Fixed Income Portfolio Risk

Managing a fixed income portfolio is not just about picking bonds; it is about understanding and controlling the sources of risk at the portfolio level. DV01 tells you how much money you lose on a one-basis-point parallel shift, but real yield curves do not move in parallel — they twist, steepen, flatten and butterfly. Key rate duration, PCA decomposition and multi-method VaR are the tools that bridge the gap between single-bond analytics and portfolio-level risk management.

This course builds a full fixed income risk engine for a 10-bond portfolio. You aggregate DV01 and key rate duration vectors across positions, use principal component analysis to decompose the yield curve's historical covariance into parallel, twist and butterfly factors, and construct a PCA hedge using three liquid futures contracts. Every step is grounded in the mechanics used on a real rates risk desk.

The course then delivers three Value at Risk methodologies for the same portfolio: historical VaR — repricing on 10 years of actual yield curve moves; parametric VaR — the Gaussian closed-form from the DV01 vector and covariance matrix; and Monte Carlo VaR — simulating correlated curve paths. You compare all three, compute backtesting statistics, and finish with a complete picture of how each methodology's assumptions affect the resulting risk number.

The project builds a risk engine for a portfolio of 10 government bonds spanning the 2Y–30Y range, with mixed long and short positions. You start by computing the DV01 of each bond and aggregating it into a portfolio DV01, then extend to key rate duration: bumping each of the standard key rate tenors (2Y, 5Y, 10Y, 20Y, 30Y) by one basis point and computing the resulting portfolio P&L to build the full KRD profile.

With the risk profile characterised, you run a PCA decomposition on 10 years of daily yield curve changes, extract the three dominant eigenvectors (parallel, twist, butterfly), and project the portfolio's KRD vector onto each factor to compute the portfolio's PC betas. You then solve for the notionals of three futures contracts (2Y, 5Y, 10Y Treasury) that neutralise the first three PC betas — a regression-based hedge that immunises against the most common curve moves.

The final section computes VaR three ways. Historical VaR repricings the portfolio on every daily curve move over the past decade and takes the 1st percentile of the resulting P&L distribution. Parametric VaR uses the Gaussian formula: DV01 vector transpose times the yield covariance matrix times DV01 vector, scaled to 99% confidence. Monte Carlo VaR simulates 10,000 correlated yield curve paths using the PCA factor structure and builds the simulated P&L distribution. All three estimates are compared, and you implement a simple exceedance-based backtest to verify the parametric model.