|Simulation|Modified VaR| Correlation| Regression| Cholesky Matrix| Distribution| Diversification|
|Skewness| Sharpe| Fund of Funds |4 Moment CAPM| Stress Test| Coskewness| Black-Litterman|
According to dictionary, Stress Testing is a form of testing used to determine the stability of a given system or entity.  In our case, finance, Stress Test allows to measure how much return an asset or a portfolio would deliver in case of dramatic change in one or several economic factors like S&P500, EUROSTOXX50, volatility VIX, 3m T-bill, 10Y T-note, Inflation, Aaa Yield or Baa Yield. For examples:

- What happens if equity markets crash by more than -30% in April 2011?
- What happens if 10Y interest rates go up by at least +1% in March 2011?
- What happens if oil prices rise by 100% in 2011, inflation increases by +3% and gold collapses by -50%, altogether?

Some software provide the asset stress return with some probabilities, use simulation or use copula to describe the relation between assets.  Other software are so complex that it takes two hours to stress test one asset or they do not allow the stress test of several economic factors or they do not stress the correlation between the economic factors (i.e. coefficients correlation between economic factors increase when the market crashes).  A good stress test model should be transparent to the user, easy to explain to a client, allow to stress test an asset which has never had an historical negative return and correctly forecast future asset stress returns.  

The following model computes an asset or portfolio stressed return with a scenario on multiple economic factors and on their respective correlation coefficients:

with 
the expected beta between the asset and the factor, using the expected correlation between the economic factors Fi equal to:

and the most significant factor between the asset and each factor Fi defined as:


Computing the stress test for a hedge fund (10 years track record, max historical monthly loss of -3.82%) using the above model would give the following results:

1) The green cells represent the economic factors' assumptions



2) The hedge fund return (i.e.-26.07%) over one month is shown in the last column, assuming the above assumptions are realized:



3) The hedge fund return (i.e.-58.47%) over one month is shown in the last column, assuming the above assumptions are realized and the economic factors' historical correlation coefficients are increased:



The Stress Test model is available in AlternativeSoft platform.