I fixed a bug -- please give it a try and post your results and suggestions here. I recommend only running it on daily tic data, due to the use of the batch transform to compute the moving average.

See http://icml.cc/2012/papers/168.pdf for a complete description of the algorithm.

--Grant

Clone Algorithm

1414

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Cumulative performance:

Algorithm
Benchmark

Custom data:

Total Returns

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Alpha

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Beta

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Sharpe

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Sortino

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Max Drawdown

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Benchmark Returns

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Volatility

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Returns | 1 Month | 3 Month | 6 Month | 12 Month |

Alpha | 1 Month | 3 Month | 6 Month | 12 Month |

Beta | 1 Month | 3 Month | 6 Month | 12 Month |

Sharpe | 1 Month | 3 Month | 6 Month | 12 Month |

Sortino | 1 Month | 3 Month | 6 Month | 12 Month |

Volatility | 1 Month | 3 Month | 6 Month | 12 Month |

Max Drawdown | 1 Month | 3 Month | 6 Month | 12 Month |

import numpy as np #globals for get_avg batch transform decorator R_P = 1 #refresh period in days W_L = 5 #window length in days def initialize(context): # http://money.usnews.com/funds/etfs/rankings/small-cap-funds context.stocks = [sid(27796),sid(33412),sid(38902),sid(21508),sid(39458),sid(25899),sid(40143),sid(21519),sid(39143),sid(26449)] context.m = len(context.stocks) context.price = {} context.b_t = np.ones(context.m) / context.m context.eps = 2.5 #change epsilon here context.init = False set_slippage(slippage.VolumeShareSlippage(volume_limit=0.25,price_impact=0)) set_commission(commission.PerShare(cost=0)) def handle_data(context, data): if get_avg(data,context.stocks[0]) == None: return if not context.init: rebalance_portfolio(context, data, context.b_t) context.init = True return m = context.m x_tilde = np.zeros(m) b = np.zeros(m) # find relative moving average price for each security for i, stock in enumerate(context.stocks): price = data[stock].price x_tilde[i] = get_avg(data,stock)/price ########################### # Inside of OLMAR (algo 2) x_bar = x_tilde.mean() # Calculate terms for lambda (lam) dot_prod = np.dot(context.b_t, x_tilde) num = context.eps - dot_prod denom = (np.linalg.norm((x_tilde-x_bar)))**2 # test for divide-by-zero case if denom == 0.0: lam = 0 # no portolio update else: lam = max(0, num/denom) b = context.b_t + lam*(x_tilde-x_bar) b_norm = simplex_projection(b) rebalance_portfolio(context, data, b_norm) # update portfolio context.b_t = b_norm #log.debug(b_norm) @batch_transform(refresh_period=R_P, window_length=W_L) #set globals R_P & W_L above def get_avg(datapanel,sid): prices = datapanel['price'] avg = prices[sid].mean() return avg def rebalance_portfolio(context, data, desired_port): #rebalance portfolio current_amount = np.zeros_like(desired_port) desired_amount = np.zeros_like(desired_port) if not context.init: positions_value = context.portfolio.starting_cash else: positions_value = context.portfolio.positions_value + context.portfolio.cash for i, stock in enumerate(context.stocks): current_amount[i] = context.portfolio.positions[stock].amount desired_amount[i] = desired_port[i]*positions_value/data[stock].price diff_amount = desired_amount - current_amount for i, stock in enumerate(context.stocks): order(stock, diff_amount[i]) #order_stock def simplex_projection(v, b=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: John Duchi ([email protected]) Python-port: Copyright 2012 by Thomas Wiecki ([email protected]). """ v = np.asarray(v) p = len(v) # Sort v into u in descending order v = (v > 0) * v u = np.sort(v)[::-1] sv = np.cumsum(u) rho = np.where(u > (sv - b) / np.arange(1, p+1))[0][-1] theta = np.max([0, (sv[rho] - b) / (rho+1)]) w = (v - theta) w[w<0] = 0 return w

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