Value at Risk - Multi Asset Class Portfolio

[HLFX]

Hello,
I am attempting to build a Value at Risk Model that is somewhat unique and I would like to hear some thoughts on what is appropriate. I am attempting to build a model that includes equities, index positions, commodity, and fx positions. I am concerned that volatility measures of each instrument are not comparable because each asset class trades differently. Once I understand how to build this model I am hoping to take it one step further and replace whichever method I first choose with an implied volatility measure. I know there is much controversy surrounding this, but it is more practice than anything. I am uncertain as to how to derive implied correlation between these assets.

I will be using Bloomberg and Excel. I am brand new to the forum and to using a Bloomberg Terminal/Bloomberg API so please forgive me for any novice behavior. Any help is appreciated.

 

[chiyui]

I don't fully understand what you mean but I'll try to post my opinion anyway.

Firstly I think that volatility measures are comparable if you use the same measure for all the asset classes. For example, the standard deviations of all asset classes are comparable because their unit is all in %. So I think you need not find any measures that are invariant of trading activities as you mentioned.

Another issue is, the value at risk of your portfolio is just the quantile of the probability distribution of your portfolio. So I think it depends on what probability distribution your portfolio belongs to. Say for example, if it is the normal distribution, then you just use μ-Zcσ to calculate the value at risk. If it is the t-distribution, you may use -tcσ. If it is the gamma distribution or other asymmetrical distribution, you gotta use other formulas (which might not contain standard deviation or volatility as the input of the formulas).

So my concern is not which kind of volatility measure you're going to use, but the method of how to find the value at risk (i.e. the formula of calculating the quantile of the probability distribution of your portfolio).

 

[HLFX]

I appreciate the response and understand what you are saying. How do I go from an implied volatility measure to implied correlation of the portfolio though. I continue to struggle with this...

 

[chiyui]

Firstly, you gotta have options positions in order to have any "implied" volatility measures. If your portfolio only contains spot assets positions, there simply doesn't exist any "implied" volatility measures then. You just need to (and can) use historical volatility (historical standard deviation) in your portfolio.

Similarly, you gotta have exchange options positions in order to have any "implied" correlation measures. (You may google what is an exchange option just in case.)
If no such positions, then you just need to (and can) use historical correlation in your portfolio.

But why must you need to use "implied" vols and corrs?

 

[HLFX]

There is no "need" other than my own curiosity to do so.

http://www.frbsf.org/econrsrch/workingp/2000/wp00-02.pdf

This is a paper/article that is essentially feeding my curiosity, but I don't understand it. I am trying to piece it all together. What is stopping me from using implied vol on the options as a vol input to my spot positions?

 

[chiyui]

Yeah you can use implied vols to be the value at risk input if you assume you can find a traded option on your spot assets. Similarly you can use implied corrs if you can find an exchange option on your spot assets in the market. Sorry for my unclear comments before.

 

[HLFX]

You are completely fine. I appreciate the input. All of my spot assets are the broad indices and commodities so finding the appropriate measures is easy. It's just the implementation aspect that I am struggling with.

Thanks again!

If you feel like it, feel free to give me the run down on exchange options and how I derive implied correlation

 

[chiyui]

Philippe Jorion's FRM handbook contains the derivation method of implied correlation (he calls it the Margrabe model). He illustrates the procedure in Chapter 17.

I want to copy his contents here. But I'm using cell phone online now so its difficult to write it here. I'll show you later when I go back to my den using my desktop computer.

 

[HLFX]

Thanks mate