Python量化投资-市值加权+等权重+均值方差+最小方差模型

# -*- coding: utf-8 -*- """ Created on Mon Sep 13 19:35:36 2021 @author: 曹进辉 """ import numpy as np import pandas as pd # 年化收益率 def annualizedRet(r, year_days): ''' @param r : 每日收益率序列 @param year_days: 一年中交易股票所有交易日期天数（股票开市的天数）一般是250天 @return : 年化收益率 ''' cum_return = (1 + r).prod() total_days = r.shape[0] Annual_Returns = cum_return ** (year_days / total_days) - 1 return Annual_Returns # 年化波动率 def annualizedVol(r, year_days, downside = False): ''' @param r : 每日收益率序列 @param year_days: 一年中交易股票所有交易日期天数（股票开市的天数）一般是250天 @param downside : 是否计算下行偏差 @return: 年化波动率 ''' if downside: semistd = r[r < 0].std() return semistd * (year_days ** 0.5) else: return r.std() * (year_days ** 0.5) # 最大回撤 def drawdown(r): ''' @param r : 每日收益率序列 @return: 最大回撤 ''' index = 1000 * (1 + r).cumprod() highwatermark = index.cummax() # .cummax是找到当前节点之前的最大收益率 drawdowns = (index - highwatermark) / highwatermark # 计算回撤 maxdrawdown = drawdowns.min() return maxdrawdown # 偏度 def skewness(r): ''' @param r : 每日收益率序列 @return: 偏度 ''' centerMoment = r - r.mean() sigR = r.std(ddof=0) exp = (centerMoment ** 3).mean() return exp / sigR ** 3 # 峰度 def kurtosis(r): ''' @param r : 每日收益率序列 @return : 峰度 ''' centerMoment = r - r.mean() sigR = r.std(ddof=0) exp = (centerMoment ** 4).mean() return exp / sigR ** 4 # VaR def varGaussian(r, level=5, modified=False): ''' @param r : 每日收益率序列 @param level: 置信水平 @param modified: 使用泰勒展开式修正VaR @return: Value at Risk-风险价值 ''' from scipy.stats import norm z = norm.ppf(level / 100) if modified is True: s = skewness(r) k = kurtosis(r) z = (z + (z ** 2 - 1) * s / 6 + (z ** 3 - 3 * z) * (k - 3) / 24 - (2 * z ** 3 - 5 * z) * (s ** 2) / 36 ) return - (r.mean() + z * r.std(ddof=0)) # 夏普比率 def sharpeRatio(r, rf, year_days): ''' @param r : 每日收益率序列 @param rf : 无风险收益率 @param year_days : 一年当中有多少个交易日 @return: 夏普比率，也称风险调整后的return ''' # 将无风险收益率转换成日收益率，然后才能进行相加或者相减 rf = (1 + rf) ** (1 / year_days) - 1 excessRets = r - rf annExcessRets = annualizedRet(excessRets, year_days) annVol = annualizedVol(r, year_days) return annExcessRets / annVol def sortinoRatio(r,rf, year_days): ''' @param r : 每日收益率序列 @param rf : 无风险收益率 @param year_days : 一年当中有多少个交易日 @return : 夏普比率，也称风险调整后的return ''' rf = (1 + rf) ** (1 / year_days) - 1 excessRets = r - rf annExcessRets = annualizedRet(excessRets, year_days) anndownsideVol = annualizedVol(r, year_days, downside=True) return annExcessRets / anndownsideVol def summary_stats(r, riskFree=0, periodsInYear=252): ''' @param r : 每日收益率序列 @param riskFree: 无风险收益率 @param year_days : 一年当中有多少个交易日 @return: 各个策略的性能（DataFrame） ''' if not isinstance(r,pd.DataFrame): r = pd.DataFrame(r) # aggregate表明每一列均调用此函数，聚集函数 annR = r.aggregate(annualizedRet,year_days = periodsInYear) annVol = r.aggregate(annualizedVol, year_days= periodsInYear) dd = r.aggregate(lambda r: drawdown(r)) skew = r.aggregate(skewness) kurt = r.aggregate(kurtosis) modVar = r.aggregate(varGaussian, level=5, modified=True) sharpe = r.aggregate(sharpeRatio, rf=riskFree, year_days = periodsInYear) sortino = r.aggregate(sortinoRatio, rf = riskFree, year_days = periodsInYear) stats = pd.DataFrame({ 'Annualized Returns': annR*100, 'Annualized Volatility': annVol*100, 'Sharpe Ratio': sharpe, 'Sortino Ratio': sortino, 'Max Drawdown': dd*100, 'Skewness': skew, 'Kurtosis': kurt, 'Cornish Fisher adj. VAR 5%': modVar*100, }) #formatting stats['Annualized Returns'] = stats['Annualized Returns'].map('{:,.2f}%'.format) stats['Annualized Volatility'] = stats['Annualized Volatility'].map('{:,.2f}%'.format) stats['Sharpe Ratio'] = stats['Sharpe Ratio'].map('{:,.2f}'.format) stats['Sortino Ratio'] = stats['Sortino Ratio'].map('{:,.2f}'.format) stats['Max Drawdown'] = stats['Max Drawdown'].map('{:,.2f}%'.format) stats['Skewness'] = stats['Skewness'].map('{:,.2f}'.format) stats['Kurtosis'] = stats['Kurtosis'].map('{:,.2f}'.format) stats['Cornish Fisher adj. VAR 5%'] = stats['Cornish Fisher adj. VAR 5%'].map('{:,.2f}%'.format) return stats.T