@Grant wrote an implementation of "On-Line Portfolio Selection with Moving Average Reversion"
I copied his source and made a small tweak to allow a no-operation backtest to complete, so others can clone his original. @Grant and @Thomas started the discussion here: https://www.quantopian.com/posts/share-algorithms-to-be-re-written-for-quantopian
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
In case folks need some light bedtime reading...here are some relevant links:
On-Line Portfolio Selection with Moving Average Reversion
PAMR: Passive aggressive mean reversion strategy for portfolio selection
http://www.cais.ntu.edu.sg/~chhoi/PAMR/
Efficient Projections onto the l1 -Ball for Learning in High Dimensions
Efficient learning of label ranking by soft projections onto polyhedra
Needless to say, it's pretty heavy stuff. As best I can tell, the secret sauce is in the last fairly recent paper cited above. I should be able to provide a full outline of the algorithm for comment, based on the above references. The implementation is not as complicated as the papers might suggest.
John - I just joined your site yesterday, so this might be a silly question, but why does your example above have no performance results for the Algorithm?
@Eric, Not a silly question at all -- The algo doesn't place orders yet!
You are probably wondering why :). A few people are working with Grant to round out the implementation, and he shared the source code before it was fully implemented to help speed the collaboration.
The posts in the forums with the blue sparkline charts are examples that have real returns. The sparkline is a compressed version of the returns. The grayscale charts are for algorithms that don't generate returns, which are usually code samples or proofs of concept like this one.
Here is a nice example of placing orders: https://www.quantopian.com/posts/papertrading-for-coursera-computational-finance-homework
thanks for asking!
fawce
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
Hello Thomas (& others),
I'm continuing our discussion from https://www.quantopian.com/posts/share-algorithms-to-be-re-written-for-quantopian.
I've realized that I'd benefit from some Python/Quantopian coding expertise (I don't have experience with Python...one of my motivations here is to get a feel for it). Here are some tasks:
Grant
Hi Grant,
Awesome to see this project progressing! Some reactions:
Will let keep you posted.
Thomas
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
Hello Thomas,
I continue to chip away at this project. One thing that is confusing is the authors' ad hoc "normalization" step at the end. If you have a look at p. 254 of PAMR: Passive aggressive mean reversion strategy for portfolio selection you'll find the basic outline of his solution to the OLMAR optimization problem (although the PAMR problem has different contraints, the math appears to be essentially the same). The murky part is captured in the authors' comment "that the non-negativity of portfolio b is not considered here since introducing this term causes too much complexity, and alternatively we project the resulting portfolio into a simplex to enforce the non-negativity constraint."
If you look at p. 1577 of Efficient learning of label ranking by soft projections onto polyhedra, the authors provide an example of how to incorporate the non-negativity constraint into the Lagrangian (the final term of the first equation on the page).
I figure that there ought to be a way to re-frame the optimization problem for clarity (although the final result is probably correct). I'll let you if I make any headway.
Hi Grant,
Yeah, this normalization is a little impractical. My guess is that the others spent quite some time to optimize with the Lagrangian multiplier that enforces b_i >= 0 but couldn't make it work. There is probably a way but I would imagine it to require some serious calculus-fu (because the authors couldn't figure it out themselves, despite having quite some incentive to do so). So my advice is (unless you really want to train using Lagrangian multipliers), just add the normalization. I ported the simplex_projection.m which seems to work just fine:
import numpy as np
def simplex_projection(v, z=1):
"""Projection vectors to the simplex domain
Implemented according to the paper: Efficient projections onto the
l1-ball for learning in high dimensions, John Duchi, et al. ICML 2008.
Implementation Time: 2011 June 17 by [email protected] AT pmail.ntu.edu.sg
Optimization Problem: min_{w}\| w - v \|_{2}^{2}
s.t. sum_{i=1}^{m}=z, w_{i}\geq 0
Input: A vector v \in R^{m}, and a scalar z > 0 (default=1)
Output: Projection vector w
:Example:
>>> proj = simplex_projection([.4 ,.3, -.4, .5])
>>> print proj
array([ 0.33333333, 0.23333333, 0. , 0.43333333])
>>> print proj.sum()
1.0
Original matlab implementation: Copyright 2011 by Bin
Python-port: Copyright 2012 by Thomas Wiecki ([email protected]).
"""
v = np.asarray(v)
p = len(v)
w = np.zeros_like(v)
# Sort v into u in descending order
u = np.sort(v)[::-1]
idx = np.argsort(v)[::-1]
# Find \rho = max{j \in [n]: u_{j}-(sum(u(1:j, 1))-z)/j >0 }
for j in range(p):
if (u[j] - (np.sum(u[:j])-z) / j <= 0):
break
# Define \theta = (sum(u(1:rho, 1))-z)/rho
theta = (np.sum(u[:j])-z) / j;
# w_{i}=max{ v_{i} - theta }
w[idx[:j]] = v[idx[:j]] - theta
return w The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
Thanks Thomas,
I've gathered from a book I borrowed and poking around the internet that the case of inequality constraints is not always so straightforward. It might not be for several days, but I'll keep plugging away at completing the full Python/Quantopian implementation.
Grant
@Grant: To better collaborate on this I'd like to try working on this on github. I uploaded what you posted, added the simplex_projection code and put it on github. The idea is that we'll give you access to that repo so that you and I (or other collaborators!) can push and pull code there.
One reason I'd like to try this is because we are thinking of ways to integrate github into quantopian so this can hopefully serve as a nice laboratory. Now we can only execute this on Quantopian so we'd have to copy&paste back and forth but this is something which will change once we figure out the right way to implement this. Would you be interested to help us out in that way?
Finally, if you don't have a github account, it's easy to create one. Just tell me your github name and we'll add you.
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
Thomas,
Sure, I'll give github a try. Please note that I don't expect to have a lot of time to pour into this on a consistent basis...but we'll see how it goes.
Grant
@Grant: Sure, there's no rush at all. Maybe we can even attract some contributors that way!
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
I just set up my github account (I think). So feel free to do whatever needs to be done there for us/others to continue working.
Great, what's your github username? You can also email me at [email protected] but it's not really secret :)
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
Just following up to share the address of the new public repo for algo scripts: https://github.com/quantopian/quantopian-algos
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
Thomas/Fawce,
Some additional implementation details:
Please consider the number of securities ("assets" in the paper) used for the authors' backtesting. If you see Table 3 on Page 6 of On-Line Portfolio Selection with Moving Average Reversion, the numbers range from 23 to 88. As I recall, Quantopian is limited to portfolios of 10 securities or fewer, correct?
The paper discusses combining multiple OLMAR portfolios (the basic algorithm), each optimized for a different look-back window, w (see the final paragraph of Section 4.3 on Page 5). The full portfolio is constructed by performance-weighting versus w, with w ranging from 3 to 30 days. Given that the Quantopian moving average transform cannot be called with a variable (e.g. mavg(3) works, but mavg(w) doesn't), the weighting over a variable look-back window could be kinda awkward to implement in Quantopian. Any ideas how to manage this in the code?
@Grant:
Re 1: This will be changed very soon with the universe selection.
Re 2: Agreed. I think we should just add an option to turn off the automagic registration of transforms and let users register transforms themselves (in zipline one can do this with self.register_transform).
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
An additional reference (thanks Thomas):
http://www.cs.berkeley.edu/~jduchi/projects/DuchiShSiCh08/ProjectOntoSimplex.m
An additional note (credit to Thomas who noted the divide-by-zero problem in the algorithm). See the top of Page 255 of:
PAMR: Passive aggressive mean reversion strategy for portfolio selection
It states "Note that in case of zero market volatility, that is, || x_t − x_bar_t 1 ||^2 = 0, we just set τ = 0."
I'm not sure how to implement this rule in the algorithm, since || x_t − x_bar_t 1 ||^2 ~ 0 will cause computation problems.
In the pamr_1_run.m MATLAB script posted at the site http://www.cais.ntu.edu.sg/~chhoi/PAMR/, the author tests for the zero volatility condition with this code:
% Step 4: Set parameters
x_bar = sum(data(t, :)) / N;
denominator = (data(t, :) - x_bar)*(data(t, :) - x_bar)';
if (~eq(denominator, 0.0)),
tau = min([C, ell/denominator]);
else
tau = 0;
end Got to say gents, look how far you have come! Makes me all nostalgic revisiting this thread :)
Good fortune
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian.
In addition, the material offers no opinion with respect to the suitability of any security or specific investment. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
