Free lesson · Prediction strategies

Event overlap and portfolio variance

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Start with the idea

Ten contracts about the same underlying event may behave like one large bet. Count economic dependencies, not listing count.

Symbols, units & horizon

w_1,w_2: dimensionless portfolio exposure weights
σ_1,σ_2: standard deviations of horizon returns as fractions
ρ: return correlation
σ_P²: portfolio return variance at the same horizon

When and why to use this

Set event-cluster limits and compare full portfolio scenarios before combining candidate bets.

Ten contracts about the same underlying event may behave like one large bet. Count economic dependencies, not listing count.

Build event groups by shared drivers and resolution logic. A pair of opposing titles can still leave a common exposure if their settlement rules differ.

The two-position variance formula includes covariance. Use scenario payout tables when binary dependence is strongly non-normal; variance is only a summary and does not bound the largest loss.

σ_{P}^{2} = w_{1}^{2} σ_{1}^{2} + w_{2}^{2} σ_{2}^{2} + 2 w_{1} w_{2} ρ σ_{1} σ_{2}

Model assumptions, derivation and arithmetic

Event overlap and portfolio variance

Expand the variance of w_1R_1+w_2R_2.
Replace covariance with correlation times both standard deviations.
Apply final portfolio weights and compare correlation scenarios.

Work it by hand

w_1=w_2=.5, σ_1=σ_2=.2, ρ=.8: variance=.01+.01+.016=.036, standard deviation about .189737. At zero correlation, variance would be .02.

Apply it in a strategy

Set event-cluster limits and compare full portfolio scenarios before combining candidate bets.
Record the input timestamp, executable quantity, currency and horizon. Reconcile the result with a cash-flow or state table.
Stress this failure condition: Historical correlations can shift at resolution and do not capture incompatible void/default states.

Research deliverable

Build and explain a event overlap and portfolio variance worksheet. Set event-cluster limits and compare full portfolio scenarios before combining candidate bets.

Evidence boundary: Synthetic arithmetic and scenarios illustrate mechanics. They are not historical returns, a paper replication, or evidence of an executable edge. Research sources and their access limitations are recorded at the end of this module.

Python implementation

Self-contained teaching example. Python 3.10+; dependencies and input conventions are shown in the code and notation. Run in your own Python environment.

# Python 3.10+; standard library unless NumPy is imported below.
# Inputs and outputs use the units defined in this lesson. Synthetic teaching example.
from math import sqrt
def pair_risk(w1,w2,s1,s2,rho):
    if min(s1,s2)<0 or not -1<=rho<=1: raise ValueError("Invalid risk inputs")
    variance=w1*w1*s1*s1+w2*w2*s2*s2+2*w1*w2*rho*s1*s2
    return variance,sqrt(max(0,variance))

print(pair_risk(.5,.5,.2,.2,.8))

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Quantitative finance and development glossary · Python resources and libraries · Research sources and limitations