财务和投资组合风险管理中的VaR？ (VaR in Financial and Portfolio Risk Management?)

VaR is an acronym of ‘Value at Risk’, and is a tool which is used by many firms and banks to establish the level of financial risk within its firm. The VaR is calculated for an investments of a company’s investments or perhaps for checking the riks levels of a portfolio managed by the wealth management branch of a bank or a boutique firm.

VaR是“风险价值”的缩写，是许多公司和银行用来确定公司内部金融风险水平的工具。 VaR的计算是针对公司投资的投资，或者是为了检查由银行或精品公司的财富管理分支机构管理的投资组合的风险水平。

The calculation may be thought of as a statistical measure in isolation. It can also be simplified to the following example statement -

可以将该计算孤立地视为统计量度。 也可以将其简化为以下示例语句-

VaR is the minimum loss which will be incurred at a certain level of probability (confidence interval) OR the maximum loss which will be realized at a level of probability.

VaR是在一定概率水平(置信区间)下发生的最小损失，或在概率水平下实现的最大损失。

The above image shows the maximum loss which can be faced by a company at a α% confidence. On a personal level VaR can help you predict or analyse the maximum losses which your portfolio is likely to face — this is something which we will analyse soon.

上图显示了公司在α ％置信度下可能面临的最大损失。 从个人角度而言，VaR可以帮助您预测或分析您的投资组合可能面临的最大损失-我们将尽快对此进行分析。

蒙特卡洛模拟 (Monte Carlo Simulations)

The Monte Carlo model was the brainchild of Stanislaw Ulam and John Neumann, who developed the model after the second world war. The model is named after a gambling city in Monaco, due to the chance and random encounters faced in gambling.

蒙特卡洛模型是斯坦尼斯拉夫·乌兰(Stanislaw Ulam)和约翰·诺伊曼(John Neumann)的创意，他们在第二次世界大战后开发了该模型。 该模型因在摩纳哥的一个赌博城市而得名，这是由于赌博中的机会和随机遭遇。

The Monte Carlo simulation is a probability model which generates random variables used in tandem with economic factors (expected return, volatility — in the case of a portfolio of funds) to predict outcomes over a large spectrum. While not the most accurate, the model is often used to calculate the risk and uncertainty.

蒙特卡洛模拟是一个概率模型，该模型生成与经济因素(预期收益，波动率—在基金组合的情况下)串联使用的随机变量，以预测大范围的结果。 虽然不是最准确，但该模型通常用于计算风险和不确定性。

We will now use the Monte Carlo simulation to generate a set of predicted returns for our portfolio of assets which will help us to find out the VaR of our investments.

现在，我们将使用蒙特卡洛模拟为资产组合生成一组预测收益，这将有助于我们找出投资的风险价值。

用Python计算VaR (Calculating VaR in Python)

We will first set up the notebook by importing the required libraries and functions

我们将首先通过导入所需的库和函数来设置笔记本

#Importing all required libraries#Created by Sanket Karveimport matplotlib.pyplot as pltimport numpy as npimport pandas as pdimport pandas_datareader as webfrom matplotlib.ticker import FuncFormatter!pip install PyPortfolioOpt#Installing the Portfolio Optimzation Libraryfrom pypfopt.efficient_frontier import EfficientFrontierfrom pypfopt import risk_modelsfrom pypfopt import expected_returnsfrom matplotlib.ticker import FuncFormatter

For the purposes of our project, I have considered the ‘FAANG’ stocks for the last two years.

为了我们的项目目的，我考虑了过去两年的“ FAANG”库存。

tickers = ['GOOGL','FB','AAPL','NFLX','AMZN']thelen = len(tickers)price_data = []for ticker in range(thelen):   prices = web.DataReader(tickers[ticker], start='2018-06-20', end = '2020-06-20', data_source='yahoo')   price_data.append(prices[['Adj Close']])df_stocks = pd.concat(price_data, axis=1)df_stocks.columns=tickersdf_stocks.tail()

For the next step, we will calculated the portfolio weights of each asset. I have done this by using the asset weights calculated for achieving the maximum Sharpe Ratio. I have posted the snippets of the code for the calculation below.

下一步，我们将计算每种资产的投资组合权重。 我通过使用为实现最大夏普比率而计算的资产权重来完成此任务。 我在下面发布了用于计算的代码段。

#Annualized Returnmu = expected_returns.mean_historical_return(df_stocks)#Sample Variance of PortfolioSigma = risk_models.sample_cov(df_stocks)#Max Sharpe Ratio - Tangent to the EFfrom pypfopt import objective_functions, base_optimizeref = EfficientFrontier(mu, Sigma, weight_bounds=(0,1)) #weight bounds in negative allows shorting of stockssharpe_pfolio=ef.max_sharpe() #May use add objective to ensure minimum zero weighting to individual stockssharpe_pwt=ef.clean_weights()print(sharpe_pwt)

The asset weights will be used to calculate the expected portfolio return.

资产权重将用于计算预期的投资组合收益。

#VaR Calculationticker_rx2 = []#Convert Dictionary to list of asset weights from Max Sharpe Ratio Portfoliosh_wt = list(sharpe_pwt.values())sh_wt=np.array(sh_wt)

Now, we will convert the stock prices of the portfolio to a cumulative return, which may also be considered as the holding period returns (HPR)for this project.

现在，我们将把投资组合的股票价格转换为累积回报，也可以将其视为该项目的持有期回报(HPR)。

for a in range(thelen):  ticker_rx = df_stocks[[tickers[a]]].pct_change()  ticker_rx = (ticker_rx+1).cumprod()  ticker_rx2.append(ticker_rx[[tickers[a]]])ticker_final = pd.concat(ticker_rx2,axis=1)ticker_final

#Plot graph of Cumulative/HPR of all stocksfor i, col in enumerate(ticker_final.columns):  ticker_final[col].plot()plt.title('Cumulative Returns')plt.xticks(rotation=80)plt.legend(ticker_final.columns)#Saving the graph into a JPG fileplt.savefig('CR.png', bbox_inches='tight')

Now, we will pick out the latest HPR of each asset and multiply the returns with the calculated asset weights using the .dot() function.

现在，我们将挑选每种资产的最新HPR，然后使用.dot()函数将收益乘以计算出的资产权重。

#Taking Latest Values of Returnpret = []pre1 = []price =[]for x in range(thelen):  pret.append(ticker_final.iloc[[-1],[x]])  price.append((df_stocks.iloc[[-1],[x]]))pre1 = pd.concat(pret,axis=1)pre1 = np.array(pre1)price = pd.concat(price,axis=1)varsigma = pre1.std()ex_rtn=pre1.dot(sh_wt)print('The weighted expected portfolio return for selected time period is'+ str(ex_rtn))#ex_rtn = (ex_rtn)**0.5-(1) #Annualizing the cumulative return (will not affect outcome)price=price.dot(sh_wt) #Calculating weighted valueprint(ex_rtn, varsigma,price)

Having calculated the expected portfolio return and the volatility (standard deviation of the expected returns), we will set up and run the Monte Carlo simulation. I have used a time of 1440 (no of minutes in a day) with 10,000 simulation runs. The time-steps may be changed per requirement. I have used a 95% confidence interval.

在计算了预期投资组合收益和波动率(预期收益的标准偏差)之后，我们将建立并运行蒙特卡洛模拟。 我使用1440次(一天中没有分钟)的时间进行10,000次模拟运行。 时间步长可以根据要求进行更改。 我使用了95％的置信区间。

from scipy.stats import normimport mathTime=1440 #No of days(steps or trading days in this case)lt_price=[]final_res=[]for i in range(10000): #10000 runs of simulation  daily_return=                     (np.random.normal(ex_rtn/Time,varsigma/math.sqrt(Time),Time))  plt.plot(daily_returns)plt.axhline(np.percentile(daily_returns,5), color='r', linestyle='dashed', linewidth=1)plt.axhline(np.percentile(daily_returns,95), color='g', linestyle='dashed', linewidth=1)plt.axhline(np.mean(daily_returns), color='b', linestyle='solid', linewidth=1)plt.show()

Visualizing the distribution plot of the returns presents us with the following chart

可视化收益分布图可以为我们提供以下图表

plt.hist(daily_returns,bins=15)plt.axvline(np.percentile(daily_returns,5), color='r', linestyle='dashed', linewidth=2)plt.axvline(np.percentile(daily_returns,95), color='r', linestyle='dashed', linewidth=2)plt.show()

Printing the exact values at both the upper limit and lower limit and assuming our portfolio value to be $1000, we will calculated an estimate of the amount of funds which should be kept to cover for our minimum losses.

打印上限和下限的确切值，并假设我们的投资组合价值为$ 1000，我们将计算出应保留的资金估计额，以弥补我们的最低损失。

print(np.percentile(daily_returns,5),np.percentile(daily_returns,95)) #VaR - Minimum loss of 5.7% at a 5% probability, also a gain can be higher than 15% with a 5 % probabilitypvalue = 1000 #portfolio valueprint('$Amount required to cover minimum losses for one day is ' + str(pvalue* - np.percentile(daily_returns,5)))

The resulting amount will signify the dollar amount required to cover your losses per day. The result can also be interpreted as the minimum losses that your portfolio will face with a 5% probability.

所得金额将表示每天弥补您的损失所需的美元金额。 结果也可以解释为您的投资组合将以5％的概率面临的最小损失。

结论 (Conclusion)

The method above has shown how we can calculate the Value at Risk (VaR) for our portfolio. For a refresher on calculating a portfolio for a certain amount of investment using the Modern Portfolio Thoery (MPT), will help to consolidate your understanding of portfolio analysis and optimization. Finally, the VaR, in tandem with Monte Carlo simulation model, may also be used to predict losses and gains via share prices. This can be done by multiplying the daily return values generated with the final price of the respective ticker.

上面的方法说明了我们如何计算投资组合的风险价值(VaR)。 对于使用现代投资组合花絮(MPT)计算一定数量投资的投资组合的复习，将有助于巩固您对投资组合分析和优化的理解。 最后，VaR与蒙特卡洛模拟模型相结合，还可用于通过股价预测损失和收益。 这可以通过将产生的每日回报值乘以相应股票的最终价格来完成。

All views expressed are my own. This article is not to be treated as expert investment advise.

所表达的所有观点均为我自己的观点。 本文不应被视为专家投资建议。

Feel free to reach out to me on LinkedIn | Twitter and drop me a message

随意接触到我的 LinkedIn | Twitter ，给我留言