如何用更小的风险，换取尽量高的投资收益？

Core Concept - The article emphasizes the importance of understanding the "collaboration" between assets in investment allocation, which is mathematically represented by "correlation" [3][4]. Asset Allocation Principles - Ideal investment portfolios should consist of assets with varying correlations: assets with a correlation close to +1 move together, those with a correlation close to -1 move inversely, and those with a correlation close to 0 operate independently [4]. - The modern portfolio theory proposed by Nobel laureate Harry Markowitz suggests that scientific diversification can significantly reduce risk without sacrificing returns [4]. Mathematical Framework - For perfectly negatively correlated assets (correlation of -1), the allocation ratio should be inversely proportional to their volatility. If two funds have the same volatility, equal allocation is appropriate [5][7]. - If the volatilities differ, the allocation should favor the asset with lower volatility. For example, if Fund A has a volatility of 10% and Fund B has 30%, the optimal allocation would be 75% in Fund A and 25% in Fund B [7]. - For assets with a correlation close to 0, the allocation ratio should be inversely proportional to the square of their volatility. This allows for optimization of the risk-return profile even among uncorrelated assets [10][13]. Investment Insights - Including negatively correlated assets in a portfolio can effectively reduce overall volatility. While perfectly negatively correlated assets are rare, seeking low or negatively correlated assets remains a valid strategy for optimizing investment portfolios [9]. - The article illustrates that even with uncorrelated assets, appropriate weight allocation can enhance the risk-return ratio. For instance, a combination of five uncorrelated assets can reduce volatility significantly compared to individual assets [15]. Addressing Concerns about Returns - The article argues that proper asset allocation does not diminish returns; rather, it can stabilize and enhance them. The key is to select high-performing assets rather than diversifying for the sake of it [17]. - Examples provided include combining U.S. stocks with A-shares, both of which have long-term annualized returns of around 8-10%, resulting in a stable combined return while reducing volatility [17]. Practical Guidelines for Portfolio Construction - Step 1: Diversify across major asset classes such as stocks (high long-term returns, high volatility), bonds (stable returns, low volatility), and commodities (inflation hedge) [21]. - Step 2: Diversify by region and strategy, investing in various markets and styles to mitigate risks [21]. - Step 3: Regularly rebalance the portfolio to maintain the desired asset allocation, selling portions of assets that have appreciated significantly and buying those that have declined [21].