This project is a result of the seminar Asset Management: Applied Portfolio Theory, held at University of Zurich in 2019.
The presentation PDF can be found here.
The implementation is based on Matlab R2019b using the Optimization Toolbox and the Financial Toolbox.
The following portfolio optimization techniques were implemented:
- Equal-weighted (1/N)
- Minimum Variance (MV)
- Maximum Sharpe Ratio (MSR)
- Equal Risk Contribution (ERC)
Shrinkage
The well-known Shrinkage method for covariance matrices has been applied, see Chen et al. (2010).
Two datasets were used:
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13 assets constisting of bonds, equities, commodities and alternative investments; heterogeneous assets.
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Dow Jones Industrial Average 30 (DJIA30), consisting of the 30 largest US corporations; homogeneous assets.
Each model's performance was assessed using OAS shrinkage of covariance matrix:
Performance
Allocation over time
Risk contribution over time
Each model's performance was assessed using OAS shrinkage of covariance matrix:
Performance
Allocation over time
Risk contribution over time
Minimum Variance method shows solid out-of-sample performance, the allocation over time is stable (including OAS covariance shrinkage), but suffers from concentration problem in low variance assets, i.e. Cash and Bonds. It does not incorporate any information about expected returns, only risk.
Maximum Sharpe Ratio method shows very unstable allocation over time (including OAS covariance shrinkage), and suffers from concentration problem in high Sharpe ratio assets, i.e. Cash and Bonds. It incorporates information about risk and return, but at the cost of an additional variable which needs to be estimated (if possible at all). The exponential smoothing used for returns estimation needs to be replaced with a better estimator in order to use this method.
Equal Risk Contribution method shows solid out-of-sample performance. The allocation over time is stable (including OAS covariance shrinkage), and suffers less from a weight concentration problem. The weight allocation is inversly proportional to the risk contribution of each asset to the portfolio. It does not incorporate any information about expected returns, only risk.
From a pure risk diversification standpoint, the risk-only portfolio optimization methods Minimum Variance and Equal Risk Contribution are recommended, because expected returns estimation is inherently difficult and results in the weight concentration problem. The risk-only methods, especially Equal Risk Contribution, tend to diversify well.