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IBBC CAPITAL ACADEMY / 2027

Resize portfolio exposures with explicit hedge arithmetic

Independent IBBC Capital draft content for self-study. Not affiliated with or endorsed by CFA Institute. New lessons await subject-matter review. No CFA designation or official PSM credit is awarded.

Learning goals

  • Calculate equity and duration hedge positions.
  • Evaluate swaps, forwards, futures and volatility instruments.

Draft · approximately 60 minutes, excluding further revision.

Decision case · fictional facts

A fictional 100 million equity portfolio has beta 1.2; the target is 0.8. One index futures contract has value 200,000 and beta 1. A bond portfolio 100 million has modified duration 6 and target 4. A suitable bond futures contract has 100,000 value and effective duration 5, conversion adjustment assumed 1. Hedge relations are approximate and ignore basis changes.

Use sensitivities rather than matching only notional

Index futures change market exposure with limited initial cash, but require margin and daily settlement. Approximate contract count is (target beta−current beta)×portfolio value/(futures value×futures beta). Negative means sell. A cross-hedge depends on stable beta and basis; changing exposures, dividends and contract rolls can cause mismatch.

For rates, match money duration or DV 01 and consider key-rate exposures, cheapest-to-deliver and conversion factors. Receive-fixed/pay-floating swaps generally add duration; pay-fixed/receive-floating generally reduces it, all else equal. A single duration match does not immunize nonparallel curves, convexity, spread risk or counterparty exposure.

Synthetic allocation still needs cash and governance

Forwards can implement customized currency or asset exposure but add bilateral counterparty and settlement risk; futures standardize terms and clearing without removing all default or liquidity risk. Total-return swaps transfer economic return under collateral terms. Volatility and variance instruments hedge different nonlinear risks; their notional cannot be equated mechanically with equity dollars.

Document authority, eligible contracts, limits, collateral, stress liquidity and roll policy before trading. A financially effective hedge may fail operationally if margin cannot be funded in a stress. Rebalance when exposure, target or contract economics change and assess all-in implementation costs.

Equity derivatives change beta without an immediate cash purchase

A 100 mportfolio has beta.8 and target 1.1. A futures contract has beta 1 and 25,000 notional, with matching exposure assumptions. Required added beta-dollar exposure=(1.1−.8)× 100 m=30 m, so buy 1,200 contracts. Alternatively, a receive-equity/pay-financing total-return swap can add exposure but has counterparty, collateral and financing terms.

Derivative notional is not the amount of initial cash invested. Monitor market exposure and funding separately; basis or beta mismatch can leave residual risk.

Variance contracts settle squared volatility units

A synthetic long variance swap pays Nvar×(realized variance−strike variance). Specify the quotation units. If volatility is quoted in percentage points, realized 25 and strike 20 imply 625 and 400 variance units. With 1,000 currency per variance point, expiration receipt is 225,000 before counterparty or settlement adjustments. This differs from a volatility swap paying a linear volatility difference.

Before maturity, use realized variance to date plus an estimate of remaining variance under the contract’s sampling and annualization, then discount as appropriate. Do not value the whole trade using only volatility already realized; short variance carries severe jump/tail risk.

Duration targets require dollar sensitivity

A 100 mportfolio moves from duration 4 to 6, requiring DV 01 increase(6−4)× 100 m×.0001=20,000 currency per bp. If a long futures contract adds 80 DV 01 under the specified hedge assumptions, buy 250 contracts. Sign, size, delivery options and basis must match the chosen rate exposure; an aggregate target can miss curve-node mismatch.

For equities, use beta-dollar exposure rather than bond duration. The hedge target must specify whether it concerns nominal value, local delta, portfolio beta or interest sensitivity; these are not interchangeable.

Overlay rebalancing still needs collateral

A 60/40 equity/bond portfolio has 100 min securities and receives 10 mcash. Target on 110 mbecomes 66 mequity and 44 mbonds. Buying 6 mequity and 4 mbond notional futures can temporarily equitize the cash while reserving it for collateral under the stated exposure assumptions. It does not eliminate basis, margin or roll costs.

Forward and futures prices reflect financing, distributions, convenience and risk adjustments as applicable. They can inform market pricing but are not guaranteed forecasts of future spot prices. Compare a tactical view with what is already embedded in prices.

Formula and assumptions

Nβ=(βtarget−βcurrent)Vp/(βfVf); ND=(Dtarget−Dcurrent)Vp/(DfVf); DV01≈Dmodified×V×0.0001

Compare with the model response after drafting
  1. Equity futures=(0.8−1.2)×100,000,000/200,000=−200: sell 200. Bond contracts=(4−6)×100,000,000/(5×100,000)=−400: sell 400.
  2. Bond DV 01 reduction=(6−4)×100 million×0.0001=20,000 per basis point; each contract DV 01=50. Stress basis, curve and margin before approval.

Errors to catch

  • Matching notional while ignoring beta or duration.
  • Assuming low initial margin means low maximum loss.

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