Topic: Value- At- Risk
In today’s capital market, there are lots of investment opportunities, and higher risks accompany an often greater chance of return. It is increasingly important for companies to properly measure their risks and set tactics to eliminate avoidable risks as well as gauge the amount of cash reserves needed for unexpected loss events. After the consequential financial crisis which occurred in the years 2007-2008, many companies across the world started to pay more attention to ways which they can manage risks in case of unforeseen events. As a result, companies adopted the concept of Value at Risk (VaR), which is a statistical measurement for risks in companies or portfolios. Banks and firms use VaR on a daily/weekly basis to assess the amount of money needed to set aside to cover them in case they get into losses.
Value at Risk is a percentage-based measurement. It is often denoted as VaR. This is the smallest loss which is exceeded with probability at most (). The following methods are used to derive the VaR, i.e. historical, the variance-covariance and Monte-carlo simulation methods. A more straightforward explanation using historical figures would be:
Suppose Bob, an investor, bought one share of Tesla stock 100 days ago at $300 per share. He wants to invest more in this stock but is indefinite about whether the probability of losing money is high. Therefore, he recorded the daily prices of the stock in the past 100 days and calculated the profit/loss using –1 on a daily basis (St is the stock price at day t). The histogram below is the Loss/Profit generated by one share of Tesla stock over 100 days.
We are now sorting them according to ascending order.
Now, suppose Bob wants to know the most severe loss that can occur 95% of the time, he can pick the fifth-highest loss start from the left from the above plot. That is -41.26, the VaR0.95. This also means there is a 5% chance the loss would be greater than $41.26. Value at Risk can be converted to a weekly VaR or even yearly VaR using the equation J-days = 1-day.
The story above demonstrates a general idea of Value at Risk using the historical simulation method. This approach uses data collected from the past to predict risks in the future. However, there are also downsides about using VaR to measure risks, since it gives no information about the severity of losses occurring with probability , and it becomes difficult to estimate for large . Yet, VaR is still widely used in risk management, and it is easy to communicate. Moreover, there is another type of Value at Risk that measures the severity of losses called Conditional VaR. CVaR estimates the weighted average of extreme losses. People usually call it expected shortfall. CVaR gives investors an idea of how much on average would their losses be if the worst-case scenario with probability occurs. CVaR is calculated using the equation below:
Where L is the loss, and u is a variable . One important property of CVaR is that it’s always greater than or equal to VaR. Yet, comparing to VaR, CVaR is more difficult to estimate.
In conclusion, Value-At-Risk is still one of the most popular measurements of risk in the world since it predicts the highest possible loss expected of an investment within a certain timeframe and even predicts a specified level of confidence. Commercial banks, large companies and investment banks use it to assess risks, evaluate the worthiness of an investment or determine how much capital reserves are needed.
Works cited.
Harper, David R. “An Introduction to Value at Risk (VAR).” Investopedia, Investopedia, 30 Jan. 2020, www.investopedia.com/articles/04/092904.asp.