## Introduction

In previous post we reviewed the basics of mean-variance optimization (MVO), and portfolios such as minimum variance and maximmum sharpe. This post continues to discuss some popular practices in asset allocation, namely risk parity and maximum diversification. Then we evaluate these allocation strategies using historical market data.

It is known that all these portfolios are special cases of MVO under some conditions. For example, MVO becomes minimum variance if expected reutrns are equal; it coincides with maximum diversification if return-risk ratios are the same across assets ([2]). The portfolio selection depends on our information and knowledge about the market. If expected return and risks are known with certainty, a maximum sharpe ratio is good choice. If expected return is hard to measure, covariance knowledge can be leveraged to construct minimum variance or risk parity portfolios. If we have no knowledge at all about the market, a naive equal-weighting portfolio will be a default option, which is also served as benchmark in our backtest.