Portfolio Selection

## Summary
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Portfolio selection is the process of choosing a group of investments that aligns with your financial goals and risk tolerance. It involves finding the right balance between potentially high-return, high-risk investments and lower-risk, lower-return options. By diversifying your portfolio across different asset classes, you aim to reduce overall risk without sacrificing potential returns.

## Description
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Modern Portfolio Theory (MPT), developed by Harry Markowitz, is a cornerstone of portfolio selection. MPT emphasizes diversification – spreading the investments across different asset classes to reduce overall risk. The theory suggests that a portfolio's risk isn't just about the individual risk of each investment, but also how their returns are correlated. Assets with low correlation can help balance your portfolio, meaning a loss in one area can be offset by gains in another. The underlying distribution, risk-return trade-off, and efficient frontier are key concepts in MPT portfolio selection.

From the lecture, we also learned the robust version of MPT, the Black-Litterman Model, incorporating an investor's views and opinions about the market along with market data. From the game theory and optimization aspect, portfolio selection could be seen as an online linear optimization algorithm, one of the problems is the complexity to achieve the optimal solution. Here, we want to investigate portfolio selection from different views and compare the methods.

## Source
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Jose Blanchet, Lin Chen, Xun Yu Zhou (2022) Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances. Management Science 68(9):6382-6410.
https://doi.org/10.1287/mnsc.2021.4155

Data-dependent bounds for online portfolio selection without Lipschitzness and smoothness (http://arxiv.org/abs/2305.13946), NeurIPS 2023. C.-E. Tsai, Y.-T. Lin, and Y.-H. Li

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## Others
> Portfolio selection is a complex field with ongoing research. There are several points to consider, including risk tolerance, investment time horizon (the gap between theoretically estimated reward and real-world reward), and rebalancing.