while the standard deviation was 10 basis points (or 0.001). Thus, 1.65is 16.5 basis
points (bp).^11 In other words, over the last year, daily yields on seven-year, zero-
coupon bonds have fluctuated (either positively or negatively) by more than 16.5 bp
10% of the time. Adverse moves in yields are those that decrease the value of the se-
curity (i.e., the yield increases). These occurred 5% of the time, or 1 in 20 days. This
is shown in Exhibit 8.3.
We can now calculate the potential daily price volatility on seven-year discount
bonds using Equation (3) as:

Given this price volatility and the initial market value of the seven-year bond port-
folio, then Equation (2) can be used to calculate the daily earnings at risk as:^12

That is, the potential daily loss on the $1 million position is $10,770 if the one bad
day in 20 occurs tomorrow.

$10,770

 1 $1,000,000 2  1 .01077 2

Daily earnings at risk
 1 Dollar market value of position 2  1 Price volatility 2

.01077 or 1.077%

 1 6.527 2  1 .00165 2

Price volatility
 1 MD 2  1 Potential adverse move in yield 2

8.4 RISKMETRICS MODEL 8 • 7

(^11) RiskMetrics weights more recent observations more highly than past observations (this is called ex-
ponential weighting). This allows more recent news to be more heavily reflected in the calculation of .
Regularcalculations put an equal weight on all past observations.
(^12) Since we are calculating loss, we drop the minus sign here.
Exhibit 8.3. Adverse Rate Move, Seven-Year Rates.
Only a 5% chance
that 7-year rates
will move up by
more than 16.5 basis
points (bp) a day
–16.5 bp –10 bp 0 10 bp +16.5 bp

1.65