Risk Management Interactive

Concentration Risk

Measure and manage exposure to single events, sports, or correlated outcomes. Diversification reduces variance without sacrificing expected return.

📊 Herfindahl-Hirschman Index (HHI)

HHI = Σ (share_i)²

share_i = Percentage exposure to segment i
< 1500 = Low concentration
1500-2500 = Moderate
> 2500 = High concentration

Interpretation

• 10000: All exposure in one segment
• 2000: 5 equal segments
• 1000: 10 equal segments
• Lower HHI = better diversification

Exposure by Sport

0 60

Total 100%

📊 Concentration Analysis

2300

HHI Score

4.3

Effective # Segments

Moderate Concentration

Risk Level: Medium

0 (Diversified) 10000 (All in one)

Exposure Distribution

⚠️ Single Event Risk

1 20

50 500

Single Event Concentration

5.0%

of total liability

✓ Acceptable Well-diversified event exposure.

🎯 Types of Concentration Risk

NFL

High correlation on Sundays, 1PM slate exposure

NBA

Back-to-back games, load management uncertainty

Parlay

Correlated legs (same game, same team)

Player

Injury exposure, single star dependence

🛡️ Mitigation Strategies

Limits & Controls

→ Max % of book on single event
→ Max exposure per sport/league
→ Parlay leg correlation caps
→ Time-based concentration limits (Sunday slate)

Active Management

→ Move lines to balance exposure
→ Hedge at other books
→ Reduce limits on concentrated outcomes
→ Real-time exposure monitoring

R Code Equivalent

# Calculate Herfindahl-Hirschman Index
calculate_hhi <- function(exposures) { 
  shares <- exposures / sum(exposures) * 100
  hhi <- sum(shares^2)
  return(hhi)
}

# Effective number of segments
effective_n <- function(hhi) { 
  10000 / hhi
}

# Classify concentration
classify_concentration <- function(hhi) { 
  if (hhi >= 2500) return("High")
  if (hhi >= 1500) return("Moderate")
  return("Low")
}

# Example
exposures <- c(35, 25, 15, 10, 10, 5)
hhi <- calculate_hhi(exposures)
cat(sprintf("HHI: %.0f - %s concentration\n", hhi, classify_concentration(hhi)))
cat(sprintf("Effective # segments: %.1f\n", effective_n(hhi)))

✅ Key Takeaways

• HHI measures portfolio concentration (lower = better)
• <1500 = diverse, >2500 = concentrated
• Single event risk should be capped

• Diversification reduces variance, not EV
• Watch for hidden correlations (same game parlays)
• Active management: move lines, hedge, limit