Module 6 — Professional Quant Topics

Risk Management — VaR, CVaR, and Position Sizing

Factor models, options pricing, risk, and microstructure — the curriculum interview desks expect.

Module lessons

Factor Models — CAPM to Fama-French to BarraOptions and the GreeksRisk Management — VaR, CVaR, and Position SizingMarket Microstructure — How Orders Become Prices

Learning objectives

  • ▸Compute parametric, historical, and Monte Carlo VaR.
  • ▸Understand why CVaR (Expected Shortfall) is the regulatory choice.
  • ▸Apply Kelly sizing and its half-Kelly variant.

FORMULA

Value at Risk

VaR_α = -inf{ x : P(L > x) ≤ 1 - α }
A 95% one-day VaR of $1M means: 'we expect to lose more than $1M on 5% of days'. It says nothing about how bad the loss is when it happens.

FORMULA

Conditional VaR / Expected Shortfall

CVaR_α = E[L | L > VaR_α]
The average loss conditional on being in the tail. Basel III moved from VaR to CVaR for exactly this reason — VaR is blind to the shape of the tail.

FORMULA

Kelly criterion

f* = μ / σ²    (continuous-time, single risky asset)
For a strategy with Sharpe 1.0 and 15% vol: optimal Kelly leverage ≈ 1.0/0.15 ≈ 6.7x.
Full Kelly is wild — most practitioners use 0.25–0.5 Kelly.

TEXT

Stress vs statistical

VaR/CVaR tell you what's likely in a normal regime. They don't tell you what happens if the SNB unpegs the franc or a sovereign defaults. Real risk desks complement statistical models with discretionary stress scenarios — '2008 + 2020 combined' or '-20% S&P + +5σ vol spike'.

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