Separating Rate and Credit Risk in Sovereign Bond Scenarios
Summary
The document describes a historical simulation for a sovereign bond portfolio. Each bond is repriced under country yield curves shifted by historical scenarios, with shifts applied across markets together to retain their co-movement. Scenario price returns are combined using current portfolio weights, and portfolio volatility is estimated from the resulting return distribution. It also gives a covariance-based formula for each bond’s contribution to portfolio volatility, which sums to total volatility.
The question is how to distinguish broad interest-rate movements from changes in sovereign credit valuation within a currency union. The answer proposes treating a riskier sovereign, such as Italy, as a credit exposure and measuring its spread against Germany or an interest-rate swap curve. Stress that spread as a credit risk factor, while assigning the underlying benchmark curve to interest-rate risk. The discussion is conceptual: it provides no scenario construction details, empirical results, or guidance on choosing between the German and swap benchmarks.
Key ideas
- Historical yield-curve shifts can be used to reprice bonds and generate portfolio return scenarios.
- Applying country curve shifts simultaneously preserves observed co-movement among bond markets.
- Bond volatility contributions can be calculated from each bond’s covariance with portfolio returns.
- A sovereign spread against a benchmark curve can represent credit risk, while the benchmark curve represents interest-rate risk.
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# Fixed Income risk attribution in the historical simulation of a sovereign bond portfolio
# Fixed Income risk attribution in the historical simulation of a sovereign bond portfolio
We use historical simulation for risk analysis. I.e. for each bond there is a repricing of the form $$ P_j = PV(\text{yield curve in scenario } j), $$ where the yield curve is the zero rates curve of the respective country (for a German bond I take the German curve, for an Italian bond the Italian, ...). The various scenarios of the yield curves are calculated from historical shifts along the curve applied to the present curve and for all markets simultaneously (thus modelling correlations among the bond markets).
Then for each bond we calculate returns $r_j = P_j/P_0-1$, thus the return of the price in scenario $j$ based on the current market price $P_0$. Then the portfolio return in scenario $j$ is calculated by $$ r_j^P = \sum_{i=1}^N w_i r_j^i, $$ where $w_i$ is the current weight of bond $i$ in the portfolio and $r^i_j$ is its return in scenario $j$. Then portfolio volatility can be estimated as the standard deviation of $r_1^P,\ldots,r_j^K$,ie. $\sigma^P$, if we have $K$ scenarios.
Furthermore I can calculate volatiltiy contributions $\sigma_i$ for each bond by $$ \sigma_i = w_i covar(r^i,r^P)/\sigma^P, $$ then $\sum_{i=1}^N \sigma_i = \sigma^P$
All this is quite standard.
In an EMU portfolio (say: Germany, France, Italy) I have various effects: overall change in interest rate levels (more or less risk free, this is more or less the German yield curve) and changes in the market valuation of more risky countries (as additional yield w.r.t the German level) - a sort of credit risk.
What methods do you apply to separate interest rate risk from credit risk in a sovereign portfolio? What are your experiences? Are there any references?
All the data I have is the curves for each country. I would like to avoid using data from credit derivatives.
## Answer by rrg (score 1, accepted)
https://quant.stackexchange.com/a/30697
This question complicates a simple issue.
Model e.g. Italian sovereign as a credit, and then treat the spread either against Germany or IRS curve, and stress as you would any financial/non-financial credit risk.
The underlying benchmark curve would naturally fall onto the interest rate risk.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.