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Hi John, am ok with the calculation of the z-score and the normal distribution table but I DON’T understand the 95% and 99% confidence level stuff. in my Emile woolf book one example had N(95%)stddev as 1.645 and the technical article also had this figure for 95% confidence level but in another example the 1.645 had changed to 1.96 ( being 95% divided by 2 = 47.5% or .4750).Simply put it, please how do we derive 95% or 99% confidence level std dev number. Thanks a lot John, really appreciate your help.
I can guess why there is the confusion – it is because normal distribution tables are used for several purposes and it depends whether it is 5% (for 95% confidence) just in one direction or symmetrically in both directions (2.5% at each end).
That may or may not make any sense (its difficult to explain in detail here).However, there are two places in the exam where normal distribution tables are relevant. One is in option pricing and the other is Value at Risk.
95% and 99% confidence levels are only relevant in Value at Risk (if you do have problems with option pricing, then check the free lectures and ask on here separately if necessary).For value at risk, I will try and explain using 95% confidence level. What we are after is calculating how far from the average we can be such there is a 5% chance of being lower.
Because the distribution is symmetrical, there is in total a 50% chance of being below the average, and therefore to get our ‘cut-off’ point we need to be up to 45% below the average (50% – 5%). To find this, we use the tables ‘backwards’ to find what value of z (the number of standard deviations) gives an answer from the tables of 45% (or 0.450). If you check with the tables then you will find that 0.4495 comes from 1.64, and 0.4505 comes from 1.65. That is why we use 1.645 as an approximation (approx. because it isn’t precisely linear).Similarly, for 99%, we look up for 49% (or 0.4900). Working backwards from the tables the nearest is 2.33 standard deviations.
(The other figures you mention are for having 5% or 1% split between both ends of the curve, which means looking up for 2.5% (equivalent to 47.5% or 0.475) or 0.5% (equivalent to 49.5% of 0.495). However this is not relevant in P4.)
I do hope all that does manage to answer your question 🙂
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