Arbitrage

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					Practical Exercise on Arbitrage



Cash and Carry model:

       1) Spot price = $400

Futures price = $450.

Interest = 10%.

Do we have an arbitrage opportunity?



t=0,

Borrow $400 for 1 yr at 10%                         $400

Buy gold in spot market for $400                    -$400

Sell 1 futures contract for $450 delivery in 1 yr   $0

Net CF= $0




T=1,

Remove gold from storage                            $0

Deliver gold against futures contract               $450

Repay loan including interest                       -$440

Net CF = $10 (PROFIT)
Reverse C and C model

Q2) Spot = $420, Futures price $450, r= 10%. Do we have an arbitrage opportunity?



T=0,

Sell gold short                                 $420

Lend $420 for 1 yr @10%INTEREST                 -$420.

Buy 1 futures contract for delivery in 1yr      0

Net CF= $0



T=1,

Collect proceeds from loan (420*1.1)            $462.

Accept delivery on futures contract             -$450

Use gold from futures delivery to repay short sale       $0

Net CF= $12. (PROFIT)




C and C involving storage costs

Same question as Q1, but with storage (transaction) costs of 3%. Is there an Arbitrage opportunity?

Adjust Spot for transaction costs, i.e, New spot price = $400(1+3%) = $412.

Repeat whole procedure in Q1. Net cash flows in t=1  -$3.20 (loss)



Reverse C and C involving storage costs

Same question as Q2, but with storage (transaction) costs of 3%. Is there an Arbitrage opportunity?

Adjust Spot for transaction costs, i.e, New spot price = $420(1-3%) = $407.40.

Repeat whole procedure in Q2. Net cash flows in t=1  -$1.86. (loss)

				
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