Value At Risk – Financial Risk Management in Python

Value at Risk (VaR) is a tool for measuring a portfolio’s risk.

Value at risk (VaR) is a measure of the risk of loss for investments. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day. … For a given portfolio, time horizon, and probability p, the p VaR can be defined informally as the maximum possible loss during that time after we exclude all worse outcomes whose combined probability is at most p. This assumes mark-to-market pricing, and no trading in the portfolio.

For example, if a portfolio of stocks has a one-day 5% VaR of $1 million, that means that there is a 0.05 probability that the portfolio will fall in value by more than $1 million over a one-day period if there is no trading. Informally, a loss of $1 million or more on this portfolio is expected on 1 day out of 20 days (because of 5% probability). Read more

There are basically 3 methods for calculating the VaR [1]

  1. Historical simulation
  2. Variance-covariance approach
  3. Monte Carlo simulation

In this post, we implement the 3rd method, i.e. the Monte Carlo simulation, in Python.  More details of the methodology can be found in Ref [1].

The simulation parameters are as follows,

  • Portfolio value: $1 Million
  • Confidence interval: 95%
  • Time horizon: 1 day
  • Underlying: SPY

We utilize 5-years daily data of SPY retrieved from Yahoo Finance. The picture below shows the VaR returned by the Python program.

Risk Management in Python, Value at Risk in Python

Note that the method presented in this post is suitable for calculating the VaR in a normal market condition. More advanced approaches such as Expected Tail Loss have been developed that can better take into account the tail risk.

References

[1] Hull, John C. (2003). Options, Futures, and Other Derivatives. Prentice-Hall

Further questions

What's your question? Ask it in the discussion forum

Have an answer to the questions below? Post it here or in the forum

LATEST NEWSInvestors are pouring cash into crypto at the highest level in 6 months as risk appetite returns and bitcoin wraps up best January since 2013
Investors are pouring cash into crypto at the highest level in 6 months as risk appetite returns and bitcoin wraps up best January since 2013

Investors made a large shift away from short-bets on bitcoin last week. The token's price has climbed about 40% in January.

Stay up-to-date with the latest news - click here
LATEST NEWSIndia’s Adani Group plans independent audit of group companies- Mint
India’s Adani Group plans independent audit of group companies- Mint

India’s Adani Group is planning to hire one of the “big six” accounting firms to assess its corporate governance and audit practices following allegations of fraud by short-selling firm Hindenburg, Mint newspaper reported on Monday. The audit will be commissioned after the group’s unit, Adani…

Stay up-to-date with the latest news - click here
LATEST NEWSRemote workers are losing ground in the work from home wars: More than half of employees went into the office last week
Remote workers are losing ground in the work from home wars: More than half of employees went into the office last week

Good news for business leaders, not so much for the work from home die hards.

Stay up-to-date with the latest news - click here
LATEST NEWSThe sizzling rally in stocks is nearing its end as investors are about to realize a recession has merely been postponed, JPMorgan says
The sizzling rally in stocks is nearing its end as investors are about to realize a recession has merely been postponed, JPMorgan says

Markets are pricing in a 59% chance of a recession, down from 90% in October. But even that could be too optimistic, JPMorgan said.

Stay up-to-date with the latest news - click here
LATEST NEWSBuzzFeed writers react with a mix of disappointment and excitement at news that AI-generated content is coming to the website
BuzzFeed writers react with a mix of disappointment and excitement at news that AI-generated content is coming to the website

The decision to use tech from ChatGPT maker OpenAI to produce content is part of BuzzFeed's broader cost-cutting strategy in a challenging economy.

Stay up-to-date with the latest news - click here

Leave a Reply