###### 7.3.9 Roll-Off Effect

Roll-off effect is an anomaly that arrises with UWMA, EWMA and other types of inference procedures. If a fixed window of historical data is used by an inference procedure, there are periodic drops in calculated value-at-risk resulting from extreme historical data points expiring from the window. Suppose a value-at-risk measure uses UWMA based on 100 trading days of historical market data. Suppose further that 99 days ago markets fell sharply. That extreme behavior would be captured in historical data point ^{–99}* r*. With a 100-day window, value-at-risk would be calculated using historical data {

^{–99}

**, …,**

*r*^{–2}

**,**

*r*^{–1}

**,**

*r*^{0}

**}, and the extreme data point**

*r*^{–99}

*would tend to boost the result. But today’s data point*

**r**^{–99}

*will be tomorrow’s data pint*

**r**^{–100}

*. Today, it is included in the data window, boosting calculated value-at-risk. Tomorrow, it will not be included in the data window, so it will no longer boost calculated value-at-risk. Unless something unexpected happens to offset the effect, tomorrow’s value-at-risk will drop. The extreme data point has “rolled off”, or expired, from the data window.*

**r**Roll-off effect can be disquieting for end users when it causes value-at-risk to drop when nothing has happened to reduce the riskiness of the portfolio. Explaining the technicalities of roll-off effect to end users can undermine confidence in avalue-at-risk system.

Roll-off effect can be mitigated by using more historical data, so each data point is weighted less. EWMA also helps, as it weights data points less immediately prior to their rolling off.

While we have described roll-off effect here in terms of its impact on inference procedures, it has a similar impact with historical simulation (discussed in Chapter 11).