Hull Book: Typo on page 282 (chapter on Black-Scholes Merton Model)

[sridhar]

On page 282 of the 6th Edition of the Hull book, he says, in the context of Example 13.1

"...There is a 95% probability that a normally distributed variable has a value within 1.96 SD of the mean..."

When I try this in Excel using NORMSINV(0.95), I get the Z value as 1.65 and not 1.96.

Only when I do NORMSINV(0.975) do I get 1.96

Is there a typo in the book or am I wrong somewhere....Methinks that the text should have said:

"Hence with 97.5% confidence...."

if the rest of the narrative is to be construed as a correct.

 

[David Harper CFA FRM]

he's right, but you still get credit for a spotting a classic bear trap

difference between confidence interval (implies two tail) and confidence level (implies one tail, what we want for VaR). NORMSINV() is one tail. But in your example, he is bounding the future average with an interval (up or down).

he could have said, 95% confidence that price will be LESS THAN $x. Then, he could use 1.65. 1.65 is still our "magic" number most of the time b/c VaR is always a C.L. that cares not about the upside tail.

or if you want to match his interval, as you found, you really need =NORMSINV(1 - 50% * [1 - confidence]).

David

 

[sridhar]

David:

Great explanation. Thanks. All clear. BTW, the Credit Risk Episode 8 newsletter -- the answers links for each of the questions -- do not have the answer. It takes me to a forum page which restates the question without the answer. Am I missing something?

--sridhar

 

[David Harper CFA FRM]

Sridhar,

I wanted to give you time to work out yourself

Just kidding. In seriousness, I sometimes take a day/two to post the answers since I really do write them up freshly (I wrote them Sunday PM) as questions i think are worth thinking about. Then, i have to answer them...

David

 

[sridhar]

Got ya! Over the next two months, there will be several weeks, where I will be away from any sort of Internet access. Which means, hopefully, I can focus on your FRM materials. This is why I like to archive your newsletters -- including the answers -- to my laptop. (Remember, a while ago., I had asked you about making the newsletter available in a downloadable format?)

On a related note, do you have a zip file that has ALL the XLS versions of your EditGrids from the FRM 2008 season?