A simple method for computing value at risk using principal components analysis and quasi Monte Carlo

Managing financial risk is a complex task for financial institutions and portfolio managers worldwide. Value at Risk (VaR) is a popular risk metric. In this paper we propose a simple approach to compute VaR using a Canadian fixed income portfolio. Our approach is three fold. First, to reduce the dimensionality, we construct orthogonal factors using Principal Components Analysis (PCA) on Canadian term structure data. Second, the entire term structure is constructed by linear interpolation from the existing spot rates. And third, to derive VaR values, we perform simulations by Quasi Monte Carlo (QMC) and compare the QMC results with those obtained by standard Monte Carlo (MC). We find that QMC converges faster than MC. However, for the same number of iterations, QMC takes more computational time. The methodology can be easily implemented with available software, since much software includes subroutines to generate QMC sequences. The normative prescription is that one should use QMC whenever PCA produces few factors explaining the original variables affecting the portfolio value.