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.
Diversification explained simply
Diversification spreads money across investments that don't move perfectly together, so one bad surprise does less damage. The lower the correlation, the more risk cancels out. In the example, a 50/50 mix of a 30% and a 20% volatility stock with correlation 0.2 has a volatility of about 19.6%, well below the 25% average.
What this diversification lesson covers
- 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
Portfolio risk formulas, explained
- 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
How to calculate portfolio risk step by step (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.
How correlation changes the 50/50 portfolio's risk
| Correlation | Portfolio standard deviation | What it means |
|---|---|---|
| +1.0 | 25.0% | No diversification benefit |
| +0.2 | About 19.6% | Most real stock pairs: a solid benefit |
| 0 | About 18.0% | Independent: a bigger benefit |
| −1.0 | 5.0% | Moves exactly opposite: most risk cancels |
Is one strong pillar safer than many? David's take
We're taught that there's strength in unity. I think there are two models of strength. The pillar is one strong, unified structure: very hard to knock down, but if it falls, everything falls. The hydra has many heads that aren't unified, and it survives losing some of them. A diversified portfolio is a hydra. Neither model is simply stronger, and weak hydras still fail: owning many poor investments isn't safety. But when you can't be sure which pillar is strong, the hydra is the one that survives surprises.
From David's concept: Pillar vs Hydra. This is David's opinion, alongside the standard textbook answer above.
Harder diversification questions
What if the two stocks were completely uncorrelated?
With correlation 0, portfolio variance = 0.0225 + 0.0100 = 0.0325, so standard deviation ≈ 18.0%.
Can diversification remove all risk?
No. As you add more stocks, firm-specific risk shrinks towards zero, but the average covariance between stocks remains. That leftover is market (systematic) risk.
Common diversification 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.