Diversification, explained.
Diversification combines exposures to reduce the impact of fluctuations that do not move together; its effectiveness depends on allocation and correlation.
Why it happens
Two labels do not necessarily represent two independent risks. When changes coincide, combining them offers little cancellation. When their fluctuations differ, one can offset some of the other's variation. The chosen weighting determines how much each contributes.
Diversification combines exposures whose changes need not coincide. The reduction in variability depends on both allocation and covariance, rather than the number of labels in a portfolio.
Read the result
Start with equal weights and change correlation. Both exposures have standard deviation ten units. The combined number is a variability measure under these assumptions, not a forecast of return or a complete measure of loss risk.
A worked example
Two equal exposures
Each exposure has standard deviation ten and receives half the allocation.
At zero correlation, the combined standard deviation is about 7.07. At perfect positive correlation, it remains ten.
The split stays identical; changing dependence changes the benefit. The special perfectly negative case cancels fluctuations at equal weights in this symmetric model.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Both exposures have zero mean and standard deviation 10 units. Combined standard deviation is 10×sqrt(w²+(1−w)²+2ρw(1−w)). The chart compares allocations at the selected fixed correlation. No price paths, return predictions or actual assets are included.
Where this idea is useful
A practical use
A business with two clients in the same industry may still face one shared demand shock. Distinct sources of income help only to the extent that their risks differ.
A common misconception
“Owning more named exposures guarantees less risk.”
Their common drivers can make them behave like one exposure. Unequal weights, tail dependence and changing correlations also matter.
What this explanation leaves out
- Standard deviation is not all risk. Tail losses, dependencies that change under stress and unequal exposure sizes matter. This symmetric model is educational, not a portfolio recommendation.
Does zero standard deviation here mean nothing can go wrong?
No. The cancellation follows exact symmetric assumptions. Real exposures can have unequal variation, changing dependence and risks outside the model.
Which apparently separate exposures depend on the same underlying condition?
Associated thinkers
Further reading
Explore the original research or the teaching reference behind this experiment.