双资产投资组合

滑动权重和相关性；观察组合 σ 沿双资产前沿移动。展示分散化为何有效的最简单方法。

滑动资产 A 的权重。观察组合标准差沿两资产前沿移动。相关性越低 → 分散化收益越大。

选择任意 2 项资产 — 拉取实时 μ、σ、ρ

资产 A

Mix any combination — e.g. NVDA + BTC-USD + GLD + AGG. Type a ticker not in the list to add it as a custom asset.

资产 B

Mix any combination — e.g. NVDA + BTC-USD + GLD + AGG. Type a ticker not in the list to add it as a custom asset.

资产 A — S&P 500 (stocks)

E[r] %

σ %

资产 B — US 10y T-Note (bonds)

E[r] %

σ %

相关性 ρ

A 的权重: 60%

闭式 MVP 权重 (w_A):10.47%

E[r_p]

7.60%

σ_p

11.42%

Sharpe (rf=0)

0.67

两资产前沿显示 A 与 B 所有加权组合。MVP (橙色) 是 σ 最低的唯一点。相关性越低,曲线越向左推——这就是分散化收益,金融中唯一的 "免费午餐"。

When you mix two assets, the portfolio return is just the weighted average of the two returns. But the volatility is NOT a simple average - it depends on correlation. When ρ < 1, you get diversification: the portfolio is less volatile than a weighted average would suggest. That's the magic Markowitz formalised.

每个实验室都基于标准教科书数学（Bodie / Kane / Marcus、Fabozzi、Tandelilin）。 Read the full methodology in the How It Works panel above.