Portfolio Diversification

Diversification is the cornerstone of modern portfolio construction. By combining assets that do not move perfectly together, investors can reduce portfolio risk without necessarily sacrificing expected returns. As the saying goes, "Don't put all your eggs in one basket"--but understanding why this works requires mastering correlation.

The Correlation Coefficient

Correlation measures the strength and direction of the relationship between two variables. In portfolio theory, the correlation coefficient (represented by the Greek letter rho, r, or sometimes r) indicates how two assets move relative to each other.

Correlation ranges from -1 to +1:

Key insight: Diversification benefits begin anytime correlation is less than +1. You do not need negative correlation to benefit from diversification--even assets with correlation of +0.8 provide some risk reduction.

CFP Exam Tip: The maximum diversification benefit occurs at correlation of -1, but in practice, most asset class correlations are positive. Finding assets with low positive correlation (0.2-0.5) is typically the realistic goal.

How Correlation Affects Portfolio Risk

When combining assets, portfolio risk depends on three factors:

1. Individual asset volatilities (standard deviations)
2. Portfolio weights
3. Correlation between assets

Portfolio Variance Formula (Two Assets):

Portfolio Variance = w1^2 * s1^2 + w2^2 * s2^2 + 2 * w1 * w2 * s1 * s2 * r12

Where:

• w1, w2 = portfolio weights
• s1, s2 = standard deviations
• r12 = correlation coefficient

Example: Consider two assets, each with 20% standard deviation and equal weights (50% each):

As correlation decreases, portfolio risk drops significantly, even when individual asset risks remain unchanged.

How Many Securities Provide Adequate Diversification?

Research consistently shows that 20-30 randomly selected securities eliminate most diversifiable (unsystematic) risk. Beyond this point, adding more securities provides diminishing marginal benefit.

The Numbers:

• 1 stock: 100% unsystematic risk
• 10 stocks: ~27% unsystematic risk remaining
• 20 stocks: ~12% unsystematic risk remaining
• 30 stocks: ~8% unsystematic risk remaining
• 50+ stocks: Approaches systematic risk only

Key Takeaway: The risk reduction curve is steep at first but flattens quickly. Going from 1 to 20 stocks provides enormous benefit; going from 20 to 100 stocks provides relatively little additional protection.

CFP Exam Tip: Remember that 20-30 securities are needed for adequate diversification. This is a commonly tested concept. Beyond 30 securities, diversification benefits diminish rapidly.

Systematic vs. Unsystematic Risk

Unsystematic Risk (Diversifiable Risk):

• Company-specific or industry-specific risk
• Examples: Management changes, product recalls, lawsuits, labor strikes
• CAN be eliminated through diversification
• Also called: unique risk, firm-specific risk, idiosyncratic risk

Systematic Risk (Non-Diversifiable Risk):

• Market-wide risk affecting all securities
• Examples: Interest rate changes, inflation, recessions, geopolitical events
• CANNOT be eliminated through diversification
• Also called: market risk, non-diversifiable risk
• Measured by beta

International Diversification

Benefits of international diversification:

• Exposure to different economic cycles
• Access to faster-growing markets
• Reduced dependence on single country's economy
• Lower correlation with domestic assets (though correlations have increased over time)
• Currency exposure can add return and diversification

Challenges of international diversification:

• Currency risk (exchange rate fluctuations)
• Political and regulatory risk
• Different accounting standards
• Higher transaction costs
• Time zone and liquidity issues
• Withholding taxes on dividends

Currency Risk in International Investing

When investing internationally, returns come from two sources:

1. Local market return (in foreign currency)
2. Currency return (exchange rate change)

Total Return = Local Return + Currency Return + (Local Return x Currency Return)

Example: A U.S. investor buys European stocks:

• European stocks rise 10% in euros
• Euro depreciates 5% against dollar
• Approximate total return: 10% - 5% = 5%
• (Actual: 1.10 x 0.95 - 1 = 4.5%)

Currency risk can hurt or help:

• If foreign currency strengthens: Currency adds to returns
• If foreign currency weakens: Currency detracts from returns
• Unhedged exposure provides some diversification benefit
• Currency movements can be as volatile as equity returns

Currency Hedging Strategies

Hedged vs. Unhedged International Investing:

Research findings on hedging:

• For international bonds: Hedging is generally recommended (bond-like returns with bond-like volatility)
• For international equities: Mixed results; some studies suggest hedging reduces diversification benefits
• Currency-hedged international equity has outperformed unhedged in some periods

Hedging instruments:

• Forward contracts: Most common for institutional hedging
• Currency futures: Exchange-traded, standardized
• Currency options: Asymmetric protection, premium cost
• Currency ETFs: Accessible for retail investors

ADRs and Currency Risk

American Depositary Receipts (ADRs) provide convenient access to foreign stocks:

• Trade on U.S. exchanges in U.S. dollars
• Dividends paid in U.S. dollars
• Subject to U.S. securities regulations

Critical point: ADRs do NOT eliminate currency risk. The underlying shares still trade in foreign currency, so exchange rate changes affect ADR value.

CFP Exam Tip: This is frequently tested--ADRs trade in dollars but do NOT eliminate currency risk. The convenience of dollar-denominated trading does not remove the underlying currency exposure.

Correlation in Practice

Typical Asset Class Correlations (Approximate):

Important observations:

• Stock-bond correlation is relatively low, making bonds good diversifiers
• International stock correlations with U.S. have increased over time (globalization)
• During market crises, correlations tend to increase (when diversification is needed most)
• Alternative investments (hedge funds, private equity) may offer lower correlations