I need to calculate the VaR of a bond portfolio consisting some zero coupon government bonds, AA bonds and BBB bonds with maturity 1-Year and 3-Year. Suppose that I have the following historical data.1. Risk-free Interest Rates in different periods„« 1-Year„« 3-Year2. Yield Spreads of AA bond in different periods„« AA 1-Year„« AA 3-Year3. Yield Spreads of B bond in different periods„« BBB 1-Year„« BBB 3-YearI model the risk factors of the bond portfolio as the interest rate change and the yield spread change. However, I do not know how to model the correlation among the risk factors. Is there any market practice to model the correlation?Which of the below method is better for calculating the VaR of the bond portfolio?Method 1-----------Just simply calculate the covariance among the 6 risk factors and use it to calculate the Portfolio VaR.Advantage: Straight forwardDisadvantage: If there are many risk factors, the covariance matrix will be very huge and hard to compute. Also, it seems that we just pool all our data together without modeling their characteristics.Method 2-----------Calculate the 3 sets of covariance1. among the Risk-free Interest Rates in different periods, i.e.. a 2x22. among the Yield Spreads of AA bond in different periods, i.e.. a 2x23. among the Yield Spreads of BBB bond in different periods, i.e.. a 2x2With the above covariance sets, we get the VaRs from the risk factors1. Risk-free Interest Rates2. Yield Spreads of AA bond3. Yield Spreads of BBB bondSuppose I can estimate the correlation among the above VaRs, I can get the portfolio VaR.Advantage: By calculating the VaRs separately and combine them then, the computation, e.g. the covariance matrix is manageable.Disadvantage: We do not know whether it is reasonable in market practice and we need to estimate the correlation among the 3 VaRs.

Vegetable Another method you could add to your list is a Monte Carlo simulation. It´s not easy I know that but it´s a more elegant way to handle this problem.You could simultaneously run a simulation for the two curves: the risk free government yield curve and a credit spread yield curve. Of course, you would have to model this two term structures. I have an article in PDF which is called "Value at Risk for Corporate Portfolios" from Journal of Fixed Income. If you want I can email you this article. I haven´t read it yet but I may take this opportunity to read it and change some ideas.regardsLeonardo

Thanks, leonardoalmeida. Your suggestion is valuable. I understand that Monte Carlo simulation is a full valuation to calculate the portfolio VaR and with it, we can neglect the problem of correlation among the risk factor.However, I need to use the parametric approach to calculate the portfolio VaR.Simply, if data is enough, I can try to find the covariance among the risk factors and includes it in the VaR calculation.However, it seems to be inappropriate because1. for any two factors, by formula only, we can find covariance among them. However, if we cannot explain this relationship, is it a real relationship?2. The computation effort of the covariance may not be affordable. Perhaps, we need to simply the calculation by making some assumptions. Would anyone suggest me how to handle the correlation among the risk factors?

Hi leonardo,quote---------------------------------I have an article in PDF which is called "Value at Risk for Corporate Portfolios" from Journal of Fixed Income. ---------------------------------Could you please mail the article to me.my email id is: mahendraprsingh@yahoo.comthanks

QuoteOriginally posted by: vegetableI understand that Monte Carlo simulation is a full valuation to calculate the portfolio VaR and with it, we can neglect the problem of correlation among the risk factor.Can we?

Hi No, we cannot avoid the correlation. In this specific problem I think that we have to run a simultaneous simulation for the two term structures. But there is a correlation parameter between the co-movement of the two curves that has to be modelled. We could add more complexity to these problem assuming that this correlation may be stochastic. But I don´t know any paper with this kind of approach. I remember that Darrell Duffie has a lot of papers from Credit Term Structure modelling. A more practical way to treat this problem is a historical simulation if you have a large enough database for these two curves. This could be a way to show only one number for the portfolio VaR. And you can improve your risk reporting and calculations showing PVBP for each curve or another measure or concept related to PVBP.Best regards

Thanks for Balaji’s correction and leonardoalmeida’s information.Suppose I just have the risk-free yield data and the yield spread data. How can I better apply this data to do the parametric VaR calculation? Method 1 or Method 2 as I described before. Any recommedation?Really thanks.