APT 3: Portfolio Diversification
Diversification means spreading money across many investments so one bad surprise does less damage. It works because stocks do not move perfectly together. The lower the correlation between holdings, the more firm-specific risk cancels out, leaving mostly market risk behind.
What you will learn
- Why holding more stocks lowers portfolio risk
- How correlation drives the size of the diversification benefit
- The two-asset portfolio variance formula
- Why risk falls toward a floor of market (systematic) risk
- How diversification links to the APT and CAPM view of risk
The formulas
- w_A, w_B
- portfolio weights (sum to 1)
- σ_A, σ_B
- standard deviations of each asset
- ρ_AB
- correlation between the two assets
- N
- number of stocks
- average covariance
- the part that remains as N grows: systematic risk
Worked example
You split money 50/50 between Stock A (σ = 30%) and Stock B (σ = 20%). Their correlation is 0.2. What is the portfolio's standard deviation?
- A's part: 0.5² × 0.30² = 0.0225
- B's part: 0.5² × 0.20² = 0.0100
- Covariance part: 2 × 0.5 × 0.5 × 0.2 × 0.30 × 0.20 = 0.0060
- Portfolio variance = 0.0225 + 0.0100 + 0.0060 = 0.0385
- Standard deviation = √0.0385 ≈ 19.6%
Answer: Portfolio standard deviation ≈ 19.6%, well below the 25% weighted average of the two stocks.
Common questions
How does diversification reduce risk?
When you hold several investments that do not move perfectly together, losses in some are partly offset by gains or smaller losses in others. Company-specific surprises cancel out, so the portfolio swings less than the average of its individual holdings.
How does correlation affect diversification?
The lower the correlation between assets, the bigger the risk reduction. With a correlation of +1 there is no benefit. With correlations below 1, portfolio risk falls below the weighted average. A correlation of −1 can, in theory, remove risk completely.
How many stocks do you need to be diversified?
Classic studies suggest most firm-specific risk disappears with around 20 to 30 randomly chosen stocks, though estimates vary and some research says more are needed. Beyond that, adding stocks helps little because the remaining risk is mostly market risk.
Can you diversify away all risk?
No. Diversification removes idiosyncratic risk but not systematic risk, which affects almost all stocks at once. That leftover market risk is what CAPM and APT say investors are paid for bearing.