A Division of Windham Capital Management, LLC

Within-Horizon Value at Risk

Asset returns vary throughout an investment time-horizon. Conventional value at risk only estimates total loss only at the end of an investment horizon without accounting for losses throughout the investment horizon. An investor may be very adverse to losses breaching a particular threshold and would therefore be interested in knowing the probability of breaching a certain level of loss at any moment during the horizon.

To estimate within-horizon variability, we use a statistic called “first-passage time probability”, which estimates the probability that an investment will breach a loss within a finite time-horizon. This method estimates the first time a particular path will breach the threshold. Multiple breaches of the threshold are considered only as a single breach.

Within-Horizon Value at Risk gives the worst outcome at a chosen probability from the beginning to any point in time during an investment horizon. There is no closed form (analytic) solution, the Windham Software uses a numerical approach to solve for this statistic.

Category:Understanding the Software -> Exposure to Loss