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Momentum Based ETF Portfolio RebalancingOptimizing Portfolio Construction For Optimal Sharpe Ratio
www.quantconnect.com
Jared Broad
CEO and Founder
We’ve built a web algorithm lab where thousands of
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April-2018 QuantConnect – Momentum Based ETF Portfolio Rebalancing Page 2
Outline
▪ Basics of Mean Variance Portfolio Construction
▪ Defining Optimization Function
▪ LEAN Algorithm Framework
▪ Implementing Our Model
▪ Testing and Researching
▪ Summary
April-2018 QuantConnect – Momentum Based ETF Portfolio Rebalancing Page 3
Reduce volatility, increase returns by
calculating optimal weight allocation of a
portfolio for minimum volatility.
Core Idea:
1) Create an estimate of returns and volatility.
2) Build portfolio of assets; allocating to each by weight.
3) Optimize weights to minimize the volatility in portfolio.
Classic Mean Variance Portfolio Construction
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Classic Mean Variance Portfolio Construction
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$-
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Jan-18 Feb-18 Mar-18 Apr-18 May-18 Jun-18 Jul-18 Aug-18 Sep-18 Oct-18
Stock A Stock B
Ideal = 50-50
Classic Mean Variance Portfolio Construction
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$-
$2.00
$4.00
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Jan-18 Feb-18 Mar-18 Apr-18 May-18 Jun-18 Jul-18 Aug-18 Sep-18 Oct-18
Stock A Stock B Stock C
Stock D Stock E Stock F
Stock G Stock H
Most real world applications have portfolios of many assets. We are seeking to find best balance of hundreds of assets.
Mean Variance Optimization Function
April-2018 QuantConnect – Momentum Based ETF Portfolio Rebalancing Page 7
Optimizers experiment with portfolios; seeking to
minimize the objective function.
Classic Mean Variance Optimization the objective
function seeks to minimize expected volatility.
Redefining Our Objective
April-2018 QuantConnect – Momentum Based ETF Portfolio Rebalancing Page 8
We will seek to optimize Sharpe Ratio instead of volatility; seeking to
minimize objective function:
𝑥 = min(𝐴𝑛𝑛𝑢𝑎𝑙 𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑅𝑒𝑡𝑢𝑟𝑛
𝑉𝑎𝑟)
This approximates the traditional Sharpe Ratio function and serves as
our weighting target.
Algorithm Framework Modules
April-2018 QuantConnect – Momentum Based ETF Portfolio Rebalancing Page 9
Assumptions and Limitations
❖ Mean Variance Optimization requires expected returns and we provide historical
values. We’re making an assumption these returns will continue in the future.
❖ Most variance approximations assume a normal distribution.
❖ Any estimation error in the return prediction magnified.
❖ The resulting portfolios can be concentrated and nonsensical. In practice its more
common to use Black-Litterman method.
April-2018 QuantConnect – Momentum Based ETF Portfolio Rebalancing Page 10
Code and Implementation
April-2018 QuantConnect – Momentum Based ETF Portfolio Rebalancing Page 11
Backtest
Summary
❖ Using portfolio construction techniques we can automatically assign weights
to our portfolio assets.
❖ This reduces the number of variables we manually define; can improve returns
and lower volatility.
Next Steps – Investigate more robust portfolio construction techniques!
(E.g. Black-Litterman).
Total Trades Drawdown Net Profit Sharpe Ratio
270 12.9% 34% 0.555
April-2018 QuantConnect – Momentum Based ETF Portfolio Rebalancing Page 12
www.quantconnect.com Thank you.
Appendix
Our Research Environment
April-2018 QuantConnect – Momentum Based ETF Portfolio Rebalancing Page 15
Coding the Idea, The Algorithm Lab
April-2018 QuantConnect – Momentum Based ETF Portfolio Rebalancing Page 16
Going Live, Deploying to Live Trading
April-2018 QuantConnect – Momentum Based ETF Portfolio Rebalancing Page 17
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