Learning objectives
You can:
- Decompose a bond position's expected return into yield income, rolldown return, the price change implied by your own curve view, expected credit loss and currency, compute all five on one position, and reconcile them to the total.
- Compute carry and rolldown on a stated curve, find the parallel move that exactly wipes out a year of it, cross-check that breakeven against the duration shortcut, and state the two conditions under which the trade fails.
- Show what a carry-and-roll position is betting against, by pricing the same bond at horizon on the unchanged curve and on the curve's own implied forwards, and reading the gap as the size of the bet.
- Build bullet, barbell and laddered structures to a single modified duration, compute their convexity, dispersion and bucket-by-bucket duration contributions, and rank their profit and loss under a parallel move, a steepening and a flattening.
- Size a duration-weighted steepener or flattener, compute its profit and loss under stated curve moves by exact repricing, and demonstrate that its answer is the same in a bull and a bear version of the same slope change up to a convexity residual you can quantify.
- Construct a butterfly, state which weighting convention you used, compute the curvature the trade is actually long or short, and identify the moves it is insulated from.
- Set an active duration against a benchmark, convert it into a tracking-error contribution, combine it with the credit leg through a stated correlation, and compute each leg's marginal contribution to the total.
- Use spread duration and duration times spread as the credit position-sizing unit, equalise the risk of two credits with different spreads, and show why equal market value and equal spread duration both get that sizing wrong.
- Decompose a credit position's excess return, compute its breakeven spread widening and its breakeven default probability, and price a top-down sector rotation against a bottom-up issuer selection on the same capital.
- Compute a hedged yield through covered interest parity, compare it against the unhedged position under stated spot paths, and write an active fixed-income policy that names a risk budget per strategy, a stop rule and a report that separates strategy return from market return.
The by-hand skill and the productivity payoff. The gate rewards the arithmetic: a rolldown off a curve, a hedge ratio from two modified durations, a breakeven widening, a marginal contribution to tracking error, an attribution that ties to the active return. The payoff is running all of it across three hundred positions every morning. The order is not negotiable, because every quantity here is one an assistant produces fluently and often wrongly. A rolldown computed against the wrong horizon point, a steepener sized on Macaulay rather than modified duration, a duration-times-spread figure built from a spread the vendor quotes over swaps while the portfolio is benchmarked to governments: each is a plausible number with a wrong meaning, and none of them looks wrong on a page.
Prerequisites & connections
Builds on. FI1.06 supplies the portfolio-level machinery that everything here rearranges: portfolio duration as a market-value-weighted object against the cash-flow-yield method, the parallel-shift assumption behind both, tracking error against a bond benchmark, and the liability-driven and index-based mandates whose active budget this node spends. FI1.05 supplies the instruments themselves and the trading arithmetic: coupon structures, day counts, settlement, matrix pricing, and the conversion of a quoted bid-ask into basis points of yield and into an off-the-run breakeven holding period, which the liquidity section here spends rather than rebuilds. FI1.02 supplies duration, convexity, dollar duration and key-rate profiles, all used here and none re-derived. FI1.03 supplies the bootstrap, the spot and forward curves, the roll-forward identity and the swap spread; the forward curve is used here as the thing a carry trade bets against, and it is taken as given rather than rebuilt. FI1.04 supplies option-adjusted spread, the effective measures that replace analytical duration when cash flows move, credit default swap mechanics and the securitisation waterfall; structured credit appears here as a position in a book, with its valuation left where it was built. E11.01 supplies issuer credit analysis, the leverage and coverage ladders, rating methodology, the recovery waterfall and the credit triangle. M7.03 supplies the macro read of the curve, the bull and bear vocabulary and the original duration-weighted steepener. AA1.07 supplies the fundamental law of active management, whose square-root exchange rate between skill and breadth decides the top-down against bottom-up argument in Worked Example 5. AA1.04 supplies rolldown at the single-position level and the capital-market-expectation inputs a curve view starts from. EC1.04 supplies covered interest parity, borrowed here rather than re-derived.