L1 Practice /Some queries

[dthigale]

Hi David,

I have some queries. Hope you /some expert on the Forum could check:

Q5. For solving the DV01, I used your solution for 5.2. Got two CPT PV one as shown by you and the other simply changing (shocking) the yield to 2.49%.

Q6 There is a typo error in the Variance calculations:
9%(120-92)^2 + 42%(100-92)^2+49%(80-92)^2 = 168

Q12: Is it assumption that the contract size is $ 100,000

Q16. Is it okay to use the Portfolio VAR = SQRT (VAR1^2 + VAR2^2 + 2VAR1*VAR2*correl const FORMULA?
I did not get the calculations for diversified VAR. Seems some typo.
I tried solving for Marginal VAR using 2 x 2 matrix but getting Standard dev as 9.08656 ( Portfolio Variance 82.5655) . Could you
show the calculations for Marginal and Comp VAR. Is is expected in Level1 to calculate MVAR /CompVAR?

Q17. I checked z values for 1 = 0.3413 and for 2 = 0.4772 and added them ( .8185) >> how did you get .0228 and .1587?

so far so good.

Thanks.

 

[David Harper CFA FRM]

Hi Dinesh:

Q5. For solving the DV01, I used your solution for 5.2. Got two CPT PV one as shown by you and the other simply changing (shocking) the yield to 2.49%.
See http://forum.bionicturtle.com/viewthread/2493/
(GARP's 5.1 formula source does contain an error; see the bold at link for my revision)
Yes, I agree it is valid to find DV01 by shocking duration.

Q6 There is a typo error in the Variance calculations:
9%(120-92)^2 + 42%(100-92)^2+49%(80-92)^2 = 168
Yes, agreed, we lost the raise powers. Thank you, fixed @ http://forum.bionicturtle.com/viewthread/2494/

Q12: Is it assumption that the contract size is $ 100,000
I don't think this is needed for Q12, but YES contract size for Treasury futures bond is $100,000.
See http://www.cmegroup.com/trading/interest-rates/us-treasury/10-year-us-treasury-note_contract_specifications.html
(i.e., 5 year and above have face value of $100,000)

Q16. Is it okay to use the Portfolio VAR = SQRT (VAR1^2 + VAR2^2 + 2VAR1*VAR2*correl const FORMULA?
I did not get the calculations for diversified VAR. Seems some typo.
I tried solving for Marginal VAR using 2 x 2 matrix but getting Standard dev as 9.08656 ( Portfolio Variance 82.5655) . Could you
show the calculations for Marginal and Comp VAR. Is is expected in Level1 to calculate MVAR /CompVAR?


Yes, it is absolutely good to use that formula. I just added to the answer @ http://forum.bionicturtle.com/viewthread/2504/
Diversified Portfolio VaR = SQRT[ Individual VaR(A)^2 + Individual VaR(B) ^ 2 + Individual VaR(A)*Individual VaR(B)*correlation ];
In this case, Individual VaR(A) = $25*5%*1.645 * SQRT(10/25) = $0.41
Individual VaR(B) = $75*12%*1.645 * SQRT(10/250) =$2.96
and diversified Portfolio VaR = SQRT [$0.41^2 + $2.96^2 + 2*0.41*2.96*0.25] = $3.0893

Please see http://forum.bionicturtle.com/viewthread/2504/ for the marginal/component VaR calcs.

Re: is expected in Level1 to calculate MVAR /CompVAR?
No, these are L2 (part 2) concepts!

Q17. I checked z values for 1 = 0.3413 and for 2 = 0.4772 and added them ( .8185) >> how did you get .0228 and .1587?
z = (82.5 - 100)/17.5 = -1 and NORMSDIST(-1) = 0.1587
z = (135 - 100)/17.5 = +2 and NORMSDIST(2) = 0.97725; i.e., as a CDF, 97.7% is "left of +2 normal deviates"
P [-1 < X < 2 ] = 0.97725 - 0.1586 = 0.8185
... please note i don't write the .1 question but rather the additional queries. This question is odd b/c it requires knowing the CDFs (?!) and the explain is a little odd, i agree with you: the 0.0228 is NORMSDIST(-2) so you get the same answer

Thanks, David

 

[dthigale]

Hi David,

Thanks you so much for replying the queries so quickly.

Your adds to the questions are so thoughtful. You have taken some extraordinary efforts..going thru those questions seems like a going through..thorough churning or crystallization process!!

Thanks a ton David.

-D.

 

[dthigale]

Hi David,

One more (silly) question:

I tried using skew = E(X-AverageX) cube / cube of standar dev formula

Is average X = 92 that is Mean, then what should be the value of X.

With reverse engg I get value of X = 103.

Same I tried with Kurtosis and I get value of X = 108.

Sorry for bothering but it would be helpful if you show the calcs.

-D

 

[David Harper CFA FRM]

Hi Dinesh,

Did you see my kurtosis/skew XLS @ http://www.bionicturtle.com/premium/spreadsheet/2.a.2._skew_kurtosis/
also, this practice from Gujarati ilustrates: http://forum.bionicturtle.com/viewthread/1269/

The (X)s are the many observations so I don't think you can extract them (reverse engineer) analytically

the skew numerator is the third moment, you can solve for that, but it's analogous to the variance (2nd moment) so trying to get (X) is akin to extracting Xs from a variance (infinite solutions, i think....)

....David

 

[dthigale]

Hi David,

Fortunaltey I just got it after trying for some time. The Numerator, as you mentioned , the calculations are similar for varinace except we
have to cube it.

Here is what I did:

skew: Numerator = 9% (120-92)^3 + 42% (100-92)^3 + 49% (80-92)^3
= 0.09 (21952) + 0.42 (512) + 0.49 (-1728)
= 1975.68 + 215.04 - 846.72
= 1344
Denominator: = 12.96^3 = 2176.78

skew = 1344 / 2176.78 = 0.6174 !

Sorry for the reverse engineering that I was trying earlier. That was out of conceptual ignorance.

-D