我具有此功能来计算收益记录。它按预期工作。
def log_returns(prices):
return np.log(prices / prices.shift(1))
data.apply(lambda x: log_returns(x))
返回的值非常接近pct_change方法。这是预期的吗?
data.pct_change()
log(A/B) = log(A) - log(B)
并且在您的情况下,A等于B的一些小变化e
。
log(A/B) = log(A) - log(B) = log(B(1+e)) - log(B)
log(A/B) = log(B) + log((1+e)) - log(B) = log(1+e)
对于较小的e
值,意味着log
是一个很好的近似值。大约1
log(1+e) ≈ e
有关更多数学解释,请参阅this SO post。
亲自看这段代码:
import pandas as pd import numpy as np small = np.linspace(0.01, 0.1, 100) df = pd.DataFrame({"vals" : small}) df["changes"] = df["vals"].pct_change() df["log div"] = np.log(df["vals"]/df["vals"].shift()) diff_log = np.log(df["vals"]) - np.log(df["vals"].shift()) df["diff log"] = diff_log diff_log = diff_log[~np.isnan(diff_log)] log_div = df["log div"].dropna().values assert(np.allclose(log_div, diff_log))
和df.head(10)
:
values changes log div diff log
0 0.010000 NaN NaN NaN
1 0.010909 0.090909 0.087011 0.087011
2 0.011818 0.083333 0.080043 0.080043
3 0.012727 0.076923 0.074108 0.074108
4 0.013636 0.071429 0.068993 0.068993
5 0.014545 0.066667 0.064539 0.064539
6 0.015455 0.062500 0.060625 0.060625
7 0.016364 0.058824 0.057158 0.057158
8 0.017273 0.055556 0.054067 0.054067
9 0.018182 0.052632 0.051293 0.051293
y,它保持y≈ log (1 + y)。有关更多信息,请参见this Mathematics Exchange post。百分比变化计算为x i + 1