Collar or Protective Put for a Concentrated Equity Holding
Priya manages an £8.4m portfolio holding 1,000,000 shares of Helio plc at £8.40. She fears a 15% fall over six months but does not want to sell because of a large unrealised gain and a lock-up. A six-month European put at £8.00 costs £0.62 per share; a six-month European call at £9.20 can be sold for £0.48. Helio pays no dividend. The risk-free rate is 3% and implied volatility is 32%, while realised volatility over the past year was 24%. Priya's mandate allows options for hedging but prohibits net option writing that leaves unlimited upside loss. She is considering (A) a protective put, (B) a collar using the £8.00 put and £9.20 call, or (C) a zero-cost collar. The investment committee asks for payoff outcomes at £7.20, £8.40 and £10.00, and whether the high implied volatility changes the decision.
1. Calculate the net premium, maximum loss, maximum gain and breakeven for (A) the protective put and (B) the collar. State whether the collar complies with the mandate.
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A. Protective put: buy £8.00 put for £0.62. Net cost = £0.62 per share, or £620,000 for 1,000,000 shares. Maximum loss = (share price − put strike) + premium = (£8.40 − £8.00) + £0.62 = £1.02 per share (12.1% of £8.40). Maximum gain is unlimited because the shares remain owned. Breakeven = £8.40 + £0.62 = £9.02. B. Collar: buy £8.00 put for £0.62 and sell £9.20 call for £0.48. Net debit = £0.62 − £0.48 = £0.14 per share, or £140,000. Maximum loss = (£8.40 − £8.00) + £0.14 = £0.54 per share (6.4%). Maximum gain = (£9.20 − £8.40) − £0.14 = £0.66 per share (7.9%). Breakeven = £8.40 + £0.14 = £8.54. The collar complies: the short call is covered by 1,000,000 owned shares, so it does not create an unlimited upside loss. It does cap upside, which is an economic cost but not a mandate breach.
2. Show the profit or loss per share at expiry for both strategies at Helio prices of £7.20, £8.40 and £10.00.
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Protective put: At £7.20: share loss −£1.20; put gain +£0.80; premium −£0.62; net −£1.02. At £8.40: share unchanged; put expires worthless; premium −£0.62; net −£0.62. At £10.00: share gain +£1.60; put worthless; premium −£0.62; net +£0.98. Collar: At £7.20: share loss −£1.20; put gain +£0.80; short call worthless; net debit −£0.14; net −£0.54. At £8.40: share unchanged; both options worthless; net −£0.14. At £10.00: share gain +£1.60; put worthless; short call loss −£0.80; net debit −£0.14; net +£0.66. The collar truncates both tails: it reduces the downside from £1.02 to £0.54 but caps the upside at £0.66.
3. How should the implied volatility of 32% versus realised volatility of 24% affect the choice? What would a zero-cost collar require?
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At 32% implied versus 24% realised, options look expensive on a simple historical-volatility comparison. That makes the outright protective put costly: Priya pays £0.62 for downside protection. The collar partly solves this by selling an expensive call against an expensive put, reducing net cost to £0.14. But high implied volatility does not automatically mean 'do not hedge'; it may reflect a genuine fear premium, skew or event risk. A zero-cost collar would require the call premium received to equal the £0.62 put premium. Since the £9.20 call is only worth £0.48, the fund would need to sell a call with a lower strike than £9.20 (or buy a lower-strike put), which caps upside more tightly. The exact strike depends on the pricing model and skew. Recommendation: if Priya's main objective is avoiding a 15% fall and she can accept a cap near £9.20, the collar is more cost-efficient in a high-volatility environment. If retaining upside is essential, the protective put is cleaner but expensive; a zero-cost collar should only be used if the tighter cap is acceptable.