# PG Butterfly Arbitrage

Goal:
Convert April PG position to risk-less butterfly arbitrage. Profit from APR 67.5 CALLS not included in credit.

Holding:
+1 APR 62.5 CALL @ 1.85
-1 APR 65 CALL @ 0.85
+5 APR 67.5 CALL @ 0.17

Zero-Risk, Zero-Profit Position:
1.85 + 0.17 = 2.02
2.02 – .85 = 1.17

-1 APR 65 @ >= 1.17 (current mkt val = 1.29)
-4 APR 67.5 @ 0.42 (current mkt val)

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Since the zero-profit position comes from the sale of 1 APR 65 CALL @ 1.17 then anything above that locks in profit at \$1/cent above 1.17.

The maximum profit at expiration is \$250 if the underlying closes at 65 on 4/15/11 and the 65 CALL is sold at 1.17.

Profit will be higher from the sale of the 4 APR 67.5 CALLS currently held but this is not included in the calculation for the arb.

Since the spread has been “legged” into starting from the long side, the higher the underlying goes before the CALL is sold the higher the profit is that gets locked in.

NOTE: The simulation uses the closing market value for the short APR 65 CALL. This position has no risk of loss to expiration.

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Goal:
Maximize profit in butterfly arb using unrealized profit in APR 67.5 CALLS and APR 62.5 CALLS.

Holding:
+1 APR 62.5 CALL @ 1.85
-1 APR 65 CALL @ 0.85
+5 APR 67.5 CALL @ 0.17

+1 PG APR 62.5 CALL @ 2.90
-3 PG APR 65 CALLS @ 1.29
-3 PG APR 67.5 CALLS @ 0.42

1.29 * 3 = 3.87
0.42 * 3 = 1.26
3.87 + 1.26 = 5.13 credit
5.13 – 2.9 debit = 2.23 credit (increase in buying power)

Final Position:
+2 PG APR 62.5 CALLS @ 2.375 (averaged w/mkt value)
-4 PG APR 65 CALLS @ @ 1.18 (averaged w/mkt value)
+2 PG APR 67.5 CALLS @ 0.17 (profit not included)

Maximum Risk of Loss:
2.375 * 2 = 4.75 debit
1.18 * 4 = 4.72 credit
0.17 * 2 = 0.34 debit
3 * (0.42 – 0.17) = 0.75 credit (profit from APR 67.5 CALLS)

-4.75 + 4.72 – 0.34 + 0.75 = 0.38 credit (maximum loss is a credit; therefore risk-less)

Maximum profit potential is \$538 on 2/4/2 vs \$262 on 1/2/1 butterfly if underlying closes at 65 on 4/15/11.

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