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How do you Construct a Hedge Using an at-the-money Put Option?

Scenario

To hedge a equity portfolio of 500 German XY shares the hedger needs 500 "rights to sell". Current share price: EUR 50

Most of the equity option contracts traded at Eurex comprise 100 shares per contract.

Hedge ratio (number of required contracts)

500 shares  =  5 contracts
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100 shares/contract

Five XY put contracts are bought.

Insurance price (put premium)

Put price: EUR 2 (corresponds to 4 percent of the share price),
total outflow for five contracts: EUR 1,000

Please note that puts can of course be sold again at any time during their lifecycle. The hedge will be finished earlier and the costs of hedging will be minimized according to the generated return.

Depending on the share performance, different scenarios (per share) are possible when the options expire.

Share price upon expiration of the option Profit/loss on the shares Profit/loss on the puts Result share + put
60 +10 -2 +8
55 +5 -2 +3
52 +2 -2 0
50 0 -2 -2
48 -2 0 -2
45 -5 +3 -2
40 -10 +8 -2

Protective Put Purchasing

poe 03 040 020 01

The hedger can still benefit from rising prices. The loss incurred when prices fall is limited to the insurance premium of EUR 2 per share. The graph of the total profit/loss shows the profile of a (synthetic) long call.

At the end of the last trading day, the put price consists solely of the intrinsic value. Intrinsic value minus the initial option price equals the profit or loss.

Formula: (Exercise price - share price) - paid option price = P/L Example: (50 - 45) - 2 = +3

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