The essential assumption behind RiskMetrics is that short-term, e.g. daily, changes
in market prices of the fundamental assets can be approximated by a zero-mean
normal distribution. Let vi (t) denote the present market value of the ith fundamental
asset at time t. Define the relative return on this asset over the time interval *t by
ri (t)•[vi (tò*t)ñvi (t)]/vi (t). The relative return is modeled by a zero-mean normal
distribution. We will term the standard deviation of this distribution the volatility,
and denote it by mi (t). Under this model, the absolute return vi (tò*t)ñvi (t) is
normally distributed with zero mean and standard deviation pi (t)óvi (t)mi (t).
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