Question

In: Economics

An investor agreed to buy 1 thousand barrels of oil forward. The forward rate is 55...

An investor agreed to buy 1 thousand barrels of oil forward. The forward rate is 55 USD per barrel. If at the time of maturity, oil is selling for 70USD per barrel, the value of the contract to this investor is:_____dollars.

An investor agreed to buy 1million Euros forward. The forward rate is 1.15 USD per Euro. If at the time of maturity, the Euro is selling for 1.08 USD per Euro, the value of the contract to this investor is:_____dollars.

if gold futures that expire in 3 months are trading for an F=$1400/oz, the interest rate is 5% (annual compounding), and the spot price of gold is $1350/oz. If there is no cost to storing, the present value of the arbitrage profits per oz are:

if gold futures that expire in 3 months are trading for an F=$1400/oz, the interest rate is 5% (annual compounding), and the spot price of gold is $1350/oz. If there is no cost to storing, an arbitrageur would:

Expert Solution

1. The investor has taken long position in the forward market at a price of $ 55 per barrel upon 1000 barrels. The payoff of long position holder can be calculated as

Payoff= $ 15 per barrel

Value of contract = 1,000 barrels * $ 15 / barrel

Value of contract = $ 15,000

2. Forward rate l, K = $ 1.15 /€

Price on date of maturity, S_T = $ 1.08 /€

Long position payoff = S_T - K

Pay off = 1.08 - 1.15 = - $ 0.07 /€

Value of contract = 1 million euros * (-$0.07/€)

Value of contract = - $ 0.07 million

3. Gold futures, F = $ 1400/oz

Time to maturity, T = 3months = 0.25 years

Interest rate, r = 5%

Spot price, S₀ = $ 1350 /oz

Theoretically the forward rate can be calculated using the following formula

In market the quoted price is $ 1400/oz while theoretical price is $1350/oz.

The arbitrageur can make profit due to this mispricing using the following steps.

At time T = 0

Borrow $ 1350 at a rate of 5% for 3 months
Buy 1 oz gold from the spot market by paying $ 1350
Take short position in the futures market at a price of $ 1400/oz

At time, T = 3 months

Sell 1 oz of gold in forward market and realize $ 1400
Pay loan along with interest = 1350e^0.05*0.25 = $ 1366.98

Arbitrageur profit = $ 1400 - 1366.98 = $ 33.02

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Rahul Sunny answered 2 years ago

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