I have a portfolio of bonds, newly issued bonds and bonds near expiry. I want to calculate VaR of the portfolio, should I consider a mix of price VaR and Rate VaR methodologies?

I you are calculating VaR because of some regulatory requirement (which is usually the case), you should follow the approach prescribed by the regulator. Otherwise it really depends on the nature of the bonds, in particular how much credit risk they are exposed to. If it’s a government bond portfolio I’d probably start with the first couple of principal components of the relevant yield curve. If credit risky I would add at least one factor to capture systematic spread risk. And then I would scratch my head over how to treat the contribution to tail risk from actual defaults. I don’t really see any simple application of “price VaR”, although I might just be confused about what that is.

Your comment about the contribution of calculating the VAR of actual defaults reminds of the very contrived counterexampleI you are calculating VaR because of some regulatory requirement (which is usually the case), you should follow the approach prescribed by the regulator. Otherwise it really depends on the nature of the bonds, in particular how much credit risk they are exposed to. If it’s a government bond portfolio I’d probably start with the first couple of principal components of the relevant yield curve. If credit risky I would add at least one factor to capture systematic spread risk. And then I would scratch my head over how to treat the contribution to tail risk from actual defaults. I don’t really see any simple application of “price VaR”, although I might just be confused about what that is.

involving bonds with default probabilities less than the confidence limit of the VAR measure, produced to demonstrate the

non-subadditivity of VAR (e.g. here, footnote on p10).

The idea that you can get a risk measure which measures zero for a very broad parameter range only goes to show VAR is

useless for such risks. It seems inevitably to be one of those worrisome situations where calculations of VAR based of market implied parameters

(default prob etc.), rather than the historical ones the textbooks demand, leads to much bigger values than the historical VAR measures.

Assuming here that the portfolio is a component of your trading book. Would go with Incremental risk charge model (IRC) ( get a distribution of losses on underlying portfolio positions driven mainly by 2 risk factors -outright default and migration risks) the other risks, the diffusion risks can be covered by VaR ( spread, IR ). The IRC should be calculated over a one-year capital horizon through a Monte Carlo simulation and some assumptions on the behaviour of correlated defaults within the portfolio over the one-year capital horizon. A bit of work involved here, especially in constructing the curves to price the bonds after default using curves calibrated to market curves as a function of country, currency, and rating. IRC is industry standard, soon to be replaced by DRC, not much different.

Also, the bond portfolio have mainly first-order effects dominant, so do not go with a full revaluation VaR model, to cut the time use a Taylor approximation to your PnL. In other words, use the delta of the bond portfolio on a daily basis as an approximation to your PnL and get the VaR from that.

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