NO.PZ202112010200002202
问题如下:
What is the approximate VaR for the bond position at a 99% confidence interval (equal to 2.33 standard deviations) for one month (with 21 trading days) if daily yield volatility is 0.015% and returns are normally distributed?
选项:
A.$1,234,105
$2,468,210
$5,413,133
解释:
A is correct. The expected change in yield based on a 99% confidence interval for the bond and a 0.015% yield volatility over 21 trading days equals 16 bps = (0.015% × 2.33 standard deviations × √21).
We can quantify the bond’s market value change by multiplying the familiar (–ModDur × ∆Yield) expression by bond price to get $1,234,105 = ($75 million × 1.040175 ⨯ (–9.887 × .0016)).
“根据Var的公式,|μmonthly-2.33σmonthly|,这个公式得到是以μ为原点,向左、向右的最大值,向左得到的是最大亏损,向右得到的是最大收益。
如果已知y的μ和σ,-2.33σmonthly得到就是△y取负的最大值,2.33σmonthly得到的就是△y取正的最大值
所以,要用2.33*0.015%*21^(1/2)得到△y取正的最大值。 ”
这段话什么意思?什么取负最大值,取正最大值,到底本题的VaR算出来是+0.0016还是-0.0016?