Definition
Diversification is spreading capital across holdings whose returns do not move in perfect step, so that the combined portfolio is less volatile than the weighted average of its parts. It mainly reduces risks specific to one company, sector or asset.
How it works
For two assets, portfolio variance is w1²σ1² + w2²σ2² + 2w1w2ρσ1σ2, where w are weights, σ are volatilities and ρ is the correlation. The lower the correlation, the larger the reduction in volatility; at ρ = +1 there is no volatility benefit from combining them.
Diversification cannot remove market-wide (systematic) risk, and adding many similar holdings gives little extra benefit. Correlations can also rise sharply in a crisis, so the protection seen in calm periods may shrink when it is most needed.
Formula / convention
σ(p)² = w1² × σ1² + w2² × σ2² + 2 × w1 × w2 × ρ × σ1 × σ2 (two assets)
Illustrative example
Illustrative: two fictional assets each have 20% volatility and are held 50/50. With w = 0.5 and σ = 0.20 for both, the variance is 0.02 + 0.02ρ, so portfolio volatility is 20.0% if ρ = 1, 17.3% if ρ = 0.5 and 14.1% if ρ = 0.
What to watch for
Diversification does not guarantee profit or prevent loss, particularly in a market-wide decline. Holding many positions can also add costs and complexity without reducing risk if they share the same underlying exposure.