Jorion Chapter 17 - SAR

[ami44]

I just read the paragraph in the study notes about the surplus at risk (SaR).

Am I missing something, or is the SaR the same as the VaR of the portfolio?
I mean Surplus = Assets - Liabilities sounds like the Value of the Portfolio to me. Consequently is the SaR the same as the VaR of the portfolio.
Am I not seeing something obvious here, or is Surplus just a redundant name for Value?

 

[ami44]

Upon further reading, I think I got it.

A normal Fond only looks at it's assets and if there is profit it will be payed out to the investors. This fond has no Liabilities to its investors and will base it's VaR calculation on the Value of it's assets.
A pension fund has Liabilities (i.e. it has to pay to it's investors according to some pension plans in the future). So it has to look at the surplus Assets - Liabilities to stay afloat. As I understand it, that's the nuance in meaning of Value at Risk and Surplus at Risk, even though technically of course Assets - Liabilities can be seen as the value of a pension fund.

 

[David Harper CFA FRM]

Hi @ami44

Yes, I think that's basically correct. I think it's key to remember that VaR, as merely a (statistical) quantile, is just a measure of a (potential) loss relative to some value; in many if not most of our cases, it's the loss relative to the asset's current value, which is like saying "relative to an expected change of zero in the current value of the asset."

When we shift from relative VaR to so-called absolute VaR, it becomes a loss relative not to the current value but rather the expected future value; so this is an example of a change in the "relative to" but it's still simple because in most cases this future expected value of the asset is a simple upward drift.

Okay but SaR is a variation that adds complexity because it's now a measure of the potential loss in the surplus which, as you say, has two key random variables: assets and liabilities. My analogy would be tracking error: just as tracking error is a standard deviation in the difference between a portfolio and a benchmark, SaR is concerned with the volatility of the difference between pension fund assets and liabilities. If the liabilities were constant, then SaR arguably reduces to VaR!

Further, this adds a complication that has plagues SaR for years in the syllabus frankly: there are at least two or three ways to measure "loss in surplus" relative to what? to S = 0 such that negative S is a shortfall; or it is a loss relative to current surplus; finally, is it relative to the expected future surplus. So, to my thinking, whereas VaR allows for either relative or absolute, SaR actually allows for three variations: loss relative to S = 0 which is a fully funded pension; loss relative to current S; or loss relative to expected S. I hope that helps,

 

[ami44]

Thanks David for your interesting thoughts about the SAR.

 

[windspiral]

I just read the P2.T8.13. Pension fund risk, and I am not able to post in the answer forum because I have insufficient privileges,could you help?
According to the (The following is quoted from P2.T8.13. Pension fund risk Question 13.2(https://forum.bionicturtle.com/threads/p2-t8-13-pension-fund-risk.5504/)):
13.2. A pension fund invests in a small number of major asset classes. Owing to the Brinson research, the pension fund assumes that "most of the variation in portfolio performance can be attributed to [its policy mix] choice of asset class;" i.e., rather than the selection of individual managers. Further, within each major asset class, the pension fund achieves diversification by allocating to many different investment managers within the asset class. Finally, the correlation between policy-mix VaR and active-management VaR is slightly negative. In percentage (%) terms, which is the most plausible order of the magnitude of the sources of risk, from most risk to least:

a. Asset VaR (most), Active-management VaR, Policy-mix VaR (least)
b. Policy-mix VaR (most), Asset VaR, Active-management VaR (least)
c. Active-management VaR (most), Policy-mix VaR, Asset VaR (least)
d. Active-management VaR (most), Asset VaR, Policy-mix VaR (least)

Due to slightly negative correlation, Why is VaR[R(Asset)] < VaR[R(Policy)]?
Consider that VaR[R(Asset)] = VaR[R(policy mix)] + VaR[R(active manager risk)]

 

[ShaktiRathore]

Hi
[R(Asset)] is combination of return attributed to policy +return due to investment mgr selection ,now VaR[R(policy mix)] is further reduced due to diversification acheived by selection of different no of mgrs for each asset class, if VaR[R(policy mix)] is Var of return due to asset classes selected,further due to diversification(allcn to diff mgrs) within asset class VaR[R(policy mix)] is further reduced to VaR[R(Asset)] so that VaR[R(Asset)]< VaR[R(policy mix)].
Thanks

 

[Nicole Seaman]

@windspiral

I have reset your forum permissions so you should have no further issues posting in the forum.

Thank you,

Nicole

 

[windspiral]

@ShaktiRathore
Thanks for your explanation, I get the point.

@Nicole Manley
Thank you, the reply post box just emerges now.