Beta hedging with KOSPI 200 futures and margin pressure
Mirinae Pension Fund manages a 300 billion KRW Korean equity portfolio with a beta of 1.15 against the KOSPI 200. The investment committee expects a temporary 12% market decline over the next three months but does not want to sell stocks because of transaction costs and tax. It decides to use KOSPI 200 futures, which have a multiplier of 250,000 KRW per index point. The current index is 350.0 and the three-month futures price is 352.0. The fund’s target beta during the hedge is 0.70. Initial margin is 15% of notional and maintenance margin is 10%. The risk manager notes that the futures basis has widened in prior stress episodes and that the fund’s custodian requires daily cash settlement. The committee asks how many contracts to trade, what happens if the index falls 12% and the futures price converges to 308.0, and what risks remain. The fund has no other derivatives positions and reports under K-IFRS.
1. Calculate the number of futures contracts needed to reduce portfolio beta from 1.15 to 0.70. Explain the sign and the notional amount.
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Hedge ratio. Number of contracts = (target beta − current beta) × portfolio value / (futures price × multiplier). = (0.70 − 1.15) × 300,000,000,000 / (352 × 250,000). The futures notional per contract is 88,000,000 KRW. The numerator is −0.45 × 300 billion = −135 billion. −135,000,000,000 / 88,000,000 = −1,534.1. The fund should short 1,534 contracts (rounding to the nearest whole contract). The negative sign means short: to reduce beta, the fund sells futures. The total short notional is about 135 billion KRW, which is 45% of the portfolio value-consistent with reducing beta by 0.45.
2. Evaluate the hedge outcome if the index falls 12% and the futures price converges to 308.0. Compare the net result with the target-beta outcome.
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Outcome if the index falls 12%. The stock portfolio's return is beta × market return = 1.15 × (−12%) = −13.8%, a loss of 41.4 billion KRW on 300 billion. The futures position is short at 352 and converges to 308, a gain of 44 points. Gain = 44 × 250,000 × 1,534 = 16.874 billion KRW. Net loss = 41.4 − 16.874 = 24.526 billion, or −8.18% of the portfolio. A portfolio with beta 0.70 would be expected to lose 0.70 × 12% = 8.4%, or 25.2 billion. The small difference comes from rounding the contract number and from the fact that the hedge is not a perfect beta replication. The hedge worked directionally.
3. Assess the margin and basis risks. What happens if the market rises 12% instead, and how should the fund prepare?
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Margin and remaining risks. Initial margin is 15% of the short notional: 0.15 × 88 million × 1,534 = 20.25 billion KRW. If the market rises 12% instead and the futures price rises to 392, the futures loss is 40 points × 250,000 × 1,534 = 15.34 billion. The margin balance falls to about 4.91 billion, below the maintenance requirement (10% of the new notional of about 150.3 billion = 15.03 billion), so the fund faces a margin call of roughly 10.1 billion and must post cash quickly. That is the main practical risk: a hedge that is correct in the long run can force cash out at the wrong time.
Basis risk remains: the futures may not converge exactly to the index, especially in stress. Rollover risk remains if the decline lasts beyond three months; extending the hedge requires new contracts at uncertain prices. The fund also gives up upside if the market rises. The committee should pre-fund margin, set a maximum hedge ratio, and monitor basis daily rather than assume a perfect 0.70 beta.