[R-sig-finance] Monte Carlo and Portfolio Optimization

con.keating@financedevelopmentcentre.com con.keating at financedevelopmentcentre.com
Mon Oct 10 14:28:29 CEST 2005


 From memory, The Chopra and Ziemba (1993) results were that errors in 
means were
approximately 8 x as important as errors in standard deviation which 
were 4 x as
important as errors in the correlation matrix.

There ia also a criticism of the Michaud resampling method by Cam 
Harvey at Duke
where he shows that it is strictly sub-optimal.

Given anyway that most returns are pretty far from Normal in the multivariate
setting if not the univariate, I wonder how accurate anyone can hope to 
be in a
mean-variance framework-I was recently working with an equity index problem
where correlations were of the order of 0.75 (quarterly data) at which levels
concentration should be expected.

Hannu's suggestions seem worth investigating.

Con Keating

Quoting Hannu Kahra <hkahra at gmail.com>:

> Silvia,
> David Jessop refers in a separate mail to Berndt Scher's book "Portfolio
> Construction and Risk Budgeting"
> http://www.amazon.com/exec/obidos/tg/detail/-/1904339301/qid=1128942250/sr=8-1/ref=sr_8_xs_ap_i1_xgl14/103-5833626-9777409?v=glance&s=books&n=507846
> .
> His latetes book is with Douglas Martin: " Introduction to Modern Portfolio
> Optimization with NuOPT, S-PLUS and S+Bayes"
> http://www.amazon.com/exec/obidos/tg/detail/-/0387210164/qid=1128942250/sr=8-2/ref=sr_8_xs_ap_i2_xgl14/103-5833626-9777409?v=glance&s=books&n=507846
> and I remember that in this book he is against using portfolio resampling
> with the Gaussian assumption.
> I recall (I do not have the references with me) that Ziemba and Kallberg
> have found that errors in the means are 10-20 times more serious (for the
> portfolio) than errors in the covariances. As a consequence the resulting
> portfolios tend to be very consentrating such that a lot of assets have zero
> weights.
> An old trick is to apply the so-called Bayes-Stein or James Stein
> estimators that shrink the sample means towards some fixed value, e.g. the
> grand mean or the return on the minumum variance portfolio. The latter is
> the approach suggested by Jorion. The Black-Litterman "model" applies
> shrinkage towards the CAPM equilibrium returns, since it applies the
> inversion of the Markowitz problem.
> Instead of using standard Markowitz optimization, benchmark related
> optimization (explained in Scherer's Portfolio Construction book) may be
> usefull.
> I hope these help.
> Hannu Kahra
> Turku Business School, Finland
> and CeRP, Italy
> On 10/9/05, Silvia Marelli <silmarelli at yahoo.co.uk> wrote:
>> Hi,
>> I am trying to build some realistic efficient
>> portfolios using some mean/variance techniques
>> (Markowitz, CAPM etc...).
>> I normally end up with an unrealistic concentration of
>> the wealth in a too limited number of assets.
>> I heard about Monte Carlo techniques to account for
>> the unaccuracy of the information available.
>> What would be a good starting point?
>> I am not experienced, so I need to keep it as simple
>> as possible.
>> Should I simply optimize many ptfs, by sampling the
>> return of each asset from a distribution which I
>> assume to be a Gaussian centered on the expected
>> return of the asset?
>> Is it possible to introduce some "noise" also in the
>> covariance matrix?
>> Then how should I "average out" the results?
>> I am not very familiar with these techniques, so if
>> anyone can suggest some online resources, I would be
>> very grateful.
>> Regards
>> Silvia
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