Surplus at Risk - Jorion Handbook

[notjusttp]

Hi David,

I have a doubt in the way this question has been solved in Jorion Handbook. Request your help on this

6. Company XYZ's pension fund has liabilities of USD 100 million and assets of USD 120 million. The annual growth of the liabilities has an expected value of 5% with 3% volatility. The annual return of the assets has an expected value of 8% with 12% volatility. The correlation between asset return and liability growth is 0.3. What is the 95% surplus-at-risk?

Solution
The expected surplus growth is -100 * 0.05 + 120 * 0.08 = USD 4.6 million. The variance of surplus growth is -100^2 * 0.03^2 + 120^2 * 0.12^2 + 2 * 100 * 120 * 0.3 * 0.03 * 0.12 = USD 190.44 million, and the standard deviation is USD 13.8 million. Therefore, the 95% surplus-at-risk is -1 * (4.6 - 1.645 * 13.8) = USD 18.1 million.

MY DOUBT

I could not quite understand why Surplus is taken just as USD 4.6 Million. It should be actually (Assets - Liabilities) at the end of the year which should be which should be ( 129.6 - 105).

Also i did not get the calculation as to how do we get USD 18.1 Million by this calculation -1 * (4.6 - 1.645 * 13.8) = USD 18.1 million.

Thanks & Rgds
Amit

 

[David Harper CFA FRM]

Hi Amit,

Your doubt is justified, this question is inconsistent with GARP's other given approach. Can you please provide the page number, I cannot find it? I have been telling GARP to standardize on a SaR method for two years b/c it the variations give confusion so I'd like to point to this example specifically ... ) Actually, the problem is compounded, as this one of two SaR variations which is further different from the SaR in Jorion's book! So there are three SaR approaches floating around the FRM)

I entered in the XLS, please see: http://sheet.zoho.com/public/btzoho/oct3-sar
related practice question here: http://forum.bionicturtle.com/viewthread/1424/

so, if we follow the method used elsewhere by GARP, you are exactly correct:
expected surplus = 24.6 (i.e., 129.6 - 105)
and SaR = -24.6 + (13.8 * 1.645) = -$1.9

they are showing the SaR relative from the initial position, so you see, this is definitional; i.e.,

SaR (relative to zero; where VaR represents the pension is underfunded; i.e., an "absolute SaR") = -$1.9 MM
SaR (relative to the expected future position of the surpllus; i.e., a "relative SaR") = $13.8 * 1.645 = $22.7
SaR (relate to the intial surplus position; what they showed here...)

Thanks, David..

Answer I'd get (consistent with your approach):
http://learn.bionicturtle.com/images/forum/oct3_sar.png

 

[notjusttp]

Hi David,

thanks for the prompt reply. the source of this question is the questions which accompany in the CD given alongwith the Jorion handbook in the Investment section...Rgds...Amit

 

[David Harper CFA FRM]

okay, yea, we've found many flaws in the CD questions, thanks, David