When building a portfolio of investments, investors and traders strive to minimize risk and potential losses. Traditional practices, such as diversification, help mitigate portfolio risk.
In order to actually reduce the risk of the portfolio and achieve the points at which the trader is satisfied with a particular loss, the trader must first understand what the potential loss of the portfolio is and make adjustments. There are various statistical tools that help traders and investors determine the risk of their portfolio, but one of the most common is Value at Risk (VaR).
- Traders and investors aim to minimize the risks and potential losses of their trading portfolio.
- One of the most common statistical tools to help determine risk and potential loss is value at risk (VaR).
- VaR measures the potential loss of a portfolio within a specified time frame with some confidence.
- There are two types of risk exposure, linear and non-linear.
- Non-linear derivatives are derivatives whose payoffs change over time, changing their position from the strike price to the spot price.
- Non-linear derivatives are accompanied by non-linear risk exposures with a distorted distribution of returns.
- The returns of the nonlinear derivatives are not normally distributed, so the standard VaR model does not work and you should use another model, such as Monte Carlo VaR, instead.
Value at risk (VaR)
Value at risk (VaR) is a statistical risk management method that determines the amount of financial risk associated with a portfolio. Portfolio VaR measures the amount of potential loss over a particular period of time with some confidence. For example, consider a portfolio with a daily value at risk of $ 5 million. With 99% confidence, the worst expected daily loss will not exceed $ 5 million. There is a 1% chance that your portfolio will lose more than $ 5 million on a particular day.
Portfolios generally have two types of risk exposure, linear or non-linear. Non-linear risk arises from non-linear derivatives. The payoff changes over time, and the location of the strike price changes to the spot price.
Derivatives can be either linear or non-linear, depending on the payout profile. It is important to use the appropriate statistical model for a particular type of derivative.
Non-linear risk exposures occur in the VaR calculation of a portfolio of non-linear derivatives. Non-linear derivatives such as options depend on various characteristics such as implied volatility, time to maturity, underlying asset price, and current interest rates.
To use the standard VaR approach, it is difficult to collect historical return data because the optional returns must be conditioned on all characteristics. If you enter all the properties related to the option into the Black-Scholes model or another option pricing model, the nature of the derivative makes the model non-linear. Therefore, the option premium as a function of the payoff curve, or underlying asset price, is non-linear because the option is wasting assets and the corresponding value is not proportional to the input due to the time and volatility part of the model.
The non-linearity of certain derivatives provides non-linear risk exposure to the VaR of the portfolio. The non-linearity can be seen in the plane vanilla call option payoff diagram. The payoff chart has a strong positive convex payoff profile for stock prices before the option expires.
When the call option reaches the point where the option is in-money, the payoff reaches the point where it becomes linear. Conversely, as call options run out of money more and more, the rate at which options lose money decreases until the option premium goes to zero.
If the portfolio contains non-linear derivatives such as options, the distribution of portfolio returns can be positive or negative skew, or high or low kurtosis. Skewness measures the asymmetry of the probability distribution around its mean. Kurtosis measures the distribution around the mean. Higher kurtosis makes the end of the distribution thicker, and lower kurtosis makes the end of the distribution thinner.
Therefore, it is difficult to use the VaR method, which assumes that the returns are normally distributed. Instead, portfolio VaR calculations with non-linear exposures are typically calculated using the Monte Carlo VaR simulation of the optional pricing model for estimating portfolio VaR.
Value at risk (VaR) is a statistical tool that measures the potential loss of a portfolio at a particular time and at a particular level of confidence. The standard VaR approach is not suitable for non-linear derivatives because the returns are not normally distributed. Other VaR approaches, such as Monte Carlo VaR, are suitable for predicting loss measurements with an irregular distribution of returns.