Portfolio construction
Correlation and diversification
Why combining tickers that do not move together lowers risk without lowering the expected return, and how to read a correlation table.
The idea in plain words
Correlation measures how two tickers move together on a scale from −1 to +1. At +1 they are the same bet; at 0 their ups and downs are unrelated, so they partly cancel; at −1 one is a perfect hedge for the other. Diversification is that cancelling: the less the parts move together, the smoother the whole.
How it is calculated
Correlation is the covariance of two tickers divided by the product of their volatilities, so it is free of units and of how volatile each one is. For two tickers with equal weights and equal volatility σ, the portfolio's volatility depends only on ρ.
ρᵢⱼ = Σᵢⱼ ÷ (σᵢ σⱼ)
Two tickers, weights ½ and ½, both with volatility σ:
σₚ = σ × √((1 + ρ) ÷ 2)
ρ = 1 → σₚ = σ ρ = 0 → σₚ = 0.71σ ρ = −1 → σₚ = 0How to use it
- Open the Correlations heatmap in a study or in the live analysis: dark cells far from the diagonal are pairs that duplicate each other.
- In the live analysis, the "as held" view flips the sign for short positions: a long and a short in two highly correlated tickers show up as a strong negative, a hedge.
- Add tickers for their low correlation to what you already hold, not only for their own return.
Drawing conclusions
- Above about 0.7: mostly the same bet (US500 and GER40, EURUSD and GBPUSD).
- Between −0.3 and 0.3: genuinely different drivers.
- Below −0.5: a hedge; it lowers risk a lot but also cancels return.
Example
Running example (used in every portfolio guide): US500, GER40, gold (XAUUSD) and EURUSD, two years of daily data. Expected returns 8%, 7%, 7% and 1% a year; volatilities 18%, 20%, 15% and 7%. US500 and GER40 move together (correlation about 0.7); gold hardly moves with the indices (about 0.04). In the example, US500 and GER40 correlate at about 0.7, so a 50/50 mix of them has 17.6% volatility. US500 and gold correlate at 0.04, and a 50/50 mix has 12.0%. Equal weights in all four tickers give 10.5% with a 5.75% expected return: the average ticker has 15% volatility, the portfolio two thirds of that.
The example's inputs are illustrative; the weights and figures are what our optimiser returns for them.
Watch out for
- Correlation measures straight-line co-movement on average; two tickers can be uncorrelated most days and still fall together in a panic.
- Correlations change: the stock–bond and stock–gold relations have switched sign more than once in the last decades.
- A short window gives a noisy estimate; read it next to a longer one.
A little history
Karl Pearson formalised the correlation coefficient in the 1890s. Markowitz (1952) showed that the risk of a portfolio depends on these co-movements, which is why diversification is often called the only free lunch in finance, a phrase widely attributed to him.
Educational content only. No portfolio model knows the future: every one of them works on estimates from the past, and nothing here is investment advice.