Estimating Tail Risk Dakota Wixom Quantitative Analyst | - - PowerPoint PPT Presentation

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Estimating Tail Risk Dakota Wixom Quantitative Analyst | - - PowerPoint PPT Presentation

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DataCamp Introduction to Portfolio Risk Management in Python INTRODUCTION TO PORTFOLIO RISK MANAGEMENT IN PYTHON Estimating Tail Risk Dakota Wixom Quantitative Analyst | QuantCourse.com DataCamp Introduction to Portfolio Risk Management in

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DataCamp Introduction to Portfolio Risk Management in Python

Estimating Tail Risk

INTRODUCTION TO PORTFOLIO RISK MANAGEMENT IN PYTHON

Dakota Wixom

Quantitative Analyst | QuantCourse.com

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DataCamp Introduction to Portfolio Risk Management in Python

Estimating Tail Risk

Tail risk is the risk of extreme investment outcomes, most notably on the negative side of a distribution. Historical Drawdown Value at Risk Conditional Value at Risk Monte-Carlo Simulation

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DataCamp Introduction to Portfolio Risk Management in Python

Historical Drawdown

Drawdown is the percentage loss from the highest cumulative historical point. Drawdown = − 1 r : Cumulative return at time t RM : Running maximum

HISTORICAL DRAWDOWN OF THE USO OIL ETF

RM rt

t

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DataCamp Introduction to Portfolio Risk Management in Python

Historical Drawdown in Python

Assuming cum_rets is an np.array of cumulative returns over time

In [1]: running_max = np.maximum.accumulate(cum_rets) In [2]: running_max[running_max < 1] = 1 In [3]: drawdown = (cum_rets)/running_max - 1 In [4]: drawdown Out [4]: Date Return 2007-01-03 -0.042636 2007-01-04 -0.081589 2007-01-05 -0.073062

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DataCamp Introduction to Portfolio Risk Management in Python

Historical Value at Risk

Value at Risk, or VaR, is a threshold with a given confidence level that losses will not (or more accurately, will not historically) exceed a certain level. VaR is commonly quoted with quantiles such as 95, 99, and 99.9. Example: VaR(95) = -2.3% 95% certain that losses will not exceed

  • 2.3% in a given day based on historical

values.

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DataCamp Introduction to Portfolio Risk Management in Python

Historical Value at Risk in Python

In [1]: var_level = 95 In [2]: var_95 = np.percentile(StockReturns, 100 - var_level) In [3]: var_95 Out [3]: -.023

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DataCamp Introduction to Portfolio Risk Management in Python

Historical Expected Shortfall

Conditional Value at Risk, or CVaR, is an estimate of expected losses sustained in the worst 1 - x% of scenarios. CVaR is commonly quoted with quantiles such as 95, 99, and 99.9. Example: CVaR(95) = -2.5% In the worst 5% of cases, losses were

  • n average exceed -2.5% historically.
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DataCamp Introduction to Portfolio Risk Management in Python

Historical Expected Shortfall in Python

Assuming you have an object StockReturns which is a time series of stock returns. To calculate historical CVaR(95):

In [1]: var_level = 95 In [2]: var_95 = np.percentile(StockReturns, 100 - var_level) In [3]: cvar_95 = StockReturns[StockReturns <= var_95].mean() In [3]: cvar_95 Out [3]: -.025

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DataCamp Introduction to Portfolio Risk Management in Python

Let's practice!

INTRODUCTION TO PORTFOLIO RISK MANAGEMENT IN PYTHON

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DataCamp Introduction to Portfolio Risk Management in Python

VaR Extensions

INTRODUCTION TO PORTFOLIO RISK MANAGEMENT IN PYTHON

Dakota Wixom

Quantitative Analyst | QuantCourse.com

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DataCamp Introduction to Portfolio Risk Management in Python

VaR Quantiles

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DataCamp Introduction to Portfolio Risk Management in Python

Empirical Assumptions

Empirical Historical values are those that have actually occurred. How do you simulate the probability of a value that has never occured historically before? Sample from a probability distribution

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DataCamp Introduction to Portfolio Risk Management in Python

Parametric VaR in Python

Assuming you have an object StockReturns which is a time series of stock returns. To calculate parametric VaR(95):

In [1]: mu = np.mean(StockReturns) In [2]: std = np.std(StockReturns) In [3]: confidence_level = 0.05 In [4]: VaR = norm.ppf(confidence_level, mu, std) In [5]: VaR Out [5]: -0.0235

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DataCamp Introduction to Portfolio Risk Management in Python

Scaling Risk

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DataCamp Introduction to Portfolio Risk Management in Python

Scaling Risk in Python

Assuming you have a one-day estimate of VaR(95) var_95. To estimate 5-day VaR(95):

In [1]: forecast_days = 5 In [2]: forecast_var95_5day = var_95*np.sqrt(forecast_days) In [3]: forecast_var95_5day Out [3]: -0.0525

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DataCamp Introduction to Portfolio Risk Management in Python

Let's practice!

INTRODUCTION TO PORTFOLIO RISK MANAGEMENT IN PYTHON

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DataCamp Introduction to Portfolio Risk Management in Python

Random Walks

INTRODUCTION TO PORTFOLIO RISK MANAGEMENT IN PYTHON

Dakota Wixom

Quantitative Analyst | QuantCourse.com

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DataCamp Introduction to Portfolio Risk Management in Python

Random Walks

Most often, random walks in finance are rather simple compared to physics:

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DataCamp Introduction to Portfolio Risk Management in Python

Random Walks in Python

Assuming you have an object StockReturns which is a time series of stock returns. To simulate a random walk:

In [1]: mu = np.mean(StockReturns) In [2]: std = np.std(StockReturns) In [3]: T = 252 In [4]: S0 = 10 In [5]: rand_rets = np.random.normal(mu,std,T) + 1 In [6]: forecasted_values = S0*(rand_rets.cumprod()) In [7]: forecasted_values Out [7]: array([ 9.71274884, 9.72536923, 10.03605425 ... ])

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DataCamp Introduction to Portfolio Risk Management in Python

Monte Carlo Simulations

A series of Monte Carlo simulations of a single asset starting at stock price $10 at

  • T0. Forecasted for 1 year (252 trading days along the x-axis):
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DataCamp Introduction to Portfolio Risk Management in Python

Monte Carlo VaR in Python

To calculate the VaR(95) of 100 Monte Carlo simulations:

In [1]: mu = 0.0005 In [2]: vol = 0.001 In [3]: T = 252 In [4]: sim_returns = [] In [5]: for i in range(100): In [6]: rand_rets = np.random.normal(mu,vol,T) In [7]: sim_returns.append(rand_rets) In [8]: var_95 = np.percentile(sim_returns, 5) In [9]: var_95 Out [9]: -0.028

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DataCamp Introduction to Portfolio Risk Management in Python

Let's practice!

INTRODUCTION TO PORTFOLIO RISK MANAGEMENT IN PYTHON

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DataCamp Introduction to Portfolio Risk Management in Python

Understanding Risk

INTRODUCTION TO PORTFOLIO RISK MANAGEMENT IN PYTHON

Dakota Wixom

Quantitative Analyst | QuantCourse.com

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DataCamp Introduction to Portfolio Risk Management in Python

Summary

Moments and Distributions Portfolio Composition Correlation and Co-Variance Markowitz Optimization Beta & CAPM FAMA French Factor Modeling Alpha Value at Risk Monte Carlo Simulations

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DataCamp Introduction to Portfolio Risk Management in Python

Good luck!

INTRODUCTION TO PORTFOLIO RISK MANAGEMENT IN PYTHON