The standard error is
2000
975
.
0
025
.
0
)
(
1
u
q
f
where
f
(
q
) is an estimate of the loss probability density at the VaR point. In this case the 0.975
point on the approximating normal distribution is NORMINV(0.975,0,6) = 11.76.
f
(
q
) is
estimated as NORMDIST(11.76,0,6,FALSE) = 0.0097. The standard error is therefore
358
.
0
2000
975
.
0
025
.
0
0097
.
0
1
u
A 99% confidence interval for the VaR is 13
í
2.576 × 0.358 to 13 + 2.576 × 0.358 or
12.077 to 13.923.
13.13. (Spreadsheet Provided)
Suppose that the portfolio considered in Section 13.1 has (in $000s) 3,000 in DJIA, 3,000 in
FTSE, 1,000 in CAC 40, and 3,000 in Nikkei 225. Use the spreadsheet on the author’s web site
to calculate what difference this makes to
(a) The one-day 99% VaR and ES that are calculated in Section 13.1.
(b) The one-day 99% VaR and ES that are calculated using the weighting-of observations
procedure in Section 13.3 and
O
=0.995
(a)
VaR is
$230,785; ES is $324,857 (see worksheets 1 to 3)
(b)
VaR is $262,456; ES is $413,774 (see worksheets 4 and 5)
