In this VAR question, why is z equal to 1.96 here instead of 1.65?

“Suppose that a firm has total assets of $75 million and an annual standard deviation of returns of 17%. What is the level of capital at which there would be a 2.5% chance of insolvency over a one-year period?”

Answer: 75000000*(0-(1.96)*(.17))=$25 Million

Where do they get 1.96 as the z-factor? Isn’t that for a 2-tailed 5% level of significance? How to know if it is 1 tailed or 2 tailed?

95% = 1.65

99% = 2.33

Since it is 97.5% it assumes 1.96 from Z-table. Plug all those formulas and you’ll be set.

btw: VaR should be always one-tailed.

Do we get a Z-table on the exam? 95% and 99% are easy enough to retain, but just wondering if we happen to get a question with a different confidence level.

I don’t think so.

In a 5% 2-tailed test, there is 2.5% probability in each tail. Remember when you were doing a two tailed test you would divide the tail risk probability by 2 and that would be the probability you looked up in the table for your z. Since this is a one tailed test, all of the probability is in one tail

We probably won’t get a z-table.

Schweser says it’s important to know 1.65 for 95% and 2.33 for 99%. But these should be the only numbers you need to know.