[R-sig-finance] Random Numbers

Kris kriskumar at earthlink.net
Sat Nov 19 01:49:42 CET 2005

Ok there are several things going on here:
i)  Michaud's resampling algorithm
ii) What i described which is doing some sort of bias reduction in your historical covariance estimation piece by resampling and if you think there is serial correlation information then do block bootstrapping
iii) What Patrick describes which is to do the resampling on the alpha. 

I don't if this is related to the original question, but what is the prefered method that is used to detect
 for a medium/long term investor that things have changed enough to rebalance?.

-----Original Message-----
From: Patrick Burns <patrick at burns-stat.com>
Sent: Nov 18, 2005 12:42 PM
To: "L.Isella" <L.Isella at myrealbox.com>
Cc: kriskumar at earthlink.net, r-sig-finance at stat.math.ethz.ch
Subject: Re: [R-sig-finance] Random Numbers

I think there are several problems with the resampled
efficient frontier, here is one: The procedure as I understand
it is to bootstrap the mean of the historical returns.  What
should be bootstrapped is the alpha generation process.
One hopes that there are few fund managers who use the
historical mean as their expected return.  Bootstrapping the
actual alpha generation process is likely to be non-trivial.

Patrick Burns
patrick at burns-stat.com
+44 (0)20 8525 0696
(home of S Poetry and "A Guide for the Unwilling S User")

L.Isella wrote:

>On 11/18/05, Kris <kriskumar at earthlink.net> wrote:
>> I dont quite follow what you mean? People do resampled eff frontier with bootstrapping/bootstrapping+jackknife but this is done on the correlation/covarianceestimation process.
>>If all you need is correlated rng take a look at V&R's MASS package rmvnorm in particular. alternatively you can use rnorm with chol to get the correlated RNG.
>Well, I mean the idea of resampled efficiency as expressed by Michaud in his book: you assume that the returns of the stocks in your ptfs are normally distributed (which is a reasonable approximation for the stocks I deal with).
>You come up with some guesses about the "true" expected rtns and the "true" covariance matrix of these assets. 
>In other words you assume that your historical data are the sample of multivariate normal distribution with certain correlations.
>Then you take random draws from this distribution and simulate several (actually plenty) sets of returns.
>For each simulated set of returns, this provides you with some average returns and correlations and you optimize a ptf on the basis of these data.
>Oversimplyfing, you repeat this procedure many times, obtain some average ptf weights along the simulated efficient frontier and you use these weights to generate the resampled efficient frontier by means of the "true" covariance matrix and "true" expected rtns.
>At least this is how I understood it. Anyone understood it differently?
>R-sig-finance at stat.math.ethz.ch mailing list

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