Back to Community
Why does maximizing returns perform worse than maximizing (price - price*returns)

I don't understand why maximizing returns yields much worse performance than maximizing (price - price*returns).

I've attached my returns maximization algorithm here.

Clone Algorithm
1
Loading...
Total Returns
--
Alpha
--
Beta
--
Sharpe
--
Sortino
--
Max Drawdown
--
Benchmark Returns
--
Volatility
--
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 quantopian.algorithm as algo
from quantopian.pipeline import Pipeline
from quantopian.pipeline.data import Fundamentals
from quantopian.pipeline.filters import QTradableStocksUS
import quantopian.optimize as opt
from quantopian.pipeline.experimental import risk_loading_pipeline
from quantopian.pipeline.factors import SimpleBeta,Returns
from quantopian.pipeline.data.builtin import USEquityPricing
from quantopian.pipeline.data import EquityPricing
import numpy as np
import pandas as pd

def initialize(context):
    beta = SimpleBeta(
           target=sid(8554),
           regression_length=260,
                    )
    pipe_beta = Pipeline(
        columns={
            'beta': beta,
        },
        screen=beta.notnull(),
    )
    algo.attach_pipeline(pipe_beta, 'pipe_beta')
    algo.attach_pipeline(risk_loading_pipeline(), 'risk_factors')
    algo.attach_pipeline(returns_pipeline(), 'returns')

    algo.schedule_function(
        rebalance,
        algo.date_rules.every_day(),
        algo.time_rules.market_open(hours=1),
    )
    
def returns_pipeline():
    base_universe = QTradableStocksUS()
    pipe = Pipeline(
        columns={
        'Returns': Returns(window_length=2),
            },
        screen=base_universe)
    return pipe

def before_trading_start(context, data):
    context.returns = algo.pipeline_output('returns')
    context.pipeline_beta_data = algo.pipeline_output('pipe_beta')
    context.risk_loadings = algo.pipeline_output('risk_factors')

def constraints(context):
    constraints = []
    pipe_beta_data = context.pipeline_beta_data.dropna()
    beta_neutral = opt.FactorExposure(
        pipe_beta_data[['beta']],
        min_exposures={'beta': -0.05},
        max_exposures={'beta': 0.05},
    )
    constraints.append(beta_neutral)
    MAX_GROSS_LEVERAGE = 1.05
    constrain_gross_leverage = opt.MaxGrossExposure(MAX_GROSS_LEVERAGE)
    constraints.append(constrain_gross_leverage)
    dollar_neutral = opt.DollarNeutral()
    constraints.append(dollar_neutral)
    MAX_SHORT_POSITION_SIZE = 0.01  # 1%
    MAX_LONG_POSITION_SIZE = 0.01   # 1%
    # Define the position concentration constraint.
    constrain_pos_size = opt.PositionConcentration.with_equal_bounds(
        -MAX_SHORT_POSITION_SIZE,
        MAX_LONG_POSITION_SIZE,
    )
    constraints.append(constrain_pos_size)
    risk_loadings = context.risk_loadings
    constrain_sector_style_risk = opt.experimental.RiskModelExposure(  
        risk_model_loadings=risk_loadings,  
        version=opt.Newest,
        #min_momentum=-0.1,  
        #max_momentum=0.1,
    )
    constraints.append(constrain_sector_style_risk)
    return constraints
def rebalance(context, data):
    returns = context.returns.dropna()
    objective = opt.MaximizeAlpha(returns['Returns'])
    algo.order_optimal_portfolio(objective = objective,
            constraints=constraints(context)
            ,)
There was a runtime error.
7 responses

And here's the maximizing (price - price*returns)

Clone Algorithm
3
Loading...
Total Returns
--
Alpha
--
Beta
--
Sharpe
--
Sortino
--
Max Drawdown
--
Benchmark Returns
--
Volatility
--
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 quantopian.algorithm as algo
from quantopian.pipeline import Pipeline
from quantopian.pipeline.data import Fundamentals
from quantopian.pipeline.filters import QTradableStocksUS
import quantopian.optimize as opt
from quantopian.pipeline.experimental import risk_loading_pipeline
from quantopian.pipeline.factors import SimpleBeta,Returns
from quantopian.pipeline.data.builtin import USEquityPricing
from quantopian.pipeline.data import EquityPricing
import numpy as np
import pandas as pd

def initialize(context):
    beta = SimpleBeta(
           target=sid(8554),
           regression_length=260,
                    )
    pipe_beta = Pipeline(
        columns={
            'beta': beta,
        },
        screen=beta.notnull(),
    )
    algo.attach_pipeline(pipe_beta, 'pipe_beta')
    algo.attach_pipeline(risk_loading_pipeline(), 'risk_factors')
    algo.attach_pipeline(returns_pipeline(), 'returns')

    algo.schedule_function(
        rebalance,
        algo.date_rules.every_day(),
        algo.time_rules.market_open(hours=1),
    )
    
def returns_pipeline():
    base_universe = QTradableStocksUS()
    pipe = Pipeline(
        columns={
        'Returns': Returns(window_length=2),
            },
        screen=base_universe)
    return pipe

def before_trading_start(context, data):
    context.returns = algo.pipeline_output('returns')
    context.pipeline_beta_data = algo.pipeline_output('pipe_beta')
    context.risk_loadings = algo.pipeline_output('risk_factors')

def constraints(context):
    constraints = []
    pipe_beta_data = context.pipeline_beta_data.dropna()
    beta_neutral = opt.FactorExposure(
        pipe_beta_data[['beta']],
        min_exposures={'beta': -0.05},
        max_exposures={'beta': 0.05},
    )
    constraints.append(beta_neutral)
    MAX_GROSS_LEVERAGE = 1.05
    constrain_gross_leverage = opt.MaxGrossExposure(MAX_GROSS_LEVERAGE)
    constraints.append(constrain_gross_leverage)
    dollar_neutral = opt.DollarNeutral()
    constraints.append(dollar_neutral)
    MAX_SHORT_POSITION_SIZE = 0.01  # 1%
    MAX_LONG_POSITION_SIZE = 0.01   # 1%
    # Define the position concentration constraint.
    constrain_pos_size = opt.PositionConcentration.with_equal_bounds(
        -MAX_SHORT_POSITION_SIZE,
        MAX_LONG_POSITION_SIZE,
    )
    constraints.append(constrain_pos_size)
    risk_loadings = context.risk_loadings
    constrain_sector_style_risk = opt.experimental.RiskModelExposure(  
        risk_model_loadings=risk_loadings,  
        version=opt.Newest,
        #min_momentum=-0.1,  
        #max_momentum=0.1,
    )
    constraints.append(constrain_sector_style_risk)
    return constraints
def rebalance(context, data):
    returns = context.returns.dropna()
    returnsAdj = data.current(returns.index,'price')  
    - returns['Returns']*data.current(returns.index,'price')
    objective = opt.MaximizeAlpha(returnsAdj)
    algo.order_optimal_portfolio(objective = objective,
            constraints=constraints(context)
            ,)
There was a runtime error.

You observe that Max(returns) results in worse performance than Max(price - price*returns) = Max(price*(1-returns)).
Honestly i don't know the answer, but i think your returns are 1-day returns, right?
So that seems to me to imply that there is a tendency for higher prices (positive 1 d returns) generally to be followed by lower prices (negative 1d returns), which is consistent with a general tendency toward short-term Mean-Reversion type of behavior. Does that make sense?

It makes sense in theory, but I've extended the time window and am seeing the same thing.

They are one day returns but I get similar results for 20 days (pure returns is only down 20%). For 200 days pure returns has a positive return (about 5%) and (price - price*returns) has returns of ~10% - slightly worse than the shorter time windows.

One question. What is the term price - price*returns or, written another way price*(1-returns), supposed to represent? It's probably obvious but help me out.

Disclaimer

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.

It's mean reversion adjusted price. The price of yesterday

I am very sorry. Still don't get it. Wouldn't yesterday's adjusted price be

price_yesterday = price / (1 + returns)

# Start with the definition of returns then do some algebra...  
returns = (price - price_yesterday) / price_yesterday  
returns = (price/price_yesterday) - (price_yesterday/price_yesterday)  
returns = (price/price_yesterday) - 1  
1 + returns = price/price_yesterday  
price_yesterday = price / (1 + returns)

Yes, by means reversion adjusted price I mean that the returns revert to the mean - so if the returns were X yesterday tomorrow they will be X-1 (obviously this is not exact - but it proves to be a better predictor than returns alone). Sorry if I wasn't clear.