Combining Portfolio Strategies and Managing Estimation Risk

# Mixing Portfolio Strategies


# Mixing Portfolio Strategies












Given a set of $N$ assets, the amount of strategies proposed in literature to diversify the investors wealth in order to find the 'optimal' portfolio is overwhelming. However, for example DeMiguel et al point out that estimation error is large in general, leading to bad out-of-sample returns for many sophisticated portfolio strategies.

In my mind it should be a straightforward idea to combine several promising allocation candidates such that the estimation risk is 'diversified' as well. In other words, given a set of portfolio weights proposed by $k$ distinct strategies $\{\omega_1,\ldots,\omega_k\}$, it could be beneficial to compute a vector $c\in\mathbb{R}^k, \left( \sum\limits_{i=1}^{k} c_i =1\right)$ based on some criteria and then investing into $\omega^*:=c_1\omega_1+\ldots +c_k\omega_k$.

I am aware of some ideas combining two portfolios via shrinkage approaches (see for example Posterior Inference for Portfolio Weights and the appendix of Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy?)

but I am would like to learn more about those ideas. Any reference or further comment directing in this direction is welcome to answer my question: What are the benefits and gains from combining several allocation strategies?

## Answer by phdstudent (score 1, accepted)

https://quant.stackexchange.com/a/24656

Not many benefits actually. As you combine different strategies you abstract yourself from what you are trying to reach. E.g. What would you get if you combine a strategy that tries to maximize Sharpe Ratio, with a strategy that maximizes Certain Equivalent? You have no idea on what that would get you. Probably it might even get you a portfolio with high turnover and so high transaction costs.

Even DeMiguel, seems to be moving towards simpler strategies. The 1/N strategy is on example. Another example is to use Parametric Portfolio Policies of Brandt, Santa-Clara and Valkanov. Even DeMiguel on one of his last papers seems to favour this approach: Fifty Ways to Beat the Market? A Portfolio Perspective on Investment Anomalies.

All in all there is no right answer to your question. You should try to mixture several strategies and see out of sample what would you get net of transaction fees. Also, you should clearly define as an investor what is your objective, either by defining that you want the maximum sharpe ratio, or maximum utility given some risk-aversion. Without a clear objective in mind is hard to define what would be the optimal strategy.