This algorithm is the LEAN implementation of the paper Momentum and Markowitz: A Golden Combination from Wouter J. Keller, Adam Butler, and Ilya Kipnis. 

The CAA model here applies mean-variance optimization over a lookback horizon of one year. The return and volatility are calculated with daily resolution and monthly rebalancing.

  •  Data 
  1. The universe includes 7 ETFs of the global market. The risky assets are ETFs of S&P 500 (SPY), EAFE (EFA), MSCI Emerging Markets Index (EEM), JPX-Nikkei 400 (JPXN), Vanguard Information Technology ETF (VGT), The cash-like assets are ETFs of 7-10 Year Treasury Bond(IEF) and 20+ Yr Treasury Bond(TLT). The backtesting period is from 2007 to 2018.
  • Method
  1. Each month we estimate the optimal mix of assets weights based on information from the prior 252 trading days and use that mix for the next month. For the covariance matrix, we used the historical covariance matrix of returns for the trailing twelve months. 
  2. As the mean-variance optimization seeks any optimal set of portfolio weights, There is the potential for the portfolio to become quite concentrated at times. To reduce this possibility, we imposed caps (max weights) on assets to enforce greater diversification as indicated in the paper. E.g. impose a cap of 25% for all risky assets and no cap (i.e. a cap of 100%) for all cash-like assets.
  • Optimization
  1.  For optimization, we tried the different methods like maximizing the Sharpe Ratio, maximizing the return given target volatility stays unchanged (We use 5% as the target volatility). In addition, we also compare the results with the equally weighted algorithm. You could change the target volatility variable in the algorithm to test the defensive and offensive model.

Results are presented below. 

  • <1> Maximizing the Sharpe Ratio