A trader owns a commodity that provides no income and has no storage costs as part of

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Question:

A trader owns a commodity that provides no income and has no storage costs as part of a long-term investment portfolio. The trader can buy the commodity for $1560 per ounce and sell it for $1558 per ounce. The trader can borrow funds at 7% per year and invest funds at 6.5% per year. For what range of 1-year forward prices does the trader have no arbitrage opportunities? Assume the bid and offer for a forward price are the same.

is my answer correct

Option1: Borrow $1560 @ 7% p.a for 6 months, buy the commodity.Money to be paid after 6 months = 1560 e^0.07(0.5)= $1615.57

Arbitrage opportunity exist for a trade if forward price > $1615.57 because then commodity can be sold at a profit after paying off the loan.

Option 2: Sell commodity at $ 1558,invest @6.5 % per annum for 6 months. Money to be received after 6 months = 1558e^0.06(0.5)= $1609.46. Arbitrage opportunity exist if the forward price < $1609.46 because then commodity can be bought back at lower value and trade can book profit.

Therefore, for trader to have no arbitrage opportunities, the range of forward price should be :

$1609.46 < Forward Price < $1615.57