 # 1. Definition

The Long Strangle use the purchase of an OTM Call and a purchase of na OTM Put, with different exercising prices, with Put strike prices being higher, and with the same expiry date.

Buying a Call Out-The-Money: buying a Call at a strike above the current share prices. Buying a Call gives you rights of buying a share until the expiry date, for the strike price.

Buying a Put Out-The-Money: buying a Put at a strike below the current share prices. Buying a Put gives you rights of selling share until the expiry date, for the strike price.

# 2. Objective

Making money in a volatile market, where prices change fast. This strategy is widely used when people expect prices to be changing for a share, but they are not quite sure about which ways. It’s used by agressive investors and is similar to the Long Straddle, but the maximum losses tend to be lower.

# 3. How it works

In this strategy an OTM Call is purchased, paying a premium. At the same time, an OTM Put is also purchased for a premium. Starting position involves a debt, as both moves incurred in payable premiums. Graphical explanation figures as folows:

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## Long Strangle Caption:

Red = Losses

Yellow = Reduced losses

Green = Profits

Earnings: gains shall be unlimited every time the underlying asset moves up or downwards. To find the profit margins, one must get the share prices at the maturity minus the strike, and also deducting the initial costs of the operation – i.e. the amount paid for the options.

Losses: losses are limited. The maximum losses are equal to the costs for setting up the operation.

# 4. Example

Consider the following data:

 Asset: Vale Date: 09/10/2013 Maturity: 10/21/2013 Share prices: 32,15 Days before expiration 41 Number of options 1.000

To set up this operation, the investor needs to buy a VALEJ31 OTM Call, paying a premium of R\$ 3.32 per option, and also buy a VALEV33 OTM Put, paying a premium of R\$ 0.89 per option. Look the summary below:

Summary:

 Option   type Asset Series Number of   options Premium Exercise   prices Results Buying a   Call Vale VALEJ31 1,000 -3.32 31 R\$     -3,320.00 Buying a   Put Vale VALEV33 1,000 -0.89 33 R\$     -890.00 Total -4.21 R\$   -4,210.00

By the expiry date, results are the following, depending on the share prices:

 Share   prices on expiration Buying a   Call Buying a   Put Results R\$     26.00 -3,320 6,110 2790 R\$     27.00 -3,320 5,110 1790 R\$     28.00 -3,320 4,110 790 R\$     29.00 -3,320 3,110 -210 R\$     30.00 -3,320 2,110 -1210 R\$     31.00 -3,320 1,110 -2210 R\$     32.00 -2,320 110 -2210 R\$     33.00 -1,320 -890 -2210 R\$     34.00 -320 -890 -1210 R\$     35.00 680 -890 -210 R\$     36.00 1,680 -890 790 R\$     37.00 2,680 -890 1790 R\$     38.00 3,680 -890 2790

Results:

Results from this strategy will be positive if prices move out of the range R\$ 31.00-R\$ 33.00, without considering the premiums paid. If share prices are lower than R\$ 31.00 by the expiration date, the option Call VALEJ31 just expires, while the option Put VALEV33 is going to be exercised, and the investor will be selling shares at R\$ 33.00. From this value, however, he needs to deduct R\$ 4.21 per option, which is equivalent to the expenses for setting up the transaction (R\$ 3.32 + R\$ 0.89). If prices are above R\$ 33.00 by the expiry date, then the option Put VALEV33 just expires, and the option VALEJ31 will be exercised, with the investor buying shares at R\$ 31.00. Again, premiums paid must be deduct from any profits made. Caption:

Red = Max losses

Yellow = Reduced losses

Green = Profits

Earnings: the operation generates earnings if Vale’s share reach any value below R\$ 28.79 or over R\$ 35.21. In this range, the following situation occurs:

If prices are lower than R\$ 28,79 on the expiry date, Call VALEJ31 just expires, while the option Put VALEV33 is exercised by the investor, who is going to sell shares at R\$ 33.00, where the value at maturity it is R\$ 28.79. In this case, the investor shall have earnings of R\$ R\$ 4.21 (R\$ 33.00 – R\$ 28.79). However, results turn to zero, as the cost for set up the operation reach R\$ 4.21 as well (R\$ 3.32 buying VALEJ31 and R\$ 0.89 buying VALEV33). That results in:

Results: R\$ 33.00 – R\$ 28.79 – R\$ 3.32 – R\$ 0.89 = R\$ 0.00

In this case, results were zero, as set up costs offset all profits made. However, for any share price below R\$ 28.79, the investor will be making money.

Now, if shares are over R\$ 35.21 at the maturity,  the option Put VALEV33 just expires, and the option Call VALEJ31 will be exercised by the investor, who can buy Vale’s share for R\$ 31.00, where the value at maturity it is R\$ 35.21. making profits of R\$ 4.21 per share. As premiums paid sum R\$ 4.21 as well, results are equal to zero. For any share price above R\$ 35.21, the investor will be also gaining.

Results: R\$ 35.21 – R\$ 31.00 – R\$ 3.32 – R\$ 0.89 = R\$ 0.00

Losses: the investor accumulates losses if share prices are any higher than R\$ 28.79 or lower than R\$ 35.21 by the expiry date. For this range, any profit eventually made by the investor is biten by the set up costs, because the profit generated in the operation is not enough to cover the cost of assembly.

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