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Lower bound on forward settlement price

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Lower bound on forward settlement price발음듣기

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In the last video we established a reasonable upper bound on the 1-year forward settlement price of gold.발음듣기

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We established that at $1150 which is essentially the sport price plus the borrowing rate to borrow $1000, plus the carrying cost of the gold.발음듣기

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What I want to do in this video is to think of a reasonable lower bound.발음듣기

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To do that let's imagine a world where instead of the forward settlement price being $1150, let's imagine a world where the forward settlement price is $1050.발음듣기

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It's still higher that the spot price.발음듣기

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Let's think of it from the the point of view of someone who wants to hold gold in a year.발음듣기

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Let's say that you are that someone and right now you have $1000 that you want to use to give you gold.발음듣기

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You want to hold the gold for the long term.발음듣기

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You have 2 options here.발음듣기

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You could just buy gold now.발음듣기

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Buy 1 ounce with your $1000 right now.발음듣기

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When you go forward a year from then your going to have that 1 once of gold plus you're going have to pay the carrying cost.발음듣기

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The safety deposit box and the insurance on the gold.발음듣기

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You're going to have 1 ounce of gold minus $50.발음듣기

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That's what you're going have to pay.발음듣기

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The other option, you say hey look instead of putting my $1000 into gold right now, let me put my $1000 into a risk-free bond. Into a risk-free bond.발음듣기

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Risk-free bond, and at the same time agree to be the buyer on the 1-year forward settlement.발음듣기

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On the 1-year forward contract.발음듣기

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I'm agreed to to be the buyer at $1050.발음듣기

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If you go forward a year, your $1000 risk-free bond is going to give you 5% interest a year.발음듣기

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You're going to have $1050.발음듣기

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This is just the interest on your bond.발음듣기

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Then you can use that to go and buy the gold.발음듣기

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Which you all ready locked in the price by agreeing to be the buyer on the forward contract.발음듣기

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Then you buy the gold.발음듣기

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In both situations you end up with an ounce of gold a year from now starting with your $1000.발음듣기

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In this situation you just have an ounce of gold and you didn't have to pay any carrying cost.발음듣기

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In this situation you have the ounce of gold and you did have to pay carrying cost.발음듣기

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So, clearly any rational person, assuming their buying the gold for the long term, would want to do this situation.발음듣기

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They save $50 over the course of the year.발음듣기

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Really, the rational price, if this were to happen everyone would want to be the buyers over here.발음듣기

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We're talking about $1050 price.발음듣기

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That's right over here.발음듣기

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This was the price in the last example.발음듣기

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Everyone would want to be the buyer on the futures contract or the forward contract.발음듣기

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That would increase the price over there.발음듣기

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Knowing you'd have less buyers on the spot contract.발음듣기

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That would decrease the price over there.발음듣기

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In general this price seems too low.발음듣기

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The price at which people would be neutral is if this price was $50 higher.발음듣기

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Then it becomes completely equivalent.발음듣기

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A rational lower bound given all of this, would have been a price of $1100. $1100.발음듣기

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In general just going back to the last video, a ration upper bound will be the spot price plus the carrying cost and the rate at which someone could borrow money.발음듣기