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Account for what would motivate someone to open a protective put or a covered call position.

FRM® Part I · Financial Markets and Products · Trading Strategies · FRM1.FM.14.a

The idea

A protective put is a long position in an asset plus a long put on it. The put sets a floor: at expiry the holder's value cannot fall below the strike, so the maximum loss is the purchase price minus the strike plus the premium paid, while upside is kept less that premium. It suits an owner who wants to keep gains but fears a sharp fall, much like insurance whose price is the premium. A covered call is the long asset plus a short call. The premium received gives only a small cushion on the downside, and gains are capped at the strike, so it suits an investor expecting a flat or mildly rising market who is happy to sell at the strike. The usual mistake is to treat a covered call as a hedge against a large fall. By put-call parity, a protective put has the same payoff as a long call plus a zero-coupon bond, and a covered call the same as a short put plus a bond.

Formulas

Maximum loss on a protective put

maximum loss = S₀ − K + p

S₀
the price paid for the asset
K
the strike of the put
p
the put premium paid

Reached at expiry whenever the asset ends at or below the strike. The premium is part of the loss and is often left out.

Breakeven price of a covered call

breakeven = S₀ − c

S₀
the price paid for the asset
c
the call premium received

Holds below the strike, where the call expires worthless. The premium is only a small cushion, so a covered call is no hedge against a large fall.

A practice question

From the question bank, with the reason each wrong option is wrong.

A portfolio manager holds a large equity position and fears a sharp decline over the next three months, but does not want to give up gains if the market rallies. Which strategy best fits this motivation?

  1. Write call options on the holding to earn premiumWhy not: A covered call caps the upside at the strike and offers only a premium cushion on the downside, which contradicts the wish to keep gains.
  2. Buy put options on the holding, accepting the premium as the cost of a floor - correct
  3. Sell index futures against the holdingWhy not: A short futures hedge removes the downside but also the upside, so gains in a rally are given up.
  4. Buy additional call options on the same equityWhy not: Adds upside exposure but does nothing to limit losses on the existing holding if the price falls.

A protective put (long asset plus long put) sets a floor at the strike while keeping the upside, less the premium paid. That is exactly the motivation described; the other choices give up upside or leave the downside open.

A harder one

An investor buys a stock at 40 and writes a three-month call on it with strike 44 for a premium of 1.80. The stock price at expiry at which the combined position breaks even is closest to:

  1. 41.80Why not: Adds the premium to the purchase price, wrong sign: premium received lowers the breakeven.
  2. 40.00Why not: Ignores the premium received, which cushions a fall in the stock by exactly that amount.
  3. 38.20 - correct
  4. 42.20Why not: Subtracts the premium from the strike instead of from the purchase price; the strike does not set the breakeven below the strike.

Below the strike the call expires worthless, so profit = (S - 40) + 1.80. Setting it to zero gives S = 40 - 1.80 = 38.20.

The hardest tier

A fund owns a stock bought at 80. It can either buy a put with strike 75 for 3.20 or write a call with strike 85 for 2.40 (both expire in three months, per share). If the stock is 70 at expiry, which strategy has the better profit and by how much?

  1. The covered call, by 0.60 - correct
  2. The protective put, by 2.60Why not: Leaves out the premium paid for the put, which overstates the put's result.
  3. The protective put, by 0.60Why not: Reverses the comparison: after both premiums the put position loses 8.20 against 7.60 for the covered call at this price.
  4. The covered call, by 5.60Why not: Counts the put premium as a cost but forgets the put's payoff at expiry, which overstates the covered call's advantage.

Protective put: (70 - 80) + (75 - 70) - 3.20 = -8.20. Covered call: (70 - 80) + 2.40 = -7.60. The covered call is better by 0.60 at 70, because the put's floor at 75 is only 5 above the price; in a larger fall the put would win.

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