Portfolio Diversification: The Power of Correlation

📊 Portfolio Diversification: Correlation & Risk

Introduction

This demonstrates how combining assets with different correlations reduces portfolio risk.

Asset	Return	Risk (σ)
Asset A	10%	20%
Asset B	8%	15%

Portfolio: w_A = 0.5, w_B = 0.5

σ_p = √[w_A²σ_A² + w_B²σ_B² + 2w_Aw_Bσ_Aσ_Bρ]

Interactive Calculator

Adjust correlation (ρ):

ρ = -1 ρ = 0 ρ = +1

ρ = +1.00

Risk: 17.5%

Current Calculation:

σ_p = √[0.01 + 0.005625 + 0.015] = 17.5%

With perfect positive correlation (ρ = +1), no diversification benefit.

Diversification Benefit:

0%

Fixed Correlation Cases

Case 1: ρ = +1

Perfect positive correlation

√[0.01 + 0.005625 + 0.015] = 17.5%

17.5%

No diversification

Case 2: ρ = 0

Zero correlation

√[0.01 + 0.005625 + 0] = 12.5%

12.5%

28.6% less risk

Case 3: ρ = -1

Perfect negative correlation

√[0.01 + 0.005625 - 0.015] = 2.5%

2.5%

85.7% less risk

Summary Table

Correlation (ρ)	Portfolio Risk	Diversification	Risk Reduction
+1 (Perfect Positive)	17.5%	None	0%
0 (No Correlation)	12.5%	Moderate	28.6%
-1 (Perfect Negative)	2.5%	Maximum	85.7%

Risk vs Correlation

Key Insights

Lower correlation = Lower risk: As ρ decreases, portfolio risk falls dramatically.

Negative correlation maximizes benefits: When assets move opposite directions, risk reduction is greatest.

Diversification works: Combining uncorrelated assets reduces overall portfolio volatility.

Practical application: Seek assets with low/negative correlation to build efficient portfolios.

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