Limitations of Yield-Based VaR for Fixed-Income Portfolios

Summary

The question proposes estimating undiversified VaR for each fixed-income instrument from historical changes in yield to maturity. The suggested process takes a lower-tail yield-return quantile, converts it into a yield move using the latest yield, and estimates the resulting price change with modified duration.

The author flags limitations, including relying on yield to maturity rather than mapping individual cash flows or bootstrapping a curve, and asks whether the general approach is sound. The document contains no answer, validation, backtest, or numerical evidence beyond the proposed calculation. It therefore serves as a prompt to examine the assumptions in yield-based VaR, including the return definition and duration approximation, rather than as an endorsed risk method.

Key ideas

• The proposed method estimates yield risk from historical log returns on yield to maturity.
• It converts a yield quantile into a price move using modified duration.
• The question itself notes that yield to maturity may not capture curve and cash-flow risk.
• No response in the document confirms whether the proposed method is valid.

Tags

# Fixed Income Var calculation


# Fixed Income Var calculation












I'm trying to calculate var for a portfolio of fixed income securities. I initially want to just calculate undiversified VaR for each instrument. I'm doing the following for each instrument

- Take historical daily log returns on YTM for coupon bond for say 2 years

- calculate mean and stdev as usual

- calculate VaR (change in yield) as -2.326*stdev(ln returns of YTM) + mean(ln returns of YTM)

- this as I understand is the 99% percentile of log returns of YTM which i then multiply with latest YTM to get actual change in yield

- Use duration formula i.e Change in price = Price * -Mod Duration * latest YTM * VaR (change in Yield)

Can someone please help me understand if this is incorrect? I know there are lot of issues with using YTM and not a cash flow mapping and also not even bootstrapping but is the general principal correct?

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