A swap desk hedges its 10-year payer position using 10-year futures and reports zero duration. The yield curve flattens, short rates rise 75 bp, long rates rise 30 bp, and the desk loses $4 million. Total duration was zero; key-rate duration was not. The hedge worked for the move that didn't happen and failed for the move that did.
Total modified duration assumes every yield on the curve moves by the same amount Δy. Real curves don't behave that way. On a typical day, short rates can move +20 bp while long rates move +5 bp, or the curve can twist with a 30-year that moves opposite the 5-year.
A portfolio with zero net duration is not a fully hedged portfolio. A hedge using a 10-year future against a barbell of 2-year and 30-year exposures will have zero duration but enormous slope risk. The 2-year and 30-year don't move with the 10-year futures contract on most days.
Risk managers fix this with a richer decomposition. Two main tools: principal components analysis and key-rate duration.
Common mistakes
- Treating risk-neutral probability as the real-world probability. p is not the probability you'd estimate from historical returns. It's the unique probability that prices expected return at the risk-free rate, killing arbitrage.
- Forgetting to test early exercise at every node for American options. American options require comparing continuation value to intrinsic at every interior node. Skipping the test gives the European price, not the American. Trap: a question describes an American put deep in the money; the European-only computation undervalues by 5-15%.
- Adding KRDs without checking the bump convention. A complete set of key-rate bumps must sum to the matching parallel curve shift. Compare the sum to duration under that same shift, not automatically to a differently defined YTM duration.
Bottom line
- Principal components analysis (PCA) commonly identifies level, slope and curvature as the main yield-curve factors; their variance shares are sample-dependent.
- Key-rate duration (KRD) measures price sensitivity to a shift at one maturity, holding adjacent rates fixed; complete key-rate bumps sum to the corresponding parallel curve duration.
- KR01 is , the dollar price change for a 1 bp shift at one key rate, used to size hedge instruments at each maturity.
- Forward bucket 01 is similar but defined on forward-rate windows rather than spot-rate maturities; both decompose interest-rate risk by maturity.
Exam shortcut
When a question asks for a fully hedged duration-zero portfolio, check whether the hedge spans all key rates. A 10-year-only hedge against a 2y/30y barbell leaves substantial slope risk even with zero total duration. Sum the KRDs and check them against the corresponding parallel curve duration before moving on.
The full lesson (about 4,921 words, 33 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.
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