Two-Asset Portfolio

Slide weights and correlation; watch portfolio σ shift along the two-asset frontier. The simplest demonstration of why diversification works.

Slide the weight of asset A. Watch portfolio standard deviation move along the two-asset frontier. Lower correlation → more diversification benefit.

Asset A — S&P 500 (stocks)

E[r] %10.0

σ %18.0

Asset B — US 10y T-Note (bonds)

E[r] %4.0

σ %7.0

Correlation ρ0.10

Weight of A: 60%0.60

Closed-form MVP weight (w_A):10.47%

E[r_p]

7.60%

σ_p

11.42%

Sharpe (rf=0)

0.67

The two-asset frontier shows every weighted blend of A and B. The MVP (orange) is the single point with the lowest σ. Lower correlation pushes the curve further left — that's the diversification benefit, the only "free lunch" in finance.

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.

Every Lab is grounded in standard textbook math (Bodie / Kane / Marcus, Fabozzi, Tandelilin). Read the full methodology in the How It Works panel above.