收益率

风险与回报

收益率

简单收益率 (Simple rate of return)：when dealing with multiple assets over the same timeframe.

$简单收益率 = \frac{ 卖出价 - 买入价 }{ 买入价 }$
对数收益率 (Logarithmic rate of return)：when make calculations about a single asset over time. $对数收益率 = \log{\frac{卖出价}{买入价}} = \log{卖出价} - \log{买入价}$

:pen: 核心就是对于单一投资品的收益率，对数收益率时序可加；对于不同投资品的截面收益率，应该用百分比收益率，因为它在截面上有可加性；另外对数收益率对建模有帮助。

参考说明

简单收益率实例

# 加载数据
import numpy as np
from pandas_datareader import data as wb
PG = wb.DataReader('PG', data_source='yahoo', start='1995-1-1')
# 计算历史收益率
PG['simple_return'] = (PG['Adj Close'] / PG['Adj Close'].shift(1)) - 1
print(PG['simple_return']) # print out as Text

用图表显示

import matplotlib.pyplot as plt
PG['simple_return'].plot(figsize=(8, 5))
plt.show()

计算平均收益率

avg_returns_d = PG['simple_return'].mean()
avg_returns_d # 结果是 0.00054655035334591408
# 计算年均收益率 
avg_returns_a = PG['simple_return'].mean() * 250
avg_returns_a # 结果是 0.13663758833647852
print(str(round(avg_returns_a, 5) * 100) + ' %')
# 结果是 13.664 %

对数收益率实例

PG['log_return'] = np.log(PG['Adj Close']/PG['Adj Close'].shift(1))
log_return_d = PG['log_return'].mean()*250
print(str(round(log_return_d, 5) * 100) + ' %' )
# 结果是 11.684999999999999 %

收益横向比较

tickers = ['PG', 'MSFT', 'F', 'GE']
mydata = pd.DataFrame()
for t in tickers:
    mydata[t] = wb.DataReader(t, data_source='yahoo', start='1995-1-1')['Adj Close']

mydata第一行的数据是 $mydata.iloc[0]$ . 效果等于 $mydata.loc['1995-01-03']$

PG 6.441071 MSFT 2.436452 F 3.307851 GE 4.087069 Name: 1995-01-03 00:00:00, dtype: float64

以第一行为基准,计算历年来的增长, 并用图表打印出来.

(mydata / mydata.iloc[0] * 100).plot(figsize = (15, 6));
plt.show()

加权收益

假设每股平均按25%的权重计算.

returns = (mydata / mydata.shift(1)) - 1
weights = np.array([0.25, 0.25, 0.25, 0.25])
np.dot(returns, weights)

out: array([ nan, 0.0065397 , -0.0092297 , ..., 0.03227913, -0.00289308, 0.01411137])

计算历史以来平均年加权收益

annual_returns = returns.mean() * 250
np.dot(annual_returns, weights)
# 结果是 0.14225289130269819

如果采用不同的加权, weights_2 = np.array([0.4, 0.4, 0.15, 0.05]), 则结果为15.71%

指数收益

tickers = ['^GSPC', '^IXIC', '^GDXI', '^FTSE']

S&P500: ^GSPC, NASDAQ: ^IXIC, DAX: ^GDAXI, London FTSE: ^FTSE

美国三大股指比较

tickers = ['^GSPC', '^IXIC', '^GDAXI']
ind_data = pd.DataFrame()
for t in tickers:
    ind_data[t] = wb.DataReader(t, data_source='yahoo', start='1997-1-1')['Adj Close']

显示结果

(ind_data / ind_data.iloc[0] * 100).plot(figsize=(15, 6));
plt.show()

个股与大盘指数比较

tickers = ['PG', '^GSPC', '^DJI']
data_2 = pd.DataFrame()
for t in tickers:
    data_2[t] = wb.DataReader(t, data_source='yahoo', start='2007-1-1')['Adj Close']

显示结果, PG 历年总体来说优于大盘.

(data_2 / data_2.iloc[0] * 100).plot(figsize=(15, 6));
plt.show()

收益率

收益率