Mock 2010 Q42 answer doesn't make any sense

Kung Chen expects the tracking stock on the Dow Jones Industrial Average (DIA) to trade within a narrow range around its current price over the near term. Based on his expectation, he believes a profitable trading opportunity is to initiate a butterfly spread strategy using call options on DIA. Osborne suggests using three one-month call options on DIA. Exhibit 3 illustrates current DIA call options expiring in one month. Chen wants a butterfly spread using a total of 200 long contracts and 200 short contracts.

Call options

• Exercice price of 88 with an option premium of 4.20
• Exercice price of 92 with an option premium of 2
• Exercice price of 96 with an option premium of 0.2

If Chen creates a butterfly spread using the three one-month call options suggested by Osborne, the maximum potential loss at expiration is closest to:

A. \$3,000. B. \$7,000. C. \$27,000.

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I get A but according to CFAI, answer is B.

Here’s how I get A.

Need 100 long contracts of the options with a strike or \$88 so you spend (100 contracts x 100 shares/contract x \$4.2) = -42,000

Need 200 short contracts of the options with a strike of \$92 so you get (200 contracts x 100 shares/contract x \$2 premium) =+40,000

Need 100 long contracts of the option with a strike of \$96 so you spend (100 contracts x 100 shares/contract x \$0.50 premium)= -5,000

Maximum loss = -42,000 + 40,000 -5,000 = +3,000

I’m wondering how they get 7,000 ?

Thank you !

What’s their explanation?

@Magicien2000, here’s their explanation. I don’t really understand the equation in bold which is I think is wrong.

A butterfly spread involves call options with three different exercise prices – the investor goes long one call each at the lowest and highest exercise prices and short two calls at the middle exercise price. In this case, Chen is long 100 calls at X1 = 88 (c1 = 4.20), short 200 calls at X2 = 92 (c2 = 2.00), and long 100 calls at X3 = 96 (c3 = 0.50). Maximum loss per contract = c1 - 2c2 +c3

= (\$4.20 - (2 × \$2.00) + \$0.50) × 100 = \$0.70 × 100 = \$70

To find the maximum loss at expiration for Chen’s spread strategy, multiply the per contract payoff by 100, or \$70 × 100 = \$7,000.

cfa2014