Derive Annualized Portfolio Volatility
Point72Quantitative Researcher · Online Assessment
Last updated
Derive portfolio volatility from factor covariance and stock-specific variance, then annualize it with consistent horizons and units.
Derive Annualized Portfolio Volatility
A stock portfolio has weight vector w. Each stock has factor exposures, the factors have a covariance matrix, and each stock has an idiosyncratic variance. Derive the portfolio's predicted volatility and explain how to annualize it without mixing return horizons or units.
Constraints & Assumptions
Bis the stock-by-factor exposure matrix andFis the factor covariance matrix.Dis diagonal with nonnegative idiosyncratic variances.- Factor and idiosyncratic returns are uncorrelated in the model.
B,F,D, andwrefer to the same universe, currency treatment, and return horizon.
Clarifying Questions to Ask
- Are weights fractions of capital, dollar holdings, or active weights?
- Is covariance daily, monthly, or already annualized?
- Do cash, leverage, hedges, and currency exposures belong in the model?
- Are idiosyncratic covariances truly assumed to be zero?
Hints
Hint 1
Project holdings into factor space: Compute the portfolio's factor exposure once, then combine its factor variance with the weighted sum of specific variances.
Follow-up questions
- How does the formula change if specific returns are correlated?
- Why can multiplying volatility by 252 be wrong?
- How would you identify which factor contributes most to total risk?
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