Ralph Vince - Portfolio Mathematics

ch02 JWBK035-Vince February 12, 2007 6:50 Char Count= 0

64 HANDBOOK OF PORTFOLIO MATHEMATICS

FIGURE 2.11 Two-tailed probability of an event’s being beyond 2 sigma

probabilities of an event in a Normally distributed random process falling

outsideof 2 standard units is:

Two-tailed probability (outside)=(1−.9772499478)∗ 2

=. 02275005216 ∗ 2

=. 04550010432

Finally, we come to the case where we want to find what the

probabilities (areas under the N′(Z) curve) are for two different values

of Z.

Suppose we want to find the area under the N′(Z) curve between

−1 standard unit and+2 standard units. There are a couple of ways to

accomplish this. To begin with, we can compute the probability of not

exceeding+2 standard units with Equation (2.21), and from this we

can subtract the probability of not exceeding−1 standard units (see

Figure 2.12). This would give us:

. 9772499478 −. 1586552595 =. 8185946883

Another way we could have performed this is to take the number 1,

representing the entire area under the curve, and then subtract the sum of