Diversification and Correlation Inside a Portfolio

What you will learn

• The difference between company-specific risk and market risk, and which one diversification removes.
• How to calculate the volatility of a two-asset portfolio from weights, volatilities and correlation.
• How to detect overlap when you combine several ETFs.
• Why correlations are not stable, especially in crises.

Explanation

Correlation between open trades was covered in the risk-management course ("Correlation and Portfolio Heat"). Here we apply it to long-term portfolios.

The risk of a single stock has two parts. Idiosyncratic risk (company-specific risk) comes from events at one company, such as a failed product. Systematic risk (market risk) affects almost all companies, such as a recession. Holding many companies across sectors and countries reduces idiosyncratic risk strongly, because company events partly cancel out. Systematic risk remains: a broad equity ETF can still fall by around half in a severe bear market.

Risk is often measured by volatility (σ, sigma): the annualised standard deviation of returns. Correlation (ρ, rho) measures how two returns move together, from −1 (opposite) through 0 (unrelated) to +1 (perfectly together). For a portfolio of two assets with weights w₁ and w₂:

σ_p = √( w₁²σ₁² + w₂²σ₂² + 2·w₁·w₂·ρ·σ₁·σ₂ )

Only if ρ = +1 is the portfolio volatility equal to the weighted average of the two volatilities. With any correlation below +1, it is lower. This "free" risk reduction is the core of diversification.

Three practical rules:

• Diversify across return drivers, not product names. Two ETFs on different but overlapping indices (for example MSCI World and S&P 500) mostly hold the same large US companies. Adding the second one increases concentration.
• Correlations change. In sharp sell-offs, many risky assets fall together and correlations rise. Equities and high-quality government bonds have sometimes moved in opposite directions, but in some periods (for example when inflation and interest rates rose quickly) both fell. Treat historical correlation as an observation, not a promise.
• More is not always better. Beyond a broad global equity fund, extra equity ETFs often add little diversification but more complexity. Real diversification comes mainly from adding different asset classes, covered in the next lesson.

Worked example

Hypothetical example: a portfolio holds 60% in an equity ETF and 40% in a bond ETF. Assumed volatilities: equities σ₁ = 16%, bonds σ₂ = 6%. All figures are hypothetical; costs and taxes are excluded.

1. Weighted average volatility (what you would get with ρ = +1): 0.6 × 16% + 0.4 × 6% = 12.0%.
2. Common terms: w₁²σ₁² = 0.36 × 0.0256 = 0.009216; w₂²σ₂² = 0.16 × 0.0036 = 0.000576; 2·w₁·w₂·σ₁·σ₂ = 2 × 0.6 × 0.4 × 0.16 × 0.06 = 0.004608.
3. With ρ = 0.8: variance = 0.009216 + 0.000576 + 0.8 × 0.004608 = 0.013478; σ_p = √0.013478 ≈ 11.6%.
4. With ρ = 0.2: variance = 0.009792 + 0.2 × 0.004608 = 0.010714; σ_p ≈ 10.4%.
5. With ρ = −0.2: variance = 0.009792 − 0.000922 = 0.008870; σ_p ≈ 9.4%.

Overlap check: an investor holds 50% in a world ETF with a hypothetical 70% US weight and 50% in an S&P 500 ETF (100% US). US share = 0.5 × 70% + 0.5 × 100% = 85%. Two funds, but more country concentration than either world fund alone.

Common mistake

Practice activity

On paper: a portfolio is 50% asset X (σ = 20%) and 50% asset Y (σ = 10%).

1. Calculate the portfolio volatility for ρ = 0.5 and for ρ = 0.
2. Compare both results with the weighted average volatility.

Key takeaways

• Diversification removes much company-specific risk but not market risk.
• Portfolio volatility is below the weighted average whenever correlation is below +1.
• Check overlap: different ETF names can hold the same companies.
• Correlations are unstable and often rise in crises; plan with caution.

Next step

Next, you will use these ideas to choose a mix of equities, bonds and cash that fits your risk level.