Learning objectives
By the end you can:
- Compute a portfolio's duration by both accepted methods, the market-value-weighted average and the cash-flow-yield method, state which one a liability comparison requires, and quantify the money-duration error that choosing wrongly introduces.
- Compute portfolio convexity and dispersion, explain what dispersion measures that duration cannot, and state the parallel-shift assumption that sits underneath every one of these measures.
- Build a cash-flow-matched (dedicated) portfolio against a multi-period liability schedule, solving backward from the last payment, and price its cost against the present value of the liabilities it retires.
- Build a duration-matched portfolio against the same schedule, verify the three immunisation conditions (present value, money duration, and dispersion and convexity at least as large as the liability's), and say why the third condition exists at all.
- Quantify structural risk: show what a duration-matched book loses under a stated twist that a parallel-shift match cannot see, and rank a barbell, a laddered build and a dedicated build by exposure to it.
- Run a contingent immunisation programme: compute the cushion, compute the trigger yield at which active management must stop, and show what the client actually receives when a manager runs past the trigger.
- Size a futures or swap overlay from a stated duration gap using basis point value, convert the requirement into contracts or notional, and report the residual the rounding leaves behind.
- Carry funded-ratio arithmetic into a bond book: compute the hedge ratio, size a glide-path step, compute levered collateral headroom from
10,000 / (leverage x duration), and state the cash call a stated selloff produces. - Write a rebalancing policy for an immunised portfolio with explicit triggers, compute the drift after one year, and cost the rebalancing trade in basis points of the portfolio.
- Explain why a bond index cannot be replicated, build a stratified sample by cell, decompose the resulting tracking error into duration, spread and idiosyncratic components, and price the trade-off between more holdings and more transaction cost.
Prerequisites & connections
Builds on. FI1.05 (Fixed-Income Instruments, Issuance and Trading) supplies the instruments themselves, together with day counts, settlement arithmetic and the matrix pricing that gives an untraded index constituent a price at all. FI1.02 supplies the entire measurement kit used here: Macaulay and modified duration, money duration and PVBP/DV01, convexity, key-rate durations, and the single-liability Redington immunisation this node extends to a multi-period schedule. FI1.03 supplies the curve, so that a bond and a liability can be valued off the same arbitrage-free spot rates rather than off separate yields. FI1.04 supplies effective duration and negative convexity, which is what any callable or mortgage exposure in the asset book actually carries. AA1.02 supplies the funded ratio, the surplus and the duration gap at the allocation level, and AA1.05 supplies the institutional client whose objectives and constraints set the mandate. DV1.01 prices the futures and swaps used in the overlay; this node only sizes them. E11.01 supplies credit, ratings and recovery, which is what the corporate and state-loan cells of a bond index are made of.
Deliberate non-overlaps, listed so that nothing here rebuilds a neighbour's material. FI1.02 owns duration, convexity, DV01 hedging and the single-liability immunisation; the extension to several liabilities, and the dispersion condition that only appears once there are several, is what is added here. FI1.03 owns bootstrapping and the term structure. FI1.05 owns instrument anatomy, coupon structures, day counts, settlement and matrix pricing, so every price used here is taken as given. AA1.02 owns risk budgeting, the funded ratio and the glide path as allocation objects; the arithmetic reappears here inside a bond book with a collateral account attached. AA1.05 owns the hedge-ratio decision at mandate level, including the Indian retirement-trust pattern of investment, and this node does not restate it. AA1.08 owns index construction, the exchange-traded wrapper and the mechanics of equity indexing, so the index material here is confined to what is different about bonds. FI1.07 (Active Fixed Income: Yield-Curve and Credit Strategies) owns every active strategy, including carry, roll-down, curve trades, credit positioning and the excess-return decomposition. E11.01 owns issuer credit analysis. MS1.03 owns repo and the funding leg that makes leverage possible.