Wednesday 6 July 2016

mini-Meucci : Applying The Checklist - Steps 10+

In this final leg of The Checklist tour we'll be looking at the Dynamic Allocation step and touch briefly on ex-post Performance Analysis.

Dynamic Allocation

Essentially this involves repeating the previous 9-steps on a periodic basis (e.g. a sequence of monthly allocations) according to a chosen allocation policy.

Examples of dynamic allocations include systematic strategies (based on signals) and portfolio insurance.

See slide #55 Dynamic Allocation (general case).

Quantitative/Systematic Strategies

Those interested in active portfolio management and who attend the ARPM bootcamp, will also have access to the ARPM Lab. In it are 2 very interesting chapters covering both the theory and practice (with code) of quant strategies, where you'll learn among other things, how to construct a characteristic portfolio (Grinold and Easton) based on your signals. For an example of such a characteristic portfolio strategy, see the youtube video on slide #56 Dynamic Allocation (video).

Example Python Code

In our toy example with the goal of constructing a low volatility equity portfolio, our chosen allocation policy will be to weight the 30 DJIA stocks according to the ex-ante minimum variance portfolio, and rebalance the portfolio at the end of each month.

We'll use an expanding historical data window of at least 3 years, apply time-conditioned weights to the observations when estimating the ex-ante distribution, and also use a simple form of shrinkage before optimizing.

To simulate such a sequence of allocations over a 3 year period, we'll use the open source Zipline package.

In [2]:
%matplotlib inline
import rnr_meucci_functions as rnr
import numpy as np
from zipline.api import (set_slippage, slippage, set_commission, commission, 
                         order_target_percent, record, schedule_function,
                         date_rules, time_rules, get_datetime, symbol)

# Set tickers for data loading i.e. DJIA constituents and DIA ETF for benchmark
tickers = ['MMM','AXP','AAPL','BA','CAT','CVX','CSCO','KO','DD','XOM','GE','GS',
           'TRV','UNH','UTX','VZ','V','WMT','DIS', 'DIA']

# Set investable asset tickers
asset_tickers = ['MMM','AXP','AAPL','BA','CAT','CVX','CSCO','KO','DD','XOM','GE',
def initialize(context):
    # Turn off the slippage model
    # Set the commission model
    set_commission(commission.PerShare(cost=0.01, min_trade_cost=1.0)) = -1 # using zero-based counter for days
    context.assets = []
    print('Setup investable assets...')
    for ticker in asset_tickers:
    context.n_asset = len(context.assets)
    context.n_portfolio = 40 # num mean-variance efficient portfolios to compute = None
    context.tau = None
    context.min_data_window = 756 # min of 3 yrs data for calculations
    context.first_rebal_date = None
    context.first_rebal_idx = None
    context.weights = None
    # Schedule dynamic allocation calcs to occur 1 day before month end - note that
    # actual trading will occur on the close on the last trading day of the month
    # Record some stuff every day

def handle_data(context, data): += 1
def rebalance(context, data):
    # Wait for 756 trading days (3 yrs) of historical prices before trading
    if < context.min_data_window - 1:
    # Get expanding window of past prices and compute returns = get_datetime().date() 
    prices = data.history(context.assets, "price",, "1d")
    if context.first_rebal_date is None:
        context.first_rebal_date =
        context.first_rebal_idx =
        print('Starting dynamic allocation simulation...')
    # Get investment horizon in days ie number of trading days next month
    context.tau = rnr.get_num_days_nxt_month(,
    # Calculate HFP distribution
    asset_rets = np.array(prices.pct_change(context.tau).iloc[context.tau:, :])
    num_scenarios = len(asset_rets)
    # Set Flexible Probabilities Using Exponential Smoothing
    half_life_prjn = 252 * 2 # in days
    lambda_prjn = np.log(2) / half_life_prjn
    probs_prjn = np.exp(-lambda_prjn * (np.arange(0, num_scenarios)[::-1]))
    probs_prjn = probs_prjn / sum(probs_prjn)
    mu_pc, sigma2_pc = rnr.fp_mean_cov(asset_rets.T, probs_prjn)
    # Perform shrinkage to mitigate estimation risk
    mu_shrk, sigma2_shrk = rnr.simple_shrinkage(mu_pc, sigma2_pc)
    weights, _, _ = rnr.efficient_frontier_qp_rets(context.n_portfolio, 
                                                          sigma2_shrk, mu_shrk)
    print('Optimal weights calculated 1 day before month end on %s (day=%s)' \
        % (,
    min_var_weights = weights[0,:]
    # Rebalance portfolio accordingly
    for stock, weight in zip(prices.columns, min_var_weights):
        order_target_percent(stock, np.asscalar(weight))
    context.weights = min_var_weights
def record_vars(context, data):
    record(weights=context.weights, tau=context.tau)
def analyze(perf, bm_value, start_idx):
        .iloc[start_idx:,:].plot(title='Portfolio Performance vs Benchmark',\
        figsize=(10, 8))

if __name__ == '__main__':
    from datetime import datetime
    import pytz
    from zipline.algorithm import TradingAlgorithm
    from zipline.utils.factory import load_bars_from_yahoo
    import pandas as pd
    import matplotlib.pyplot as plt
    # Create and run the algorithm.
    algo = TradingAlgorithm(initialize=initialize, handle_data=handle_data)

    start = datetime(2010, 5, 1, 0, 0, 0, 0, pytz.utc)
    end = datetime(2016, 5, 31, 0, 0, 0, 0, pytz.utc)
    print('Getting Yahoo data for 30 DJIA stocks and DIA ETF as benchmark...')
    data = load_bars_from_yahoo(stocks=tickers, start=start, end=end)
    # Check price data
    data.loc[:, :, 'price'].plot(figsize=(8,7), title='Input Price Data')
    plt.ylabel('price in $');
    plt.legend(loc='center left', bbox_to_anchor=(1.0, 0.5))
    # Run algorithm
    results =
    # Fix possible issue with timezone
    results.index = results.index.normalize()
    if results.index.tzinfo is None:
        results.index = results.index.tz_localize('UTC')
    # Adjust benchmark returns for delayed trading due to 3 year min data window 
    bm_rets = algo.perf_tracker.all_benchmark_returns
    bm_rets[0:algo.first_rebal_idx + 2] = 0 = 'DIA'
    bm_rets.index.freq = None
    bm_value = algo.capital_base * np.cumprod(1+bm_rets)
    # Plot portfolio and benchmark values
    analyze(results, bm_value, algo.first_rebal_idx + 1)
    print('End value portfolio = {:.0f}'.format(results.portfolio_value.ix[-1]))
    print('End value benchmark = {:.0f}'.format(bm_value[-1]))
    # Plot end weights
    pd.DataFrame(results.weights.ix[-1], index=asset_tickers, columns=['w'])\
        .sort_values('w', ascending=False).plot(kind='bar', \
        title='End Simulation Weights', legend=None, figsize=(10, 8));
Getting Yahoo data for 30 DJIA stocks and DIA ETF as benchmark...
C:\Anaconda3\envs\py34\lib\site-packages\ipykernel\ DeprecationWarning:
load_bars_from_yahoo is deprecated, please register a yahoo_equities data bundle instead
Setup investable assets...
Starting dynamic allocation simulation...
Optimal weights calculated 1 day before month end on 2013-05-30 (day=774)
Optimal weights calculated 1 day before month end on 2013-06-27 (day=794)
Optimal weights calculated 1 day before month end on 2013-07-30 (day=816)
Optimal weights calculated 1 day before month end on 2016-03-30 (day=1487)
Optimal weights calculated 1 day before month end on 2016-04-28 (day=1508)
Optimal weights calculated 1 day before month end on 2016-05-27 (day=1529)
End value portfolio = 130872
End value benchmark = 125771