N() values... supplied in the Exam or not?

[jyothi1965]

David

sorry for this repetition ( I seem to have read some where, but cant locate), does GARP provide cum. Normal tables in the exam. I recollect you having asked Diane Beebe on this issue.

If you see some of the questions of FRM 2000/1/2, it would require N() calculations, especially the distance to default N(-DD) as also calculating N(D1) and N(d2) for calculating option values. Does the TI BA II plus have this facility

Thanks

Jyothi

 

[David Harper CFA FRM]

Hi Jyothi,

To my knowledge, the TI BA II+ does NOT have the built-in facility to calculate N(d1), the standard cumulative normal distribution [i.e., =NORMSDIST() in Excel]

Yes, Diane B did tell me on the phone that *ANY* needed lookups would be indeed provided; e.g., normal tables, critical-z and critical-t.

Although, I do recommend memorizing the one- and two-tailed z-values at 95% and 99%:

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

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

Two-Tailed Test
N(+/- 1.96) = 5%
N(+/- 2.58) = 1%

I don't think any test question ever asked for N() calculation, with one exception: if the d1 happens to equal -2.33 or -1.645. That could be a test question, because those don't require our calculation. We know that N(-2.33) = 1% and N(-1.65) = 5%.

Thanks,
David

 

[jyothi1965]

Thanks David. the N() calc comes in two places - options and Distance to default. I have seen a question on the latter which again was not the standard values - this set me wondering. As usual I am unable to locate that question in a hurry...

Jyothi

 

[David Harper CFA FRM]

Jyothi -

As you know, the distance to default is the same standard cumulative normal distribution. So, a candidate can't be expected to compute at anything except 5% and 1%. Probably, those questions had a table but it got disconnected from the question in translation...David

UPDATE: I forgot, the candidate should know, in addition to N(1%) and N(5%), these N()s based on the % area under the curve at +/1, 2, and 3 standard deviations:

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

 

[jyothi1965]

David, the Q from FRM 2000 which I was talking of (this is from the CD which is supplied along with the FRM handbook)

The KMV credit risk model generates an Estimated Default Frequency (EDF) based on the distance between the current value of assets and the book value of liabilities. Suppose that the current value of a firm's assets and the book value of its liabilities are $500 million and $300 million, respectively. Assume that the standard deviation of returns on the assets is $100 million, and that the returns on the assets are normally distributed. Assuming a standard Merton Model, what is the approximate EDF for this firm?
a. 0.01
b. 0.015
c. 0.02
d. 0.03


The DD is (500-300)/100 which is 2. So we are supposed to take N(2) Now N(2.33) is .01 (1%), so N(2) would be slightly higher and therefore an educated guess would be .02

correct?

Jyothi

 

[jyothi1965]

A bank has sold $300,000 USD of call options on 100,000 equities. The equities trade at 50, the option strike price is 49, the maturity is in 3 months, volatility is 20%, and the interest rate is 5%. How does it the bank delta hedge? Round to the nearest thousand share.

a. Buy 65,000 shares.
b. Buy 100,000 shares.’
c. Buy 21,000 shares.
d. Sell 100,000 shares.

David another Example from FRM 2001 on the need to refer to N(). In order to caculate the delta hedge, we need to calculate N(d1).

A rough cut way (suggested by Jorion in the handbook) is to say that since the options are ATM, delta is about 0.5, and since the choice is between "a" and "b" we eliminate b and latch on to "a".

Jyothi

 

[David Harper CFA FRM]

Jyothi-

Yikes, I think the first question would be inappropriate to this year's assigned reading. But no matter. I stand corrected, because they do expect you to know these classics (I forgot to list above because they are so common)

+/- 1 standard is about 68%
+/- 2 standard deviations is almost 95.5%
(+/- 3 standard deviations is 99.7%)

So, yes, agreed: DD = -2, and since two distributions cover 95.5%, N(-2) = 1/2 of (1-95.5%) or 2.25% (or 2.25% is what you would eyeball).

Now the reason it would be an (very difficult, probably unfair) question this year: you'd have to know that KMV EDF tends to be higher due to fat tails, but even then, it's a mapping based on historical (empirical) data not a plus up formula. So, the best you could do is get 2.25% and GO HIGHER because EDF > N(). So, the answer should be 3%. But wow this would be unfair question....but regarding the N(), I forgot the common 68%/95.5%/99.7% but you still can eyeball these...it's the jump from N() to EDF() that gives me doubts...

David

 

[David Harper CFA FRM]

Jyothi,

On the second question, i didn't write these lame questions from six years ago You don't NEED to calculate N(d1), you just need to know the call option delta is less than one but probably greater than 0.21. But, it is still a terrible question, that i hope GARP has outgrown. You'd have to do a nontrivial calc to get d1 and then, you'd need a table or spreadsheet to get N(d1) = 0.65. It is really bad multiple question technique to ask for a numerical result but to know it can't be directly solved and rather require the test taker to interpolate based on the incorrect choices... bad question (unless they gave an N() table)...

(I don't teach the overly mechanical 0.5 delta rule. First of all, it's sort of WRONG, even for at-the-money calls. the CALL 0PTION delta ranges from 0 to 1.0. More importantly, it may cause some to miss important ideas about delta: that it is a varying first derivative, bounded by 0 for deep out of money calls and 1.0 for deep in the money calls). I am not fond of defending these old questions, some are clearly not good...I stand by, you don't need to calculate N(), or z-value or t-values because: that is what Diane Beebe told me...

David

 

[jyothi1965]

D

completely agree.

In any case the actual EDF is supposed to be calibrated from thier internal database so in that sense, nobody will really know how to jump from N() to EDF. But for Risk managers seeking to pass the FRM, this will do I suppose!

Thanks as always.

J