Calculate Reverse Engineered Volatility

You can calculate the SRRI for Total and Absolute Return funds by reverse engineering the Value at Risk (VaR) based Volatility under the assumption of risk neutrality. The annualization and calculation is based on a 12 month risk free rate input.

For example, for a 99% confidence level VaR with a holding period equal to a number of time intervals (T) of 1/m years, the relevant volatility  is calculated by reverse engineering the following formula:

where:

and  is the risk free rate valid at the time of the calculation, using 365 days for annualization using the following annualization calculation:

((12 month risk free rate/100)+1)^(1/365)

The end date defined in the report profile is the effective date used in reverse engineered volatility calculation.

To reverse engineer the VaR Volatility equation:

1. Starting with the original equation,
   
   

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   subtract VaR from both sides of the equation, multiply T through the first term, and rearrange the order of items in various terms.
   
   

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2. Define the following variables:
   
   

3. Substitute a, b, and c into the latest equation. The equation is reduced to a standard quadratic equation:
   
   

   
   This equation has two solutions, called roots, for

    that are given by the quadratic formula:
   
   

4. Solve for

The reverse engineered solution to   is the positive root of the quadratic formula. The algorithm uses the assumption that the risk free rates are not already de-annualized. This is done during the calculation process using a default of 365 days for annualization. The calculation is based on the inputs previously discussed, along with the number of trading days.