Value at Risk

Based on a probability distribution, Value at Risk (VaR) quantifies the expected loss under extreme market conditions. It measures the potential loss in value of a risky asset or portfolio over a specified period for a given confidence interval, typically 95% or 99%.

If we assume that returns are independent and identically distributed, then VaR is a quantile of the return distribution. Mathematically, this means that VaR solves the following equation:

Where:
p(x)dx= the probability that the next return will fall between x and x + dx
c = confidence level

StyleADVISOR offers the following two Value at Risk (VaR) options:

  • The ability to normalize the volatility in calculating VaR.
  • The ability to set the VaR confidence level.

Volatility Normalize:

To calculate volatility normalized VaR and CVaR, we transform a manager's return series such that the ith return becomes:

Where:

Once we have the volatility normalized return series, we calculate VaR and CVaR in the normal ways, only using the normalized returns instead of the unnormalized returns. To transform back into real-space at time i, we add  to the VaR or CVaR estimate, and then multiply by .

As a rule of thumb, if you are interested in how much an investment might lose in a typical period over the next several years, leave Volatility Normalize unchecked. Alternatively, if you are interested in how much an investment might lose in the next period alone, check Volatility Normalize and set the Trailing Window Size to a value of 20 or greater.

There is no upper limit to the Trailing Window Size value. However, as the Trailing Window Size value grows, the response to changing market conditions is dampened.

Confidence (%):

To change the VaR cutoff point, ener a new value for Confidence (%). Typical values are 95% and 99%.

Cornish-Fisher Value at Risk:

To calculate a Cornish-Fisher VaR we make the assumption that the return distribution is nearly normal but has a small amount of skewness and kurtosis. In this case, we can calculate VaR by:


Where:

Power Point presentation of Lessons from the Crisis: Benefits & Pitfalls of Value at Risk by our "Math Guy", Dr. David Kirkman, Ph.D., Mathematician. 

Learn more about Value at Risk by reading Understanding Value at Risk and Conditional Value at Risk by Marc Odo, CFA, CAIA, CFP, Director of Applied Research.

Learn more in depth about Value at Risk by reading The Zephyr Implementation of Value at Risk and Conditional Value at Risk by David Kirkman, Ph.D., Mathematician.

 
 

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