This video by explains the concept of mapping fixed income portfolios to risk factors. Why map portfolios to risk factors? It’s a shortcut because portfolios are complicated; e.g., even delta-normal VaR employing a covariance matrix contains n(n+1)/2 pair-wise correlations in a dreaded “curse of dimensionality.” The reality of a portfolio’s true risk exposure is both […]

# VaR Mapping

## Bond Returns Value at Risk (VaR) as Bond Risk

Bond risk can be measured by “price returns value at risk (VaR)” where the price returns VaR is linked to yield VaR with duration. This video is regarded by David from Bionic Turtle.

## Mapping a European Stock Option

A European stock option can be mapped to two positions: 1. A Long position in the asset, plus 2. a short position in underlying bill (i.e., interest rate factor). This video is developed by David from Bionic Turtle.

## VaR of Forward Foreign Currency Contract

First, we used the formula for the value of a forward contract to identify the three risk factors. This is the essential mapping idea: we characterize the portfolio as a set of exposures to underlying risk factors. In this case, a forward currency contract maps to a long position in a foreign currency spot rate, […]

## Undiversified Bond Value at Risk (VaR)

This video illustrates the calculation of undiversified value at risk (VaR) for a two-bond portfolio. This video is developed by David from Bionic Turtle.

## Diversified Bond Value at Risk (VaR)

In the previous video, we learned about the calculation of the un-diversified VaR of the two-asset bond portfolio. This video explains Jorion’s Table 11-4 which calculates diversified value at risk (VaR) for the same bond portfolio. The key difference is that diversified VaR should be lower to reflect the benefit of imperfect correlations. This video […]