[R-SIG-Finance] CVaR portfolio-optimization vs. utility maximization..

[Brian G. Peterson]

Well, there are a couple things likely going on here....

Your choice of confidence threshold is really important.  The highly 
risk averse investor might be better off using VaR with a high threshold 
than CVaR, despite its nonlinearity.

Whether you have enough data to fit a copula is important.

If you're doing this in a portfolio context, I'd argue that flattening 
from a multivariate distribution to a univariate CVaR number, even with 
a copula, misses the component contribution to risk.  See "Component 
Expected Shortfall" or "Component CVaR"

Regards,

    - Brian

John Seppänen wrote:
> Brian,
>  
> Thanks for your answer. I am using scenarios in optimization. 
> Scenarios are drawn from a multivariate distribution that is built by 
> fitting univariate return distributions and then gluing the 
> distibutions with a copula. Thus the non-normality of assets should be 
> taken into account.. I am assuming the reason for my "findings" are 
> that the CVaR puts "only" a linear penalty for returns below the 
> quantile and I am wondering how optimal this is for a (highly) risk 
> averse investor... 
>  
> -John
>
> 2010/1/27 Brian G. Peterson <brian at braverock.com 
> <mailto:brian at braverock.com>>
>
>     John Seppänen wrote:
>
>         Hi all!
>
>         My question itself is not related to R so my apologies for
>         that. I ran
>         scenario optimizations in S-Plus with respect to variance and
>         CVaR as a risk
>         measures (based on Scherer & Martin's (2005) book). My assets
>         where
>         mostly negatively skewed and fat-tailed and I expected the
>         resulting
>         portfolio from CVaR-optimization to have less tail-risk than
>         the the
>         portfolio from variance-optimization. However, I noticed the
>         opposite which
>         is surpirising because the markowitz optimization is often
>         accused of
>         being tail-risk maximization when assets are negatively skewed
>         (e.g. hedge
>         funds).
>
>         In many sources CVaR is said to be "the measure" for downside risk
>         measurement. However, I am not able to find a discussion about
>         how well CVaR
>         relates with the utility maximization framework.. who should
>         optimize with
>         respect to CVaR if it increases the tail-risk? Computational
>         easiness is not
>         a good reason..   Any references or thoughts about the subject
>         would be
>         appreciated..
>          
>
>     Use modified CVaR instead.  It handles non-normal distributions.
>
>     And, being an *R* finance list, all that functionality is already
>     available in R, including optimizing using modified CVaR as one of
>     your objectives.
>
>     Cheers,
>
>      - Brian
>
>     -- 
>     Brian G. Peterson
>     http://braverock.com/brian/
>     Ph: 773-459-4973
>     IM: bgpbraverock
>
>
>


-- 
Brian G. Peterson
http://braverock.com/brian/
Ph: 773-459-4973
IM: bgpbraverock