Approximating opf with p/2 or something
Whit
I've been away for a while and have just reviewed the threads.
The idea of a quick, closed-form approach to estimating opf appears in
a couple of places in the threads. It also appears to have been a
quiet topic for a while. I stumbled across it in a phone chat with
Murray today. He mentioned Brady and Joshua. Joshua and I haven't
chatted in months (my fault) and I haven't met Brady (yet).
Recognizing that you've been on the road for the index deployment
(congrats again!), what's the status, as you see it, of knowledge
about the accuracy and robustness of a shortcut estimation of opf for
a single system and, more interestingly, f for each marketsystem in a
multi-system test?
Here's part of the original thread on the topic:
"The contention is that p/2 will minimize this term, on average, as
the number of out-of-sample tests -> infinity. The inclusion of B, as
you mention, wheres it may make things less robust (because it
introduces another parameter) MAY make for a better estimate in the
out-of-sample
tests.
"I just don;t know. If anyone wants to perform these tests, please do
so and share with the group. Otherwise, at some point in the coming
weeks, I shall. If I do, I will use the data Russ put up for us."
Best,
Whit
RVince
Please pardon the delay in my response. In short, we know that as the
size of losses approach 0 (i.e. as the ratio of avg win / avg loss
approaches infinity) the value for f that is optimal approaches p, or
the sum of hte probabilities of winning scenarios -- a point of
singularity (because when loss reaches 0, the f that is optimal is 1)
So, assuming a stable p in the future (and, to avoid problems of
heteroskedasticity with repect to p, we can make a large sample of the
past for p. and a large future window such that p and p`, i.e. "future
p" are nearly equal) we can be certain that the f that is optimal in
the future (i.e the peak of the landscape along that axis) will be
between 0 and p` (and where it is, specifically, a funciton of the
distribution of actual future outcomes, or this distribution
approximated by future avg win / future avg loss.).
Since TWR = G ^ T where T is the number of plays, by choosing a best
guess for f` (future peak of the landscape on tng 2hat axis) as p`/2,
we minimize the outliers for f, having the effect very much in
determining statistical variance when you reduce the outliers.
Finally, if correlation reduces to +1.0, we need to scale by the
number of components. For example, if I determine my opt f on one
component, 2:1 coin toss, as .25, and I am going to play two of these,
when r=0, the peak is .23,.23. However, if r= 1, the peak is .125, .
125. Thus, if I take the optimal for a market system, traded alone,
snad divide it by the nuber of market systems, I determine the peak of
the landscape (as a "best guess") when r=1 between all components.
Example. 2 coins paying X:1. X is any positive number (can even be
<1). I miminze the damage done by missing the peak by using p`/2 for
each, so .25 for each. Divinding .25 by the number of components, .125
for each. So I estimate the peak for two coin tosses in the future (I
do not know if they will be profitable or not even!) as .125., 125 and
I am best guess optinal for r=1.0
Ralph
Whit
So as far as you've heard, no one has tested this yet, with Russ' data
or anything else?
What would we expect the output to look like? Something like this?
datestamp, opf_mktsys1, quickf_mktsys1, opf_mktsys2, quickf_mktsys2
datestamp, opf_mktsys1, quickf_mktsys1, opf_mktsys2, quickf_mktsys2
datestamp, opf_mktsys1, quickf_mktsys1, opf_mktsys2, quickf_mktsys2
?
RVince
Not a matter of testing. We know that f in the future will be bound
between 0 and p'. By using p' / 2 we minimize the outliers, and in
effect, minimize the price paid for missing the peak of the curve
(hence it is a "best guess") since with each elapsed holding period,
the difference (in terms of geomean hpr) at a specified point and what
IS the peak is raised to the power of elapsed holding periods (think
Vairiance, which is the difference between outlier and mean, squared)
Ralph
Whit
OK, how about two marketsystems, one with p=0.25 and another with
p=0.70? This differs from the prior example because the "coins" are
not identical.
I simply get best-guess-f's of 0.125 and 0.35 and I'm done?
That really *is* convenient.
Best,
Whit
RVince
future. And it's not what will be optimal in the future, but a best
guess in terms of paying the least price for missing what will be the
optimal. And it meets that criterion for a correlation of +1.0.
It's THAT simple. But then, it assumes that expected growth optimality
(in extremely turnbulent times, i.e. when correltion == 1.0) is your
criterion.
RVince
I simply get best-guess-f's of 0.125 and 0.35 and I'm done?
Those are your p'/2 answers -- you need to divide eash by the number
of components (2 in this case) so your results should be .0625 and .
175.
Whit
Ronald Brandt
> Subject: Re: Approximating opf with p/2 or something
> From: whitne...@gmail.com
> To: leverage-sp...@googlegroups.com
Brady Preston
a component would be made of a system and a market. All a system
really does is change the equity curve of the market.
On Dec 10, 10:06 pm, Ronald Brandt <ronbran...@msn.com> wrote:
> I am asking Ralph for further clarification of this. If you have 12 components (ie. market systems) but only trade a maximum of 6 market systems concurrently (in any combination of the 12), then I assume you divide your p'/2 answers by 6 and not 12, correct?
>
> Best regards,
>
> Ron
>
>
>
> > Date: Sun, 4 Dec 2011 13:52:13 -0800
> > Subject: Re: Approximating opf with p/2 or something
> > From: whitneybro...@gmail.com
> > > > > > > > Whit- Hide quoted text -
>
> - Show quoted text -
Ronald Brandt
> Subject: Re: Approximating opf with p/2 or something
Brady Preston
Sorry, did not fully understand what you where saying. In this case it would be 6, because you are only holding 6 at a time.
Brady Preston
I don’t believe that we are assuming that correlation is always 1, but it could become 1 like in 2008
From: leverage-sp...@googlegroups.com [mailto:leverage-sp...@googlegroups.com] On Behalf Of Henry Patner
Sent: Wednesday, December 14, 2011 8:56 AM
To: leverage-sp...@googlegroups.com
Subject: Re: Approximating opf with p/2 or something
Maybe this is a silly question but if you assume that correlation between positions is 1,
then why have multiple positions on at the same time instead of simply betting optimal f*
in the single position that results in the highest portfolio growth rate?
Joshua Ulrich
We're not assuming correlations *are* 1. We're assuming they *may
approach* 1 at some unknown point in the future. This method ensures
that, if correlations were to become 1, our total size across all
positions wouldn't be larger than betting on one system at the optimal
level.
In essence, we're trying to be conservative because our knowledge of
future correlations is uncertain and the cost for being wrong to the
right of the optimal value is so severe.
Best,
--
Joshua Ulrich | FOSS Trading: www.fosstrading.com
On Wed, Dec 14, 2011 at 7:55 AM, Henry Patner <hpa...@gmail.com> wrote:
> Maybe this is a silly question but if you assume that correlation between
> positions is 1,
> then why have multiple positions on at the same time instead of simply
> betting optimal f*
> in the single position that results in the highest portfolio growth rate?
>
>
> On Wed, Nov 23, 2011 at 1:41 PM, RVince <rvin...@hotmail.com> wrote:
>>
RVince
But just what IS that benefit of diversification? I think the reason
Josh and Brady and I are all seeking to be optimal when correlations
go to +1.0 is merely because of the magnitude of the moves then is so
much more amplified than in more "normal," periods. i.e. the benefit
of being optimal in the outlier periods far outweighs the offset of
being sub-optimal in the more normal periods. Ralph Vince
On Dec 14, 12:06 pm, Henry Patner <hpat...@gmail.com> wrote:
> Joshua and Brady - thanks for the responses. Much appreciated.
>
> On this topic. If you have multiple systems or positions and correlation
> is not 1, do people prefer using f* to size the aggregate of the systems
> relative to bankroll or each system relative to bankroll. In other words,
> should f* be applied to the basket of bets rather than each individually or
> vice verse?
>
> For example, take a simple coin flip paying $2 in successful outcomes for
> every $1 wagered. Probability of success is 50%. Now if you allow for two
> simultaneous coin flips, probability of net success (defined as making
> money) increases to 75%.
> It seems you would want to apply f* to the aggregate expectations of the 2
> coins rather than each individually and the fact that the bets are not
> correlated increases your probability of success which increases your f*.
>
> Furthermore, since, in this example the bets have identical probabilities
> and pay-offs, you know they would be equal weight but if you allow for the
> fact that you might be offered different odds on various bets, I'm not sure
> how you would select and size each individually in the basket. It seems
> that the discussion on p/2 assumes you should just equal weight your
> capital among the systems. However, if one system has far higher expected
> returns and a low failure rate, wouldn't that system be a larger portion of
> your basket?
>
> One thought is that f* needs to be applied to the basket because only the
> basket captures the benefit from diversification and so only the basket
> captures the true probabilities and pay-offs of the capital in your
> bankroll that is at risk. But then how do you size the components of the
> basket?
>
> On Wed, Dec 14, 2011 at 10:40 AM, Joshua Ulrich <josh.m.ulr...@gmail.com>wrote:
>
> > Henry,
>
> > We're not assuming correlations *are* 1. We're assuming they *may
> > approach* 1 at some unknown point in the future. This method ensures
> > that, if correlations were to become 1, our total size across all
> > positions wouldn't be larger than betting on one system at the optimal
> > level.
>
> > In essence, we're trying to be conservative because our knowledge of
> > future correlations is uncertain and the cost for being wrong to the
> > right of the optimal value is so severe.
>
> > Best,
> > --
> > Joshua Ulrich | FOSS Trading:www.fosstrading.com
>
> > On Wed, Dec 14, 2011 at 7:55 AM, Henry Patner <hpat...@gmail.com> wrote:
> > > Maybe this is a silly question but if you assume that correlation between
> > > positions is 1,
> > > then why have multiple positions on at the same time instead of simply
> > > betting optimal f*
> > > in the single position that results in the highest portfolio growth rate?
>
Henry Patner
RVince
This is just one crude, therefore, IMHO, "robust" method of estimating
the peak in the future, using the p`/2 approach because of the known
asymptote.(I dont even USE the peak, even though I am necessarily on
the landscape -- I just need to have an idea where it will be. Using
the peak is always risky business!).
THe other caveat is that the peak is something that IS seen
asymptotically, i.e. as the number of holding periods approach
infinity. For one play, in a positive expectation opporttunity, it is
always at 1.0, then migrates downward to it;s peak. So the asymptotic
peak will always be suboptimal, always to the left of that point that
actually does maximize expected geometric growth. Your other issues, I
will try to answer below:
On Dec 16, 6:54 pm, Henry Patner <hpat...@gmail.com> wrote:
> Thanks Ralph.
> The changing correlation issue is tricky. On one hand, you invest in
> multiple systems rather than your best system because of the belief that
> there is some benefit to diversification. On the other hand, you size the
> multiple systems as if correlations were going to 1 (e.g. there is no
> benefit to diversification) to avoid blowing up during a crisis.
>
> If you are not investing in levered instruments, can't get margin called
> and have long term capital, would you still want to optimize around the
> mark to market periods of crisis or would you optimize around the normal
> periods and bet full f*?
That's a function of your criterion. If your criterion is to maximize
expected geometric growth, then yes. It;s also a function of your
horizon. Will you be out of the game before the next crisis, then yes,
if not -- how will you survive the next crises then?
> If you are investing in levered instruments, can get margin called and/or
> don't have long term capital, then for all practical purposes shouldn't you
> bet partial f* in your system with the best expected returns because you
> need to act as if correlations are 1 at any point in which it matters?
Only based on the past 30 years or so experience -- not a mathematical
fact. The normal periods have essentially mattered very little
compared to those periods of extreme volatility. Again consider a
"portfolio" comprise of two 2:1 coin toss games, say, where each of
the four possible outcomes is .25 (hence, corr=0). Clearly there will
be runs where HH and TT are very prevelant, and periods where they
come in about 1/4th the time each, the more normal periods.
Our problem is that when things go HH and TT a lot, the moves are no
loner really 2:1, but tend to expand. In my case, though it may be
germane wherre the peak is, to me, all of the time, remember we are
projecting into the future, and it is precisely in those times of
panic and euphoria that I want to have a handle on where the peak is.
> Also, any thoughts on whether it makes more sense to apply f* to each
> individual system or to the basket of systems? Does the policy of sizing
> by P/2 then dividing equally among the systems side-step the question of
> whether equal weighting among different systems with different return
> expectations makes sense?
Yes, but like I started outr saying ,this is a crude, robust means for
guessing the peak of the landscape in the future that assumes the
future is in meltdown mode. Here, we are dividing each compoenents p`/
c by N, the same as multiplying it by 1/N, thus, mutliplying it by an
equal weighting. SO:
best guess f = p` / 2 * W
where:
W = 1/ N
All of the W's for the compoentns sum to 1. You could use any scheme
you wanted to on the W's (as long as they all sum to 1, you are
guessing with the caveat that it is a period where correlations all go
to 1). -Ralph Vince