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Topic: Gold Market Arbitrage (Read 2880 times) |
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william wu
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Gold Market Arbitrage
« on: Jul 23rd, 2008, 12:13am » |
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Gold costs $450 per ounce, and can be sold for $440 per ounce.
You can borrow funds from the bank at 6% per year, and invest funds at 5.5% per year.
For what range of 1-year forward contract prices of gold does the trader have arbitrage opportunities? (Find necessary and sufficient conditions.)
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Grimbal
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Re: Gold Market Arbitrage
« Reply #1 on: Jul 23rd, 2008, 1:15am » |
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It seems to me that for a price >$477 (450+6%) forward sales price in one year, you can borrow money now to buy gold and sell it in one year with a profit.
If you already have gold and the forward price is <464.20 (440+5.5%) , you better sell the gold, invest the money, and buy gold back in one year.
Is there a different forward price for buying and selling?
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| « Last Edit: Jul 23rd, 2008, 1:21am by Grimbal » |
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william wu
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Re: Gold Market Arbitrage
« Reply #2 on: Jul 23rd, 2008, 1:18am » |
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Hello Grimbal,
In this problem we assume that the price is the same for both buying and selling forward contracts.
Those are the right conditions. Proving that they are also necessary is more challenging though.
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Grimbal
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Re: Gold Market Arbitrage
« Reply #3 on: Jul 23rd, 2008, 7:25am » |
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Is it? isn't it just a maximization over a single variable: how much gold to hold?
In fact there is one more case: if you already have some money. It "costs" you only 5.5% if you use it to buy gold instead of investing it.
So if you already have some money and some gold, there are 5 possibilities:
- convert your money to gold and borrow money to buy more gold
- convert your money to gold only
- hold
- convert your gold to money
- convert your gold to money and borrow more gold and sell it too. In a year, buy the gold back and return the gold. But I am not sure it is an option to borrow gold.
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william wu
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Re: Gold Market Arbitrage
« Reply #4 on: Jul 24th, 2008, 4:44pm » |
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Yes I think there are at least two variables: there's how many units of gold to buy/sell at time 0, and how many units of money to borrow/invest at time 0. Also we have to consider long positions and short positions in the forward. I hadn't thought about borrowing gold ... dunno if we can do that.
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