Machine Learning for Trading--1-7 Sharpe Ratio and Other Portfolio Statistics

• 计算每日Portfolio的资产价值–Get the Daily Total Value of the Portfolio
• 累积回报率，日均回报率，日回报率方差
• 夏普比例–Sharpe Ratio

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计算每日Portfolio的资产价值–Get the Daily Total Value of the Portfolio

• Step 1: 生成一个包含price和dates的DataFrame
• Step 2: Price 以第一行为基准进行归一化处理，得到Normalized Price
  • normed = prices/prices[0]
• Step 3: 乘以配置比例
  • alloced = normed * allocs
• Step 4: 计算每日价格 position value
  • pos_vals = alloced * start_val
• Step 5: 计算每日Portfolio的资产价值
  • port_val = pos_vals.sum(axis=1)

累积回报率，日均回报率，日回报率方差

• Cumulative Return Rates: cum_ret = (port_val[-1]/port_val[0] - 1)
• Average Daily Return Rates: avg_daily_ret = daily_rets.mean()
• Standard Deviation of Daily Return: std_daily_ret = daily_rets.std()

夏普比例–Sharpe Ratio

• Sharpe Ratio （SR） – 它反映了单位风险基金净值增长率超过无风险收益率的程度
• SR = E[Ra - Rb]/Sigma_a – E:期望值, Ra:投资回报率, Rb:无风险投资的回报率, Sigma_a:额外投资收益回报率方差
• 对于基于日、周、月的采样数据，计算annual sharpe ratio需要乘以一个修正值
  • Daily: sqrt(256)
  • Weekly: sqrt(52)
  • Monthly: sqrt(12)
• SR = sqrt(k) * mean(daily_rets - daily_rf) / std(daily_rets)