Free tools
Diversification lab
Holding more than one thing lowers the ups and downs of the whole, but only as far as the holdings move independently. Give every holding the same volatility and every pair the same correlation, and this lab shows the volatility of an equal-weight portfolio as holdings are added, the floor it approaches, and how quickly it gets there. It is arithmetic on a model you set, not a description of any real portfolio.
1 moves in lockstep, 0 independently; below 0, more holdings soon become impossible.
Portfolio volatility—
Floor as holdings grow—
Holdings to get within 10% of the floor—
Portfolio volatility against the number of holdings.
How it works
With N holdings of equal weight, each with volatility σ, and the same correlation ρ between every pair, the portfolio’s volatility is σ × √(1/N + (1 − 1/N) × ρ). The first term is the part each holding has on its own, and it shrinks as N grows. The second is the part they share, and it does not: as N grows the volatility approaches σ × √ρ, the floor.
The holdings count shown for the floor is the smallest N whose volatility is at most 1.1 times the floor, from N ≥ (1 − ρ) ÷ (0.21 × ρ). The higher the correlation, the sooner the curve flattens and the higher it stays. At a correlation of 0 there is no floor above zero: the volatility keeps falling as σ ÷ √N.
Negative correlation
Every pair cannot be strongly opposed at once: if A moves against B and B against C, A and C tend to move together. For one common correlation to be possible among N holdings it must be at least −1 ÷ (N − 1), so at −0.2 the model allows at most six. The chart stops where the model does. The equal-weight portfolio's volatility reaches zero only where the correlation is exactly −1 ÷ (N − 1) for a whole number of holdings, as −0.2 is for six; at −0.15 the limit is seven holdings and a little volatility remains.
What it leaves out
Real holdings have different volatilities and different correlations, and both change over time; correlations often rise when prices fall sharply. Volatility also measures how widely returns vary, not how far a portfolio can fall. Use the lab to see what a set of assumptions implies, not to judge how any real collection of holdings behaves.