Hi David,
When is 1 std.deviation 68% area and when it is 84% area and so on for other std.deviation multiples? Which are numbers in this regard that we have to memorize like 1.96 S.D.=95%, etc.?

Regards,
Mudaltiru.

Hi Mudaltiru,

GARP has told me that any distribution lookups will be provided so they do not need to be memorized. Based on this guidance (FYI, prior threads on this here and here), my advice here is:

You should memorize the following:

1. In regard to a one-tailed test of NORMAL distribution

N(-1.645 or -1.65) = 5%
N(-2.33 or -2.326) = 1%

2. In regard to either a NORMAL or a STUDENT’S T DISTRIBUTION, a test statistic materially greater than 2.x is generally significant. Where test stat = (sample mean - hypothesized mean)/[(standard error)*SQRT(n)].

#1 above because 95% confidence (5% significance) and 99% confidence (1% significance) are likely the only VaR confidences against normality that you will encounter (please note we encounter other confidences in the FRM, namely 99.9% for non-normal credit and non-normal operational risk Basel II and 99.98% in DB LDA. But our normal VaRs are likely to only include 95% and 99%). #2 above because if the test stat is > 2, you probably won’t need a lookup table.

Probably you do *not* need to memorize the following, but as they *might* be needed I recommend them:

N(-1) = 15.9% because +/- 1 standard deviation is 68% area under curve
N(-2) = 2.3% because +/- 2 standard deviations is 95.4% area under curve
N(-3) = 0.3% because +/- 3 standard deviations is 99.7% area under curve

Finally, please don’t let memorization interfere with intuition about the symmetrical distributions we study (normal, student’s t). A question may give you N() CDFs and want you to use the symmetry of the distribution to get an answer.

Here is a good example from last year, of a question that does not require memorization but does require intuition.

David