[R-SIG-Finance] [R-sig-finance] robust portfolio optimization

[Brian G. Peterson]

Patrick's point is still correct.  With only two years of data, you have 
basically one year of in-sample data and one year of out-of-sample data. 
  This is hardly enough to build any reliable statistical inference on 
for anything other than a minimum risk portfolio (and even that is 
highly questionable).

I'd say that the first step should be to get more data.  Ideally this 
would be by getting additional history on the target investments, and 
doing the optimization over a longer time frame.

If you still don't have enough data, you could combine a distributional 
assumption from a "similar" industry or company and do a Bayesian or 
Monte Carlo historical simulation, although you'd want to try to do 
conditional/dependent variance to get reasonable covariances. 
Basically, this then becomes a very hard problem.

We also haven't addresses what the meaning of "robust" is here, but I'll 
let the original poster comment on what they meant without inferring too 
much.

Regards,

   - Brian

ning zhang wrote:
> you could split the data into training and testing periods. Find the
> optimised weight by using the training dataset, then apply this weights into
> the testing period to see whether the performance is consistance. If it is
> consistance, then it is a good model.
> 
> On Tue, Jul 1, 2008 at 10:44 AM, Patrick Burns <patrick at burns-stat.com>
> wrote:
> 
>> I pretty much understand all of the solutions
>> that have been offered.  What I don't understand
>> is the original question.
>>
>> How do you know if your solution is
>> good or not?  Given that you have two years of data
>> and you are talking about samples of one year, a
>> reasonable plan would be to test an out-of-sample
>> period (a day, a week, ...) and then move the in-sample
>> data that amount.  Only a year of out-of-sample data
>> seems rather short to me.
>>
>> You want to get good returns.  I think it is safe to say
>> that the amount of predictive power in a year of daily
>> returns is infinitesimal, no matter how much fancy footwork
>> you do.  A test of optimization technology without a good
>> predictive model for returns is going to be driven by noise
>> unless you are creating minimum variance portfolios (or
>> some other minimum risk).
>>
>>
>> Patrick Burns
>> patrick at burns-stat.com
>> +44 (0)20 8525 0696
>> http://www.burns-stat.com
>> (home of S Poetry and "A Guide for the Unwilling S User")
>>
>>
>> Enrico Schumann wrote:
>>
>>> there are lots of choices how to obtain the `robust solution' you want.
>>> maybe optimise the weights to give the *mean* sharpe/sortino whatever, or
>>> to
>>> maximise a quantile (or the lowest) of the objective functions of your
>>> 1,000
>>> data sets.
>>>
>>> -----Ursprüngliche Nachricht-----
>>> Von: r-sig-finance-bounces at stat.math.ethz.ch
>>> [mailto:r-sig-finance-bounces at stat.math.ethz.ch] Im Auftrag von ning
>>> zhang
>>> Gesendet: Dienstag, 1. Juli 2008 09:55
>>> An: Enrico Schumann
>>> Cc: r-sig-finance at stat.math.ethz.ch
>>> Betreff: Re: [R-SIG-Finance] [R-sig-finance] robust portfolio optimization
>>>
>>> you could sign the random weight to each assets first, and then calculated
>>> portfolio variance as well as portfolio return. Finally, you could use
>>> monte
>>> carlo simulation to optimise the weight of each asset, which gives you the
>>> best sharp ratio.
>>>
>>>
>>>
>>> On Tue, Jul 1, 2008 at 8:02 AM, Enrico Schumann <enricoschumann at yahoo.de>
>>> wrote:
>>>
>>>
>>>
>>>> how about bootstrapping? keeping the cross-sectional correlation in the
>>>> data is fairly simple by sampling whole rows from your returns matrix
>>>> (assumed of dimension observations times returns), but the serial dependence
>>>> is more difficult. if you have an idea how this serial dependence looks like
>>>> (or, say, you know what parts you want to reproduce in your scenario sets)
>>>> you may fit a regression model capturing this dependence and then resample
>>>> from the residuals. if you want a rather non-parametric approach, block
>>>> bootstrapping may be a technique to look at.
>>>>
>>>> i think patrick burns has a tutorial on bootstrapping on his homepage
>>>> http://www.burns-stat.com/
>>>>
>>>> enrico
>>>>
>>>> -----Urspr|ngliche Nachricht-----
>>>> Von: r-sig-finance-bounces at stat.math.ethz.ch
>>>> [mailto:r-sig-finance-bounces at stat.math.ethz.ch] Im Auftrag von
>>>> maratikus
>>>> Gesendet: Mittwoch, 27. Februar 2008 21:49
>>>> An: r-sig-finance at stat.math.ethz.ch
>>>> Betreff: [R-SIG-Finance] [R-sig-finance] robust portfolio optimization
>>>>
>>>>
>>>> I am exploring robust portfolio optimization.  I have historical daily
>>>> data for 20 stocks over 2 year period.  i'd like to simulate 1,000 datasets
>>>> of 1 year each that have autocorrelation and cross-correlation properties
>>>> similar to those of the historical data.  Then I'd like to find allocation
>>>> that maximizes minimum risk-adjusted return over 1,000 datasets.  All
>>>> suggestions are appreciated!