# VaR for corporate bonds

I am trying to create a simple risk calculation for the portfolio (ignoring correlations for the moment). I have some corporate bonds with limited daily price changes. Any one have ideas how I can get a VaR (95%) for these assets given their limited pricing history? Is there any easy way to use CDS for the name instead of corporate bond prices (if i can find a long enough history)

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It's very common to work in spreads rather than price for this calculation. The simplest approach would be to get an implied spread for each bond, and then allow the spreads to vary in simulation according to an equity-style factor model. Each spread simulation can then be mapped back to bond prices by reversing the formula.

A few points:

• If you can, you should use option adjusted spreads, but that involves somewhat complicated interest rate models. Z spreads are a simpler choice.
• Be sure to allow for default in your simulations, since a default will have a large negative effect on portfolio value.
• Importance sampling will get better resolution.
• Many people prefer Expected Shortfall to VaR because VaR is not a coherent risk measure.
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cheers. I was thinking about doing a stress with DV01. The reason I wanted to use VaR was just to give an overall portfolio 'risk' measure to be used to compare portfolios. I think if i am consistent with the DV01 estimate it will allow me to get some risk measure for the bond part of the portfolio, the question is just how much. If am using annualized volatility for the equity part (at 16-18%) I would need to get something for IG near 4.5% and HY 11.5% – Avi Oct 23 '12 at 19:29

If you have CDS data, take ( cds spread changes * the dv01 of the cds / cds notional ) to get a percent change in cds. you can use that as a proxy for bond price volatility.

Note that in bad times, cash tends to underperform cds so you need to increase the volatility of your bond relative to the cds. if your cds volatility is 3%, multiple that by say 1.5 to be conservative. additionally, you will need to adjust by the ratio of the cds dv01 to the bond dv01.

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