Unsystematic Risk

#Definition

Unsystematic risk (also called diversifiable, idiosyncratic, or specific risk) is risk that affects individual positions but not the entire portfolio. In prediction markets, unsystematic risk is the uncertainty specific to a single market or outcome—whether a particular candidate wins, a specific policy passes, or an individual event occurs.

Unlike systematic risk (which affects all positions), unsystematic risk can be reduced or eliminated by holding multiple uncorrelated positions. This is the fundamental principle behind portfolio diversification.

#Why It Matters in Prediction Markets

Understanding unsystematic risk is essential for portfolio construction:

Diversification opportunity: Prediction markets offer many independent events. Holding positions across uncorrelated markets reduces overall portfolio risk without sacrificing expected return.

Position sizing decisions: Unsystematic risk determines how much to allocate to any single position. Concentrating in one market means taking on maximum unsystematic risk.

Risk-adjusted returns: A diversified prediction market portfolio can achieve higher Sharpe ratios than concentrated positions by eliminating diversifiable risk.

Drawdown reduction: Multiple uncorrelated positions smooth portfolio performance. Losses in one market are often offset by gains in others.

Bankroll preservation: Reducing unsystematic risk helps traders survive inevitable losses in individual positions and continue trading long-term.

#How It Works

#Systematic vs. Unsystematic Risk

Systematic risk (non-diversifiable):

• Affects all or many positions simultaneously
• Cannot be eliminated through diversification
• Examples: economic recessions affecting all policy markets, platform failures

Unsystematic risk (diversifiable):

• Affects only specific positions
• Can be reduced by holding multiple uncorrelated positions
• Examples: specific candidate scandals, individual regulatory decisions, particular sports outcomes

#The Diversification Effect

When positions are uncorrelated, combining them reduces overall volatility:

Single position: If you hold only "Candidate A wins" at $0.55:

• Outcome: Win (+$0.45) or Lose (-$0.55)
• High variance: 100% of portfolio swings on one outcome

Two uncorrelated positions: Hold "Candidate A wins" and "Policy X passes" (unrelated events), each at half portfolio:

• Possible outcomes: Win both, win one, lose both
• Moderate variance: Only 25% chance of maximum gain or loss

Many uncorrelated positions: Hold 20 independent positions:

• Outcomes cluster toward expected value
• Low variance: Extreme gains and losses become rare

#Mathematical Relationship

For uncorrelated positions with equal size and equal volatility:

Portfolio Volatility = Position Volatility / √(Number of Positions)

Example:
- Single position volatility: 50%
- 4 positions: 50% / √4 = 25%
- 16 positions: 50% / √16 = 12.5%
- 100 positions: 50% / √100 = 5%

Diversification provides diminishing but continuing benefits as positions increase.

#Quantifying Risk Reduction

import math

def calculate_portfolio_variance(assets, correlation=0):
    """
    Calculate portfolio standard deviation assuming equal weight and uniform correlation.
    Illustrates how risk drops as N (assets) increases.
    """
    n = len(assets)
    avg_volatility = sum(assets) / n
    
    # Formula for variance of an equally weighted portfolio
    # Var_p = (1/n)*Avg_Var + ((n-1)/n)*Avg_Covar
    
    variance = (1/n) * (avg_volatility**2) + \
               ((n-1)/n) * (correlation * avg_volatility**2)
               
    return math.sqrt(variance)

volatilities = [0.50] * 20 # 20 assets with 50% vol each
risk_uncorrelated = calculate_portfolio_variance(volatilities, correlation=0)
risk_correlated = calculate_portfolio_variance(volatilities, correlation=0.5)

print(f"Risk (Uncorrelated): {risk_uncorrelated:.1%}") # ~11%
print(f"Risk (Correlated): {risk_correlated:.1%}")     # ~36% (Diversification works less well)

#Numerical Example

Concentrated portfolio: $10,000 in single election market at$0.60

• 60% chance: Win $4,000 (portfolio up 40%)
• 40% chance: Lose $6,000 (portfolio down 60%)
• Expected value: +$400, but extreme outcomes likely

Diversified portfolio: $1,000 each in 10 independent markets, all at$0.60

• Expected wins: 6 out of 10
• Expected outcome: Win $2,400, Lose$2,400 on average → Net +$400
• Distribution clusters around expected value
• ~5% chance of 9+ wins; ~5% chance of 3 or fewer wins
• Portfolio rarely swings more than ±20%

Same expected value, dramatically reduced variance through diversification.

#Correlation Matters

Diversification only reduces risk when positions are uncorrelated:

Uncorrelated positions (ideal for diversification):

• City council election and technology company earnings
• Sports championship and monetary policy decision
• Different countries' elections (often)

Correlated positions (limited diversification benefit):

• Two candidates in same party's primary
• Multiple markets on related economic policies
• Elections in same region/country (sometimes)

When positions are correlated, they tend to win or lose together, reducing diversification benefit. Joint probability of correlated losses is higher than for independent positions.

#Examples

Sports betting portfolio: A trader bets on 50 independent sports outcomes over a season, each with slight edge. Any individual game is highly uncertain (unsystematic risk), but across 50 games, results cluster toward expected value. The trader's skill shows in aggregate results, not individual games.

Election season diversification: During a major election cycle, a trader holds positions in 15 different races across multiple states and levels (presidential, senate, house, governors). While each race is uncertain, the diversified portfolio produces more predictable overall returns than concentrating in a single race.

Concentrated risk realization: A trader puts entire bankroll into one primary election at $0.70. The favored candidate loses an unexpected upset. Portfolio drops 70% on a single outcome. The unsystematic risk of that specific race was not diversified.

Imperfect diversification: A trader holds 10 prediction market positions, but all are on related economic policies (interest rates, inflation, employment). When economic conditions shift, all positions move together. Despite appearing diversified, the portfolio carries substantial systematic risk to economic factors.

#Risks and Common Mistakes

Assuming independence when correlated: Many prediction market outcomes share underlying factors. Elections in the same country, policies from the same administration, or events in the same industry may be correlated. Treating them as independent underestimates risk.

Over-diversification: Beyond a certain point, adding positions adds complexity and transaction costs without meaningfully reducing risk. 20-30 truly independent positions capture most diversification benefit.

Ignoring systematic risk: Diversification eliminates unsystematic risk but not systematic risk. Platform risk, regulatory changes, or broad market liquidity crises affect all positions regardless of diversification.

Diversifying away edge: If your edge exists only in specific market types, diversifying into markets where you have no edge dilutes overall performance. Diversify within your area of competence.

Equal weighting by default: Not all positions deserve equal allocation. Size positions based on edge and confidence, not just diversification goals.

#Practical Tips for Traders

• Assess correlation explicitly: Before considering positions "diversified," ask whether they share underlying factors. Political positions in the same election cycle may be more correlated than they appear.

• Target 10-20 independent positions: This captures most diversification benefit without excessive complexity. Beyond 20, additional positions offer diminishing risk reduction.

• Balance diversification with edge: Don't add positions just for diversification. Each position should have positive expected value on its own merits.

• Track portfolio-level performance: Monitor overall portfolio volatility, not just individual position outcomes. Diversification success shows in reduced portfolio variance.

• Stress test for hidden correlations: Ask "what scenario would cause multiple positions to lose simultaneously?" If you can easily identify such scenarios, you have correlated risk.

• Rebalance as positions resolve: As markets settle, your effective diversification decreases. Add new uncorrelated positions to maintain risk reduction.

• Use Kelly criterion with diversification: Kelly sizing naturally accounts for diversification—optimal sizing depends on overall portfolio, not just individual position edge.

#Related Terms

• Risk Management
• Correlation
• Drawdown
• Kelly Criterion
• Expected Value (EV)
• Volatility
• Joint Probability

#FAQ

#What is unsystematic risk in simple terms?

Unsystematic risk is the risk that comes from individual positions—whether a specific candidate wins, a particular policy passes, or a single game goes your way. It's "diversifiable" because holding many unrelated positions smooths out this risk: some win, some lose, but the overall portfolio becomes more predictable. It's the opposite of systematic risk, which affects everything at once.

#How many positions do I need to diversify?

The benefit of diversification follows a square root rule: going from 1 to 4 positions cuts volatility in half; going from 4 to 16 cuts it in half again. Practically, 10-20 truly independent positions capture most of the diversification benefit. Beyond that, you get diminishing returns while adding complexity and transaction costs.

#Can I eliminate all risk through diversification?

No. Diversification eliminates unsystematic (position-specific) risk but not systematic risk—risks that affect all positions simultaneously. In prediction markets, systematic risks include platform failures, regulatory changes, and broad market liquidity crises. A fully diversified portfolio still carries these non-diversifiable risks.

#Are all prediction market positions uncorrelated?

No. Many positions share underlying factors. Elections in the same country, policies from the same government, or events in the same industry may be correlated. Positions are truly uncorrelated only when the underlying events have no shared causes or influences. Assessing correlation requires thinking about what drives each outcome.

#How does diversification affect expected returns?

Diversification reduces risk without reducing expected return—that's its power. If each position has 5% expected return, a portfolio of 10 such positions also has 5% expected return but with much lower volatility. This is why diversification improves risk-adjusted returns (like Sharpe ratio) even when raw expected returns stay the same.