pandas 对于给定的回报分布，计算风险价值或“最可能的损失”
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Calculating Value At Risk or "most probable loss", for a given distribution of returns
提问by Just another wombat
Given historical daily returns, how can I calculate the portfolio allocation for a single stock position, based on not losing more than 10% of the starting portfolio value over 21 days? (with 95% confidence.)
给定历史每日回报，基于 21 天内不超过初始投资组合价值的 10%，我如何计算单个股票头寸的投资组合分配？（有 95% 的置信度。）
Based on some starting code of e.g.
基于例如的一些起始代码
import numpy as np
from scipy.stats import norm
returns = [-0.01, -0.02, -0.01, 0.04, 0.02, 0.01, -0.03]
mu = np.mean(returns)
std = np.std(returns)
valueAtRisk = norm.ppf(0.05, mu, sigma)
However, the above only tells me my risk for 1 day. My question goes in the other direction; what can I allocate given the distribution of returns, assuming that I don't want to lose more than 10% over 21 days.
但是，以上仅告诉我我 1 天的风险。我的问题是另一个方向；假设我不想在 21 天内损失超过 10%，考虑到回报的分布，我可以分配什么。
I would prefer an answer that can be computed directly, but a Monte Carlo answer would be acceptable.
我更喜欢可以直接计算的答案，但蒙特卡罗答案是可以接受的。
Thanking you kindly for your help.
衷心感谢您的帮助。
回答by Jianxun Li
import numpy as np
returns = np.random.randn(1000)
Assuming returns are independently and identically distributed (i.i.d.), then the volatility of T days equals to the product of sqrt(T) times one-day-volatility.
假设收益独立同分布（iid），那么T天的波动率等于sqrt(T)乘以一天波动率的乘积。
# one-way 5% quantile, critical value is 1.64
VaR_21 = returns.std() * np.sqrt(21) * 1.645
VaR_21
Out[72]: 7.4161618430166989
Alternatively, you can do bootstraps. That's randomly select 21 days from historical dataset, calculate the return over this randomly drawed 21 days. Plot the histogram and get the 5% quantile.
或者，您可以进行引导。那是从历史数据集中随机选择 21 天，计算这个随机抽取的 21 天的回报。绘制直方图并得到 5% 的分位数。
def generate_random_index(n=21):
# could set replace to False as well
return np.random.choice(np.arange(1000), size=n, replace=False)
VaR_simulated_21 = []
n_bootstrap = 10000
for _ in range(n_bootstrap):
VaR = returns[generate_random_index(21)].sum()
VaR_simulated_21.append(VaR)
plt.hist(VaR_simulated_21)
np.percentile(VaR_simulated_21, q=5)
Out[108]: -8.0686958215041216
