Risk Management and Portfolio Management
Measuring risk
Candidates must handle volatility, beta, VaR, CVaR (expected shortfall), stress testing, scenario analysis, and drawdown. VaR is a loss threshold at a given confidence level over a horizon; it says nothing about the size of losses beyond it, which is why CVaR and stress tests matter. Under i.i.d. assumptions, VaR scales with the square root of time: a 1-day 95% VaR of $1m becomes roughly $1m x sqrt(10) = $3.16m over 10 days.
Portfolio management covers mean–variance optimization, the efficient frontier, risk budgeting, factor exposures, tracking error, rebalancing policy, and performance metrics. The Sharpe ratio uses total volatility, the Sortino ratio uses downside deviation, and the information ratio uses tracking error against a benchmark.
Traps
- Calling VaR a worst-case loss. A 95% 1-day VaR is breached about 5% of days - roughly 12 to 13 times a year.
- Applying normal-distribution intuition to fat-tailed alternative strategies.
- Believing diversification always works. Correlations rise in crises, and illiquid assets may show artificially low measured correlation due to smoothing.
- Forgetting that leverage scales return and risk together, leaving Sharpe unchanged while drawdowns grow.
Worked rule of thumb
Risk budgeting: a sleeve with 20% weight and 25% volatility in a portfolio targeting 10% volatility contributes 0.20 x 0.25 = 5% - half the risk budget from one-fifth of the assets. Compute contributions before adding capital, not after a drawdown.