June KOSPI200 Basis: Direct Basket, ETF Route, and the Options-Implied Forward
On 12 March the KOSPI200 closes at 352.40. The June KOSPI200 futures contract, which expires in 78 days, settles at 355.10; the multiplier is 250,000 KRW. The 91-day CD rate is 3.55%, but the proprietary desk's all-in funding cost through its prime-brokerage line is 3.90%. The consensus dividend yield on the KOSPI200 basket over the remaining contract life is 1.45% annualized. The desk can buy the 200 constituent stocks for 0.02% commission plus 0.04% market impact each way and can trade the futures for 0.005% commission each way. Alternatively it can buy a KOSPI200 ETF, which trades at a 0.15% premium to NAV, charges 0.15% per annum, and costs 0.03% impact each way. The desk's risk limit requires at least 25bp of expected return over the holding period after all costs; capital is the basket plus 15% initial margin on the futures notional. Separately, the June 352.5 call trades at 8.15 and the June 352.5 put at 5.90.
1. Compute the fair futures price, the implied financing rate embedded in 355.10, and decide whether the direct cash-and-carry trade clears the 25bp hurdle. Show the per-contract arithmetic.
Read the worked answer
Fair value. F* = S × exp((r − q) × T), T = 78/365 = 0.21370.
- At the 3.90% funding cost: (0.0390 − 0.0145) × 0.21370 = 0.005236 → F* = 352.40 × 1.0052494 = 354.25.
- At the 3.55% CD rate: (0.0355 − 0.0145) × 0.21370 = 0.004488 → F* = 353.99.
So the no-arbitrage band is roughly 353.99–354.25. The market at 355.10 is 0.85 points rich versus the desk's own funding cost, i.e. 0.241% of the index.
Implied financing rate. Solving r = ln(F/S)/T + q = ln(1.0076617)/0.21370 + 0.0145 = 0.03572 + 0.0145 = 5.02%, against a 3.90% funding cost - a 112bp annualized pickup, about 0.24% over the 78 days.
Per contract (direct basket):
- Gross: 0.85 × 250,000 = 212,500 KRW.
- Entry cost 0.06% × 88,100,000 = 52,860; exit cost 0.06% ≈ 52,860; futures 0.005% × 2 × ~88,800,000 ≈ 8,880. Total ≈ 114,600 KRW.
- Net ≈ 97,900 KRW on 88,100,000 of notional = 0.111%, or 9.7bp on capital of ~101,400,000.
Decision: the trade is real but does not clear the desk's 25bp hurdle. The 0.24% gross edge is more than halved by round-trip execution costs, and the return on capital is smaller still because 15% margin sits alongside the fully funded basket. Reject, or revisit only if impact costs fall.
2. The desk switches to the ETF route. Recompute and explain why the conclusion flips, and what that implies about 'riskless' arbitrage.
Read the worked answer
ETF route, same 354.25 fair value:
Gross edge is unchanged at 0.85 points = 0.241% of notional. Costs:
- Premium to NAV paid on entry: 0.15%
- Impact 0.03% each way: 0.06%
- Management fee 0.15% × 78/365: 0.032%
- Futures commission: 0.01%
- Total ≈ 0.252%
Net = 0.241% − 0.252% ≈ −0.01%, before any tracking error. The trade is now marginally loss-making and clearly fails the hurdle.
Why it flips. The direct basket pays commission and impact but buys assets at fair value. The ETF charges the same kind of costs plus a premium to NAV - you pay 0.15% above what the underlying is worth. That premium is only recoverable if it is still there when you exit; assuming convergence to NAV before expiry, the arbitrageur donates the premium to the market.
Implication. 'Riskless' basis arbitrage is a statement about the theoretical relation, not about the trade. The executable question is always: which vehicle can I actually hold to expiry, at what all-in cost, and how much of the mispricing survives? Here the mispricing is ~24bp; realistic frictions are 25bp+. That is why index-futures basis dislocations of a few tenths of a percent persist without being instantly arbitraged away, and why desks compute the edge net of their own funding line rather than against a government yield.
3. Using the 352.5 call at 8.15 and put at 5.90, derive the options-implied forward and state whether an arbitrage exists against the 355.10 futures price. What would you check before trading?
Read the worked answer
Parity in forward form. For European options on the index: C − P = (F − K) × exp(−rT), so the forward implied by the option prices is
F_implied = K + (C − P) × exp(rT) = 352.5 + (8.15 − 5.90) × exp(0.0355 × 0.21370) = 352.5 + 2.25 × 1.0076153 = 352.5 + 2.2671 = 354.77.
Note this uses the actual futures-implied financing, so the dividend yield cancels; no separate dividend estimate is needed.
Gap: the futures market says 355.10, the options market says 354.77 - the futures are 0.33 points rich, or about 82,500 KRW per contract (0.094%).
Trade if genuine: buy the call, sell the put (synthetic long), and sell the futures. The position is delta-neutral and locked at expiry, provided the short put's margin and the futures margin are funded.
What to check first:
- Executable prices, not last trades. 0.33 points is inside a plausible bid-ask on two option legs; quoting mid-prices is not a tradable edge.
- Costs. Three legs of commission plus exchange fees; a 0.10–0.15 point cost base leaves only ~0.18–0.23 points and fails a 25bp-type hurdle once margin capital is counted.
- Margin and funding on the short put - the synthetic long is not free of capital charges, and a short put carries margin that rises if volatility spikes.
- Staleness. Check timestamps: the futures settle at the close while the option prints may be minutes old, which alone can create a phantom 0.3-point gap.
Conclusion: a textbook parity deviation exists on paper, but at 0.33 points it is a soft signal. Verify live quotes and cost; execute only if the executable gap remains above roughly 0.25 points.