Estimating Bond VaR from Treasury Yield and Credit Spread Changes
Summary
The note outlines a historical-simulation method for estimating a bond’s value at risk from changes in the US Treasury curve and the bond’s credit spread. First, convert historical clean prices into bond yields using the appropriate settlement dates. Then estimate the bond’s current price sensitivity to a one-basis-point yield move. For each historical scenario, separate the bond-yield change into benchmark-rate and spread components, and apply the current sensitivity to estimate each component’s contribution to profit or loss. Sort the combined scenario P&Ls and select the loss at the chosen percentile; component or marginal VaR can help attribute risk to each factor.
The approach simplifies valuation by treating yield sensitivity as the full P&L effect. It omits convexity, accrued interest, financing costs, and other time-related P&L. The answer also cautions that using today’s sensitivity may be unreliable when historical yields differ substantially from current yields. The document describes a practical approximation, not a full repricing framework.
Key ideas
- Convert historical bond prices to yields using the correct historical settlement dates.
- Estimate current price sensitivity to a one-basis-point yield change.
- Separate each scenario’s bond-yield move into benchmark-rate and credit-spread changes.
- Apply current sensitivity to both factors, combine their P&Ls, and take the selected loss percentile.
- The approximation omits convexity and other P&L sources and can weaken when past yields differ greatly from current yields.
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Full text
# Estimating VaR of bond due to changes in the US yield curve # Estimating VaR of bond due to changes in the US yield curve I am attempting estimate the 99% 10-day VaR of an investment grade bond due to changes in the US yield curve. The data provided is the daily prices of the bond over time. In addition I have the Daily treasury yield curve rates. I understand how to carry out a historical simulation for the 99% VaR, however this will give the VaR due to all risk factors not just the changes in yield curve. So far I have calculated the n-1 scenarios for returns of the bond and the changes in yields for each maturity but cannot figure out how to continue, any help would be appreciated. ## Answer by Dimitri Vulis (score 2) https://quant.stackexchange.com/a/63201 Something like the following is likely to be acceptable to whoever looks at your VaR methodology. Convert your historical (clean) price to yields of your bond (remember to use the right historical settlement date). I think for this exercise you can get away with ignoring the convexity and also ignoring the accrued, cost of financing, and other P&L due to passage of time. I.e. assume that the yield01 * the change in your bond's yield is the entire P&L. Calculate the sensitivity of today's price to 1 basis point change in yield. On each historical date, you have a change in your bond's yield, decomposed into the change in the benchmark yield and the change in your bond's spread to benchmark. These are your two market factors. Multiplying the latter two changes by today's sensitivity to 1bp yield change tells you each factor's contribution to the P&L under this historical scenario. To get the VaR, you sort the net P&Ls and take the 99th percentile. You can use marginal/component VaR to see how much comes from each market factor. This approach would have problems if the historical yields are very different from the yield now.
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