Value-at-Risk is a measure of the maximum potential change in the value of a portfolio, with a given probability, over a pre-set horizon. Value-at-Risk answers the question: how much can I lose with x% probability over a given time horizon?
HedgeOne uses improved analytical methods to calculate Value-at-Risk.
It is well known that the price P of a bond can be approximated by duration and convexity as follows:
P = P(0) - PDdr + PCdrČ/2
Here r is a vector of interest rates, dr is an infinitesimal change, and D and C can be expressed in terms of derivatives of P with respect to r.
In HedgeOne, we replace infinitesimal changes by discrete, "macro" steps, chosen in proportion to the volatility of r. We "stress" the price P at three different levels of r. A quadratic spline can then be drawn through these three values. This curve closely describes the dependence of P on r.
Notice that the same procedure can be carried out when r is replaced by any risk factor affecting P. HedgeOne calculates analogs of duration and convexity for a wide family of risk factors, and combines them in a total Value-at-Risk expression.
We support the following factors in Value-at-Risk.
Interest rate changes at any key rate
Yield curve shape changes
Interest rate volatility
Exchange rate level
Exchange rate volatility
Equity level
Equity volatility
Commodity level
Commodity volatility
HedgeOne performs a stress test for each factor, then calculates Value-at-Risk by combining information from all stress tests. The distribution of the price value P can be analyzed from the volatilities and correlations of the risk factors, which are available from JP Morgan’s RiskMetrics™. Total Value-at-Risk is then broken down into Interest Rate Risk, Exchange Rate Risk and Equity Risk.
HedgeOne has the ability to handle mixed-type portfolios.
Key Benefits
Composite Value-at-Risk
Stress Testing
Quadratic Approximation
Draws on Market-Standard JP Morgan RiskMetrics data