Diversified VaR of two positions

A book holds two positions: $1,000,000 in asset A (daily return σ = 2%) and $1,000,000 in asset B (daily return σ = 3%), with return correlation ρ=0.5\rho = 0.5. Returns are jointly normal (mean ≈ 0). Compute the combined 95% 1-day VaR of the book, in dollars, using z0.95=1.645z_{0.95}=1.645. (Round to the nearest hundred dollars.)

Show hints (2)+
  1. Combine the dollar vols with σP2=σA2+σB2+2ρσAσB\sigma_P^2=\sigma_A^2+\sigma_B^2+2\rho\sigma_A\sigma_B before applying zz.
  2. Then VaR =1.645 σP=1.645\,\sigma_P; compare to the naive sum of standalone VaRs to see the diversification benefit.

Answer

Reveal answer →

71700 (± 300)

Create a free account to see the full worked solution and track your progress.

Interview format: Hedge Fund Quant, Prop Trading

Related questions