CVaR portfolio-optimization vs. utility maximization..
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 Sepp?nen 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 Sepp?nen 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