Nov
9

## Combined Portfolio Construction Strategies

A short summary of an excellent paper "Markowitz Meets Talmud: A Combination of Sophisticated and Naive Diversification Strategies" by Jun Tu and Guofu Zhou, published at Journal of Financial Economics, July, 2010.

where the combination parameter delta lies between 0 and 1. Our purpose is to calculate the parameter delta by minimizing the loss function given by

Luckily we could get a closed-form solution, please refer to the original paper for detail.

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**Motivation**: The modern portfolio theory pioneered by Markowitz (1952) is widely used in practice, but its value is questionable since the estimated Markowitz's optimal portfolio rule and its various sophisticated extensions not only underperform the naive 1/N rule proposed by Talmud (that invests equally across N assets), but also lose money on a risk-adjusted basis in many real data sets when the sample size is small. Can we combine these two types of strategies to achieve a better performance?**Argument**: As the Markowitz's method is unbiased but with sizable variance when the sample size is small, 1/N is biased but without variance, a combination of them is thus decreasing biases and increasing variance compared with simple 1/N rule.**Method**: let w(e) be the equal weight for each asset, w(bar) be the weight generated by those sophisticated models such as Markowitz, the combined weight iswhere the combination parameter delta lies between 0 and 1. Our purpose is to calculate the parameter delta by minimizing the loss function given by

Luckily we could get a closed-form solution, please refer to the original paper for detail.

**Conclusion**: In short,when applied to the real datasets, the combination rules generally improve from their uncombined Markowitz-type counterparts and can perform consistently well, and some of them can outperform the 1/N rule in most of the cases. However, the authors applied their model to a very limited data sample, more backtesting is required before applying.**People viewing this post also viewed:**

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