Why Expected Value Matters in Trading
Before placing any trade, a quant asks: "What is my expected P&L?" This is the foundation of every strategy evaluation.
Consider a simple bet: 60% chance to win $100, 40% chance to lose $80. Should you take it?
E[P&L]=0.6($100)+0.4(−$80)=$28 Positive expected value. But this alone is not enough - we need to understand risk.
Variance: Quantifying Uncertainty
Two strategies can have identical expected returns but wildly different risk profiles. Variance captures this spread.
For our bet above, the variance tells us how much our actual returns will deviate from $28 on average:
σ2=0.6(100−28)2+0.4(−80−28)2=7776 The standard deviation is $88.18 - meaning high volatility relative to our $28 edge. This is a risky bet despite positive EV.
Portfolio Construction
The key insight of modern portfolio theory: combining assets with low correlation reduces overall risk without sacrificing returns.
For two assets A and B, portfolio variance depends on their covariance:
σp2=w2σA2+(1−w)2σB2+2w(1−w)Cov(A,B) When Cov(A,B) < 0, the cross-term is negative - diversification benefit.
Why Expected Value Matters in Trading
Before placing any trade, a quant asks: "What is my expected P&L?" This is the foundation of every strategy evaluation.
Consider a simple bet: 60% chance to win $100, 40% chance to lose $80. Should you take it?
E[P&L]=0.6($100)+0.4(−$80)=$28 Positive expected value. But this alone is not enough - we need to understand risk.
Variance: Quantifying Uncertainty
Two strategies can have identical expected returns but wildly different risk profiles. Variance captures this spread.
For our bet above, the variance tells us how much our actual returns will deviate from $28 on average:
σ2=0.6(100−28)2+0.4(−80−28)2=7776 The standard deviation is $88.18 - meaning high volatility relative to our $28 edge. This is a risky bet despite positive EV.
Portfolio Construction
The key insight of modern portfolio theory: combining assets with low correlation reduces overall risk without sacrificing returns.
For two assets A and B, portfolio variance depends on their covariance:
σp2=w2σA2+(1−w)2σB2+2w(1−w)Cov(A,B) When Cov(A,B) < 0, the cross-term is negative - diversification benefit.