Diversification and Risk Correlation

## How Correlation Affects Portfolio Risk In a portfolio of independent bets, each bet's variance is additive. In a portfolio of correlated bets, the effective combined variance is higher than the sum of individual variances. ## When Bets Are Correlated - **Same event, multiple markets:** Backing Team A to win + Over 2.5 goals in the same match. These are positively correlated — if A wins big, both likely win. - **Same league, same round:** Backing all home teams in a round of fixtures. If there is a league-wide unusual result pattern (extreme weather, refereeing tendency), all bets move together. - **Same model inputs:** If all your bets use the same xG model and that model has a systematic bias, all bets are affected the same way. ## Quantifying Correlation Impact For two bets with equal variance V and correlation ρ: Portfolio variance = 2V + 2ρV = 2V(1 + ρ) At ρ = 0 (independent): Portfolio variance = 2V → σ_portfolio = √2 × σ_single At ρ = 0.5 (moderate positive correlation): Portfolio variance = 3V → σ_portfolio = √3 × σ_single A 0.5 correlation between two bets increases portfolio risk by 22% relative to independent bets. ## The Practical Diversification Target - No single event: maximum 3% total exposure - No single league on a single match day: maximum 8% total exposure - No single model bias: spread modelling approaches across sports and methods ## The Uncorrelated Ideal The most valuable diversification is across genuinely uncorrelated sports and time periods. Football bets on Saturday are uncorrelated with basketball bets on Sunday — different sports, different teams, different models.