data)\n", " # Perform the holdout method k times and calculate eps_kFold\n", " eps_kFold = np.mean([self._simulate(data) for i in range(self.k)])\n", " # Set WasRadius to mean from k holdout runs\n", " self.eps_N.setValue(eps_kFold)\n", " # Solve the M_N model.\n", " self.M_N.solve()\n", " # Out-of-sample performance for x_N(eps_kFold)\n", " out_perf = self.sample_average(\n", " self.x_N.level(), self.t_N.level(), SimSet2_Holdout.valids)\n", " # J_N(eps_kFold)\n", " cert = self.M_N.primalObjValue()\n", " return out_perf, cert, eps_kFold\n", "\n", " def _simulate(self, data):\n", " '''\n", " Method to perform the holdout technique for a given dataset. This \n", " is called k times within each call to the simulate method. Works\n", " analogously to the simulate method of SimSet2_Holdout class.\n", "\n", " Returns:\n", " eps_holdout: WasRadius selected in one holdout run\n", " '''\n", " # Split data into test and train\n", " train, self.test = train_test_split(data, test_size=1/self.k)\n", " # Set TrainData parameter for the N*(k-1)/k model\n", " self.dat.setValue(train)\n", " # Solve N*(k-1)/k model iteratively for a range of radii\n", " saa, x, t, J_N = zip(*self.iter_radius(SimSet2_Holdout.eps_range))\n", " # Select Wasserstein radius that minimizes out-of-sample perf\n", " min_arg = np.argmin(saa)\n", " return SimSet2_Holdout.eps_range[min_arg]" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "# Range of cardinality values to consider\n", "N_range = np.append(np.concatenate([np.arange(1,10)*10**(i) for i in range(1,3)]),1000)\n", "\n", "kFold_results = []\n", "\n", "for N in N_range:\n", " # List of 200 independent datdasets of cardinality N\n", " n_data = [normal_returns(10,N) for i in range(200)]\n", " # Instance of SimSet2_kFold class with cardinality N\n", " kFld = SimSet2_kFold(N)\n", " # Running the k-fold cross validation over each dataset\n", " kFld.validate(n_data)\n", " kFold_results.append(kFld)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "N_plot(kFold_results, 'k-fold cross validation method', 'sim2_kcross.jpg')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Portfolios driven by reliability" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "class SimSet3(DistributionallyRobustPortfolio):\n", " m = 10\n", " eps_range = np.concatenate([np.arange(1, 10)*10.0**(i)\n", " for i in range(-3, 0)])\n", " valids = normal_returns(10, 2*10**5)\n", "\n", " def __init__(self, beta, N, k=50):\n", " # Number of resamples\n", " self.k = k\n", " # Reliability threshold\n", " self.beta = beta\n", " # Instantiate Fusion model\n", " super().__init__(SimSet3.m, N)\n", "\n", " def bootstrap(self, data_sets):\n", " '''\n", " Method to iterate over a list of independent datasets via the iter_data\n", " generator method so as to apply the bootstrap technique to each dataset\n", " and then save the results.\n", " '''\n", " self.perf, self.cert, radii = zip(*self.iter_data(data_sets))\n", " self.rel = np.mean(np.array(self.perf) <= np.array(self.cert), axis=0)\n", " self.radii = np.mean(radii, axis=0)\n", "\n", " def simulate(self, data):\n", " '''\n", " Method called within the iter_data generator.\n", "\n", " Returns\n", " out_perf: out-of-sample performance calculated with validation data\n", " cert: performance certificate (optimal objective for M)\n", " eps_btstrp: radius selected from holdout method\n", " '''\n", " # List to store reliability\n", " rel = []\n", " # Perform k resamples\n", " for i in range(self.k):\n", " # Split data into test and train\n", " train, self.test = train_test_split(data, test_size=1/3)\n", " # Resample train data up-to size N\n", " train = resample(train, n_samples=self.N)\n", " # Set TrainData parameter to train\n", " self.dat.setValue(train)\n", " # Iterate through a range of Wasserstein radii\n", " rel.append(list(self.iter_radius(SimSet3.eps_range)))\n", " # Sum reliability over all resamples (for each epsilon)\n", " rel = np.sum(rel, axis=0)\n", " # Smallest radius that has reliability over 1-beta\n", " _id = next(i for i, r in enumerate(rel) if r >= self.k*(1-self.beta))\n", " eps_btstrp = SimSet3.eps_range[_id]\n", " # Set TrainData parameter to data\n", " self.dat.setValue(data)\n", " # Set WasRadius parameter to eps_btstrp\n", " self.eps.setValue(eps_btstrp)\n", " self.M.solve()\n", " # Out-of-sample performance for x_N(eps_btstrp)\n", " out_perf = self.sample_average(\n", " self.x.level(), self.t.level(), SimSet3.valids)\n", " cert = self.M.primalObjValue()\n", " return out_perf, cert, eps_btstrp\n", "\n", " def solve(self, epsilon):\n", " '''\n", " Method called within the iter_radius generator.\n", "\n", " Returns\n", " reliability: SAA of out-of-sample performance <= certificate(epsilon)\n", " '''\n", " # Set WasRadius parameter to epsilon and solve\n", " self.eps.setValue(epsilon)\n", " self.M.solve()\n", " # Calculate out-of-sample performance SAA estimator using test\n", " saa = self.sample_average(self.x.level(), self.t.level(), self.test)\n", " # Boolean to state if the certificate is greater than SAA estimate\n", " return saa <= self.M.primalObjValue()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "# Range of cardinality values to consider\n", "N_range = np.append(np.concatenate(\n", " [np.arange(1, 10)*10**(i) for i in range(1, 3)]), 1000)\n", "# Reliability threshold: 1 - beta = 0.9\n", "beta = 0.1\n", "\n", "bootstrap_results = []\n", "for N in N_range:\n", " n_data = [normal_returns(10,N) for i in range(200)]\n", " # Instance of SimSet3 class with cardinality N\n", " btstrp = SimSet3(beta,N)\n", " # Running the bootstrap method for each dataset\n", " btstrp.bootstrap(n_data)\n", " bootstrap_results.append(btstrp) " ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "N_plot(bootstrap_results, \"1 - $\\\\beta$ = {}\".format(1-beta), 'sim3_90.jpg',\n", " y_l = [[-1.5, 1.5], [-2.5, 10], [0, 1]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Impact of sample size on Wasserstein radius" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(5, 4), dpi=150)\n", "fig.suptitle('Impact of sample size on Wasserstein radius')\n", "\n", "# Wasserstein radius vs sample size N\n", "# HoldouN_rangeethod\n", "ax.plot(N_range, [h.radius for h in holdout_results], color='blue',\n", " linestyle='--', label='$\\widehat{\\epsilon}^{hm}_N$ Holdout')\n", "# k-fold cross validation method\n", "ax.plot(N_range, [k.radius for k in kFold_results], color='green', \n", " marker='>', label='$\\widehat{\\epsilon}^{cv}_N$ k-fold')\n", "# Bootstrap method (reliability driven portfolio)\n", "ax.plot(N_range, [b.radii for b in bootstrap_results], color='tomato', \n", " marker='<', label=r'$\\widehat{\\epsilon}^{\\beta}_N$ $1 - \\beta = 0.9$')\n", "\n", "ax.set_xscale('log')\n", "ax.set_yscale('log')\n", "ax.set_xlabel('N')\n", "ax.set_xlim(10, 1000)\n", "ax.set_ylim(0.005, 0.5)\n", "ax.set_ylabel('Average Wasserstein radii')\n", "ax.grid(which='major',alpha=0.4)\n", "ax.grid(which='minor',alpha=0.3)\n", "ax.legend()\n", "plt.savefig('radius_v_samplesize.jpg', dpi = 150, bbox_inches='tight')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The results provided in this notebook were computed on a laptop with Intel® Core™ i7-10875H processor and 32 GB RAM." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\"Creative
This work is licensed under a Creative Commons Attribution 4.0 International License. The **MOSEK** logo and name are trademarks of Mosek ApS. The code is provided as-is. Compatibility with future release of **MOSEK** or the `Fusion API` are not guaranteed. For more information contact our [support](mailto:support@mosek.com). " ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.6" } }, "nbformat": 4, "nbformat_minor": 4 }