Measuring Market Risk - Reserve Bank of India

MEASURING MARKET RISK 7
2.5 VaR Expressed in Percentage and Other Forms
As seen, VaR is defined in terms of the change/loss in value
of a portfolio. In practice, distribution of return (either percentage
change or continuously-compounded/log-difference 3 ) of the financial
position may actually be modeled and thus, VaR may be estimated
based on percentile of the underlying return distribution. Sometimes
percentiles of return distribution are termed as ‘relative VaR’ (see for
instance, Wong, et al., 2003). On this perception, the VaR for change
in value may be termed as ‘absolute/nominal VaR’.
Thus, the percentile ξ p
corresponding to left-tail probability p of
distribution of k-period percentage change itself is the relative VaR
(expressed in per cent) with specified parameters and corresponding
(absolute) VaR would be [(ξ p
/100)W t
]. Alternatively, if ξ p
represents
the p-percentile for log-return (in per cent), then (absolute) VaR can be
expressed as [{exp(ξ p
/100)-1}W t
]. In our paper, unless otherwise stated,
we use the term VaR to indicate ‘relative VaR’ (expressed in per cent).
2.6 The h-period VaR from 1-period VaR
Another point to be noted relates to the estimation of multiperiod
VaR (i.e. VaR corresponding to multi-period ‘time horizon’,
say h-day). In practice, given probability level ‘p’, 0