Question

On April 6, 2020, the price of Apple Inc. stock was 262.43. Assume you observe the following prices of European PUTS on the stock:   

Strike	Premium
$245	$6.16
$250	$5.15
$255	$12.22
$260	$13.45

There are three optons for which one can construct an arbitrage butterfly strategy. The minimum profit per share for this strategy is_____  , and the maximum profit per share is______

Answer 1

A butterfly is a spread with three different strike prices. Using puts, the investor buys 2 European puts, one with low strike price and the one with high strike price and sells 2 puts with an intermediate strike price.

1. Case 1

Strike	Premium
$245	$6.16
$250	$5.15
$255	$12.22

Cost of entering = 6.16+12.22-(2*5.15) = $8.08

Maximum profit will be at the center strike ie. if the stock price is $250 at expiration

Maximum profit = $255-$250-$8.08 = -$3.08

Maximum loss = Premium paid = $8.08

2. Case 2

Strike	Premium
$250	$5.15
$255	$12.22
$260	$13.45

Cost of entering = 5.15+13.45-(2*12.22) = -$5.84

Maximum profit will be at the center strike ie. if the stock price is $255 at expiration

Maximum profit = $260-$255+$5.84 = +$10.84

Maximum loss = Premium gain = -$5.84

The minimum profit per share for this strategy is $5.84 , and the maximum profit per share is $10.84

3. Case 3

Strike	Premium
$245	$6.16
$255	$12.22
$260	$13.45

Cost of entering = 6.16+13.45-(2*12.22) = -$4.83

Maximum profit will be at the center strike ie. if the stock price is $255 at expiration

Maximum profit = $260-$255+$4.83 = +$9.83

Maximum loss = Premium gain = -$4.83

The minimum profit per share for this strategy is $4.83 , and the maximum profit per share is $9.83