The Short Term Value At Risk Model Considers Zero Mean Returns. What this means is actually very simple, but has quite a few implications in the assumptions underlying the model.

Why do we use mean returns of Zero ?

Short Term VaR does not take into account returns which might offset losses and this despite the fact that the portfolio might be accumulating income throughout the day (dividends, coupons, etc). 
This is the easiest way to compute VaR and is also the most conservative because our Value-at-Risk will not be offset by returns. 
Regulators and the wide acceptance of the Parametric approach have made this approach a de-facto standard. It also makes perfect sense for a trader who is marking to market his positions on a daily basis.

Why is it more conservative ?
It is more conservative because returns would reduce our losses.
If, in our case the positions had returned, say 50 000 USD, and we had decided to take these returns into account, our VaR would have actually been  900 000 USD, not 1 Mio USD.  ((600 k -50k) =550k*1.645 = approx 900k)

What's the difference between mean zero and mean return models ?

The mean zero framework or stationarity assumptions crops up in different parts of the model:

- The computation of the Returns.
- The computation of Value at Risk. In the simulation methodology (historical &    
   Monte-Carlo) the drift is dropped from the model. In the Parametric square root of time is apllied directly.
- In a conditional correlation framework (see Kupiec) a multivariate regression is performed on the variance-covariance matrix, but the mean return is dropped altogether.





hese are essentially Four hort Term VaR does not take into account returns which might offset losses and this despite the fact that the portfolio might be accumulating income throughout the day (dividends, coupons, etc). 
This is the easiest way to compute VaR and is also the most conservative because our Value-at-Risk will not be offset by returns. 
Regulators and the wide acceptance of the Parametric approach have made this approach a de-facto standard. It also makes perfect sense for a trader who is marking to market his positions on a daily basis.

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