# 5.10 PAMR · PAMR ： 基于均值反轉的投資組合選擇策略 - 修改版 > 來源：https://uqer.io/community/share/55a4c52bf9f06c6dd3e17f0f 策略思路： 該策略的主要思想是用一個損失函數反映均值反轉性質，即如果基于前一期相對價格的預期收益值大于一定閾值，損失值將線性增長；否則，損失為0 策略實現 m個資產每日調倉：對每個資產，收益高于總資產平均收益者，減持；收益低于總資產平均收益者，增持 具體參見文獻： http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.421.579&rep=rep1&type=pdf ```py from CAL.PyCAL import * from numpy import * import pandas as pd import numpy as np from pandas import DataFrame import cvxopt from cvxopt import matrix from cvxopt.blas import dot import cvxopt.solvers as cs # parameters used in updatePAMR sensitivity = 0.8 C = 600 start = datetime(2012, 12, 1) end = datetime(2015, 5, 1) benchmark = 'HS300' universe = set_universe('SH180') capital_base = 1e8 refresh_rate = 1 window = 1 tickers = [stk[0:6] for stk in universe] portfolio = DataFrame(1.0, index = universe, columns = ['prePosition', 'position', 'relative_price']) def initialize(account): account.amount = capital_base account.universe = universe account.days = 0 def handle_data(account): today = account.current_date today_str = today.strftime("%Y%m%d") for stk in universe: hist_close = account.get_attribute_history('closePrice', 2) hist_pre_close = account.get_attribute_history('preClosePrice', 2) try: portfolio['relative_price'][stk] = hist_close[stk][-1]/hist_pre_close[stk][-1] #print stk, today_str, portfolio['relative_price'][stk] except: continue portfolio['relative_price'] = portfolio['relative_price'].fillna(1.0) portfolio['prePosition'] = portfolio['position'] a = portfolio['prePosition'] b = portfolio['relative_price'] portfolio['position'] = normalizePortfolio(updatePAMR(a, b, sensitivity, C)) for stk in portfolio.index: try: stk_amount = capital_base*portfolio['position'][stk]/hist_close[stk][-1] order_to(stk, stk_amount) except: continue def lossFunction(portfolio, relative_price, sensitivity): # define a e-insensitive loss function # portfolio vector: b # price relative vector: x # sensitivity parameter: e # then: loss = max(0, dot(x,b) - e) portfolio_return = portfolio.transpose().dot(relative_price) if portfolio_return < sensitivity: return 0 else: return portfolio_return - sensitivity def normalizePortfolio(portfolio): # original portfolio vector: b_origin # find b = argmin(|b - b_origin|^2) under condition: # sum(b_i) = 1 and b_i > 0 for all i # solve the problems using Quadratic Programming Method: # http://abel.ee.ucla.edu/cvxopt/userguide/coneprog.html#quadratic-programming n = portfolio.shape[0] S = cvxopt.matrix(0.0, (n,n)) S[::n+1] = 1.0 S = S.T*S pbar = cvxopt.matrix(portfolio.values).T*(S + S.T) pbar = pbar.T G = cvxopt.matrix(0.0, (n,n)) G[::n+1] = -1.0 h = cvxopt.matrix(0.0, (n,1)) A = cvxopt.matrix(1.0, (1,n)) b = cvxopt.matrix(1.0) cvxopt.solvers.options['show_progress'] = False x = cs.qp(S, -pbar, G, h, A, b)['x'] b = portfolio.copy() for i in range(0, n): b.ix[b.index[i]] = x[i] return b def updatePAMR(portfolio, relative_price, sensitivity, C): # update portfolio by PAMR2 methods: # PAMR: Passive Aggressive Mean Reversion Strategy for Portfolio Selection. # Bin Li, Peilin Zhao, Steven C.H. Hoi, and V. Gopalkrishnan. # Machine Learning, 2012, 87(2), 221 - 258. loss = lossFunction(portfolio, relative_price, sensitivity) avg_ret = relative_price.sum()/relative_price.shape[0] tmp = ((relative_price - avg_ret)**2).sum() + 1.0/2/C tau = loss/tmp return portfolio - tau*(relative_price - avg_ret) ```