Generic Mapping process

[Kavita.bhangdia]

Hi David,

Jorion says :

If current market value not fully allocated to risk factors, then remainder allocated to cash?

Why is this is so?
Is cash is a a risk factor? ( I dont suppose so)..
Then why is the remainder allocated to cash? why can't this be idiosyncratic risk etc?

Thanks,
Kavita

 

[brian.field]

This is a good question! Let's assume that none of the market value is attributable to identified risk factors, then we should allocate all of it to cash?

This is what he is saying no?

Doesn't make sense to me either.

 

[Kavita.bhangdia]

This is a good question! Let's assume that none of the market value is attributable to identified risk factors, then we should allocate all of it to cash?

This is what he is saying no?

Doesn't make sense to me either.

HI Brian,

Is it really possible to invest ONLY IN idiosyncratic risk according to your question?

From what I understand, everything else can be attributed to a risk factor..

From my understanding any asset can be broken into generic risk factors + idiosyncratic risk..
And more granular the risk factors are, the smaller is going to be idiosyncratic risk.

Thanks,
Kavita

 

[Dr. Jayanthi Sankaran]

Hi Kavita and Brian:

From an asset allocation perspective, cash could refer to Treasury bills....

Jayanthi

 

[brian.field]

Here is the passage:

 

[brian.field]

It also occurred to me that these "factors" are "market risk" factors. This should be obvious, I suppose, since it is in the Market Risk arena, but when I was thinking about, i was considering other risk factors, like Credit Risk, etc. For example, how could a Ba rated bond and a AAA rated bond be aggregated without contemplating the differences in credit risk. Then, I concluded that the "credit risk" related risks will be covered in the credit risk topic (is this true? what about liquidity risk, etc.,) and, from a price risk, or market risk perspective, both bonds could justifiably be aggregated into one "yield" risk factor.

 

[brian.field]

Although, after looking at Jorion's Mapping chapter again, and also at BT question P2.T5.62.1, it looks like "credit ratings" can be used as risk factors. This is a bit nebulous for me since credit ratings should fall under the "credit risk" umbrella no? Sure, credit rating changes have a corresponding price impact, but I don't really understand why ratings would be market risk factors unless they are simply used as an aggregation condition, i.e., combine all Aaa bonds into one segment, combine Aa bonds into another, etc., i.e., similar to traditional dimension reduction clustering techniques....

 

[Dr. Jayanthi Sankaran]

Hi Brian - have you looked at the JP Morgan CreditMetrics Technical Document? Although I have to read it all over again because I have forgotten much, they compute the VAR due to Credit taking into account:

• Rating migration likelihoods due to changes in credit rating
• Default recovery rates due to seniority
• Present value of bond revaluation due to credit spread changes
• Correlation Matrix

In the case of swaps (market-driven instruments) credit risk and market risk are intimately coupled because of an inherent optionality. This optionality stems from the fact that we face a loss on the transaction if the counterparty defaults only if we are in-the-money.

To treat products like swaps, we need to propose an integrated model of credit and market risk. Such a model would describe both the correlations of swap exposures across a portfolio (swaps based on the same interest rate would tend to go in-or out-of-the-money together) and the correlations between credit and market moves (swap counterparties might be more likely to default in one interest rate regime than in another). We need to capture the most crucial influences of market volatilities to the credit risks of market-driven instruments.

Although not complete (we need to look into bonds!), I hope that throws some light to your question!

Thanks!
Jayanthi

 

[brian.field]

No, I haven't looked at it Jayanthi....or at least I don't remember looking at it. Thanks for sharing.

 

[Dr. Jayanthi Sankaran]

You can download the JP Morgan CreditMetrics Methodology for free from the Internet, if you are interested....Meanwhile, I will most definitely look into the bonds part for integrated market cum credit risk when I get a chance!

Thanks
Jayanthi

 

[Mkaim]

Hi David,

The mapping process for linear and non linear derivatives is throwing me off. Is the LOS below even that relevant for the exam purpose? If yes, can you help me figure out where the VaR are coming from for these derivatives? I tried looking for a worksheet for Jorion Chapter 11 but can't seem to find it, I do see it for Chapter 6.

"Describe the method of mapping forwards, commodity forwards, forward rate agreements, interest-rate swaps and options."

 

[brian.field]

Looks like we're asking the right questions. Here is an excerpt from the Messages in Academic Literature.... reading.

 

[brian.field]

...

 

[Dr. Jayanthi Sankaran]

Thanks Brian - it is indeed interesting. Along those lines, what occurred to me (correct me if I am wrong!) is the potential correlation between the collateral and loan portfolio. There could be an interaction between market risk and credit risk in the banking book. Any thoughts on this?

Jayanthi

 

[brian.field]

That is exactly right @Jayanthi!

If you can make to the end of the Messages in Academic Literature reading.....which is a tremendous challenge, the last section is absolutely fascinating! It addresses the idea of Active Portfolio management actually magnifying systemic risk, i.e., the notion of VaR being "procyclical" which I didn't fully understand until making it through this reading. As much as I hated this reading, it was worth it in the end!

 

[Dr. Jayanthi Sankaran]

I can imagine Brian - it is a Basel Committee Working Paper!! Thanks for sharing...

Jayanthi

 

[QuantMan2318]

Hi David,
The mapping process for linear and non linear derivatives is throwing me off. Is the LOS below even that relevant for the exam purpose? If yes, can you help me figure out where the VaR are coming from for these derivatives? I tried looking for a worksheet for Jorion Chapter 11 but can't seem to find it, I do see it for Chapter 6.

"Describe the method of mapping forwards, commodity forwards, forward rate agreements, interest-rate swaps and options."

Hi @Mkaim
I doubt GARP would test the Mathematical procedure for Mapping the Linear and Non Linear Derivatives to their Risk Factors; Check the GARP published 2016 Exam syllabus guide from GARP, if it shows 'compute' for a topic, then the computation would be tested; since you state 'Describe', I think only the process understanding is required:

That being so, Let me tell you that Derivative securities as their name suggests is basically a derivation of their underlying securities which in turn become their basis for the risk factors; therefore to map the derivative securities to their risk factors, break them into their constituents by taking a partial derivative of the Derivative securities w.r.t their Risk factors, you get simpler securities' valuation/position.

In short, you are replicating a position in Derivatives with an equivalent position in multiple simpler securities.
Compute the VaR for these positions, the VaR is nothing to be afraid of, what Jorion has done is to take the SD of the value of the above positions for a month and multiplied them by the quantile (1.65 for a 95% confidence level); that data he could have got from any market sources.

The formula for the individual VaR is just the Position value*VaR% while component VaR is MarginalVaR*Position Value*weight ( I am simplifying, for more on Individual and Component VaR see the Investment Management Part of Part II) Add the Individual VaRs for the Total VaR or Risk of the Derivative and the Component VaR for the Diversified VaR of the Derivative - all broken into their Risk factors as well as in toto

 

[QuantMan2318]

And @brian.field

I was reading your insights on Diversification; Integrated approach, the above post also made me wonder, if correlations increase during periods of stress as they always do, then the computation of Marginal and Component VaR would be wrong as well. So much for the Mapping of Derivatives into Risk factors

So, no matter how many PhDs and Quants come in droves and undertake all their AI models, this always be an inexact Science, if I may use the term requiring careful monitoring and adjustments to the correlations and dynamic adjustments to the positions; So Humans are a must? or if the guys at MIT or Stanford find a Machine Learning Algo for this?

 

[Mkaim]

Hi @Mkaim
I doubt GARP would test the Mathematical procedure for Mapping the Linear and Non Linear Derivatives to their Risk Factors; Check the GARP published 2016 Exam syllabus guide from GARP, if it shows 'compute' for a topic, then the computation would be tested; since you state 'Describe', I think only the process understanding is required:

That being so, Let me tell you that Derivative securities as their name suggests is basically a derivation of their underlying securities which in turn become their basis for the risk factors; therefore to map the derivative securities to their risk factors, break them into their constituents by taking a partial derivative of the Derivative securities w.r.t their Risk factors, you get simpler securities' valuation/position.

In short, you are replicating a position in Derivatives with an equivalent position in multiple simpler securities.
Compute the VaR for these positions, the VaR is nothing to be afraid of, what Jorion has done is to take the SD of the value of the above positions for a month and multiplied them by the quantile (1.65 for a 95% confidence level); that data he could have got from any market sources.

The formula for the individual VaR is just the Position value*VaR% while component VaR is MarginalVaR*Position Value*weight ( I am simplifying, for more on Individual and Component VaR see the Investment Management Part of Part II) Add the Individual VaRs for the Total VaR or Risk of the Derivative and the Component VaR for the Diversified VaR of the Derivative - all broken into their Risk factors as well as in toto

@QuantMan2318 -- Thank you so much! Very much appreciated.

 

[Mkaim]

Looks like we're asking the right questions. Here is an excerpt from the Messages in Academic Literature.... reading.

View attachment 476
View attachment 477

@brian.field - This is helpful as well... Thanks a lot!