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Cutting Beta from 1.18 to 0.85 - and the Margin Call Three Weeks Later

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Cutting Beta from 1.18 to 0.85 - and the Margin Call Three Weeks Later

The KOSPI200 Blue-Chip Focus Fund runs a 60 billion KRW long-only equity portfolio with an estimated beta of 1.18 against the KOSPI200. The manager expects a turbulent three months around the June election but does not want to sell stocks, for tax and market-impact reasons. He decides to cut effective beta to 0.85 using June KOSPI200 futures trading at 350.00, multiplier 250,000 KRW. The firm charges 15% initial margin on futures notional, and the fund keeps a 2 billion KRW cash buffer specifically for variation margin. Three weeks later the KOSPI200 has risen 8.0%, the portfolio has returned 7.2% because the manager quietly sold two high-beta holdings and realised beta fell to 1.05, and the June futures trade at 378.60. The prime broker has issued a margin call, and the manager asks whether to lift the hedge, keep it, or resize it.

1. Compute the initial hedge and the collateral it requires, and identify the residual risks the manager is carrying.

Read the worked answer

Contract count. Hedge ratio needed = 1.18 − 0.85 = 0.33. Notional per contract = 350.00 × 250,000 = 87,500,000 KRW.

N = 0.33 × 60,000,000,000 / 87,500,000 = 19,800,000,000 / 87,500,000 = 226.3 → short 226 contracts (rounding down leaves a small residual long beta, which is the conservative choice).

Collateral. Initial margin = 226 × 87,500,000 × 0.15 = 2.966 billion KRW, posted in addition to the 2 billion variation buffer.

Residual risks:

  1. Beta estimation error. 1.18 is a historical estimate; if true beta is 1.25, the achieved beta is 0.92, not 0.85.
  2. Basis risk. Futures track the KOSPI200; the portfolio's sector mix means the hedge may not offset idiosyncratic or sector moves - the 7.2% versus 8.0%×1.18 divergence is exactly that.
  3. Dividend and roll effects. The futures price drifts down by expected dividends; a three-month horizon crosses one roll.
  4. Margin liquidity risk. The hedge consumes cash precisely when the market rises - a funded, marked-to-market short has an opposite cash-flow profile to the portfolio, and the two do not net at the prime broker.
  5. Discipline risk. The manager retains the right to trade the underlying, which silently changes the hedge ratio - as happened here.

2. Three weeks later, quantify the position: portfolio value, futures P&L, current effective beta, the number of contracts now needed, and whether the 2 billion KRW buffer covers the call.

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Portfolio. 60bn × 1.072 = 64.32 billion KRW (gain 4.32bn).

Futures P&L. Price move = 378.60 − 350.00 = 28.60 points × 250,000 = 7,150,000 KRW per contract × 226 = −1.616 billion KRW.

Net economic result: +4.32bn − 1.616bn = +2.70bn. The hedge cost about 1.6bn of upside; that is the intended outcome of cutting beta, not a failure.

Current effective beta. Hedge notional marked to today = 226 × 378.60 × 250,000 = 21.391bn. 21.391 / 64.32 = 0.3326. Effective beta = 1.05 − 0.3326 = 0.717 - the position is now over-hedged relative to the 0.85 target, because realised beta fell and the portfolio grew.

Contracts now required. Target hedge notional = (1.05 − 0.85) × 64.32bn = 0.20 × 64.32bn = 12.864bn. Notional per contract at 378.60 = 94.65m. N = 12.864bn / 94.65m = 135.9 → 136 contracts short; buy back 90.

Does the buffer cover the call? Variation loss of 1.616bn against a 2.0bn buffer leaves about 384m of headroom. Each index point on 226 contracts = 226 × 250,000 = 56.5m KRW, so a further 6.8 points (about 1.8%) rally would exhaust the buffer. It covers today's call but not comfortably; resizing to 136 contracts also cuts the per-point exposure to 34.0m KRW and relieves the pressure.

3. Advise the manager: lift, keep, or resize the hedge - and how should he explain the futures 'loss' to the investment committee?

Read the worked answer

Recommendation: resize, do not lift.

  • Lifting converts a 0.717 effective beta back to 1.05 at the moment the manager's original view (a turbulent three months) has not changed. That is a directional bet dressed as a reaction to a paper loss.
  • Keeping 226 contracts leaves the fund over-hedged by 0.133 of beta - roughly 8.6bn of unintended short exposure - and keeps the margin buffer one 1.8% rally away from exhaustion.
  • Buy back 90 contracts to reach 136, which restores 0.85 and reduces the per-point margin exposure by 40%.

The roll. If the hedge must run past June, roll the remaining 136 into the next contract. Cost is the basis difference plus commissions, typically a few bp of notional; do it on a liquid day, and re-estimate the dividend assumption before choosing the timing.

Explaining the futures loss:

  1. Present the total result, not the futures account: portfolio +4.32bn, futures −1.616bn, net +2.70bn versus +4.32bn unhedged. The fund gave up 1.6bn of upside to buy protection that, in the event, was not needed - the same as an insurance premium.
  2. State clearly that the loss is a cash-flow location, not an economic loss; the offset sits in the equity book and has not been realised.
  3. Disclose the two control failures: the manager changed the portfolio's beta after sizing the hedge, and the sizing was not re-estimated. Add a standing rule - recompute the hedge ratio at every margin call and at least monthly.
  4. Record the revised mandate: target beta 0.85 ± 0.05, 136 contracts, margin buffer policy, and the trigger at which the buffer is topped up rather than the hedge cut.