Question

3. You observe that the current spot price of gold is TL400 per ounce. You also observe that the yield curve is flat and all maturities up to one year have an interest rate of 12 percent. Since gold is a popular underlying asset in the derivatives markets, you are interested in identifying any mispricing that may allow you to earn arbitrage profits. When you look up gold forward contract prices, you see that there is a contract with a one year maturity whose current price is TL410 per ounce. The size of this forward contract is 100 ounces of gold per contract. Assume that there are no transaction costs in the spot or forward markets.

a. Calculate the theoretical fair price for the forward contract.

b. Based on the price you calculated in part (a) and the price you observe in the market, comment on whether it is possible to earn an arbitrage profit. If your answer is yes, then specifically describe the transactions at time 0 and T and calculate the arbitrage profit.

c. Assume that there is also a gold futures contract with a one year maturity and the same contract size that is available on the futures exchange. This contract is marked to market on a daily basis and the initial (at time 0) price of the futures contract is also TL410. Assume that the futures contract price stays constant except for the following four days during the year:

Time in Days | Price in $ |

0 (initial) | 410 |

100 | 400 |

180 | 375 |

300 | 360 |

350 | 420 |

Assume that on day 0, you take a long position in one futures contract at the initial price of TL410 per ounce. Also assume that on the expiration day of the contract (t = 365), the spot price of gold is TL420 per ounce. Assume that there are no initial or maintenance margin requirements but you have to pay for your losses or will get paid whenever you have a gain. During the one year that you hold your long position, you borrow at 12 percent to finance all your losses and you lend at 12 percent whenever you have a gain. Calculate your final profit on this futures transaction. Compare this profit with the profit you have calculated in part (b) and, if the two profits are different from each other, explain the reason for this difference.

Answer #1

**A) Theorectical forward price F _{0}**

Forward price, F_{0} = S e^{RT}

= 400 * e^{0.12 * 1}

^{= 450.997 or appro per ounce}

^{B) Abritrage profit}

- Theoretical forward price = 450.997
- Actual forward price = 410

The actual future price is lower than the theoretical price, this clearly means there is an arbitrage opportunity available.

Arbitrage strategy to be used at time 0:

- Buy forward contract (Initial value = 0 or no cost to be paid to enter the contract)
- Short 100 ounces of gold (receives TL40,000)
- Lend money at risk free rate (lend TL 40,000 @ 12%)

Arbitrage strategy to be used at time T:

- Collect income on loan ( FV of 40,000 = 40,000
(1+12%)
^{1}= 44,800 or in other words your 40,000 has grown now to 44,800) - Take delivery of Forward contract (Buys back gold for 410 *100 = 41,000)
- Return borrowed commodity

**Arbitrage profit** = (44,800 - 41,000) =
**TL 3,800**

Question 19 Revision booklet:
Assume that the spot price of gold is $1,500 per ounce, the
risk-free interest rate is 2%, and storage and insurance costs are
zero.
a) What should be the forward price of gold for delivery in 1
year?
b) If the futures price is $1550, develop a strategy that can
bring risk-free arbitrage profits.
c) Calculate the profit that you can make by following that
arbitrage strategy.

The spot price of gold today is $1,505 per ounce, and
the futures price for a contract maturing in seven months is $1,548
per ounce. Suppose ACG puts on a futures hedge today and lifts the
hedge after five months. What is the futures price five months from
now? Assume a zero basis in your answer.

The spot price of gold is $1,975 per ounce. Gold storage costs
are $1.80 per ounce per year payable monthly in advance. Assuming
that continuously compounded interest rates are 4% per year, the
futures price of gold for delivery in 2 months is closest to:
Select one:
$1,989.51
$1,988.51
$1,975.51

Suppose the current price of gold is $250 per ounce and that the
future spot price one year from now is projected to be $350. Assume
a riskless rate of 8%.
If storage costs are 3%, what rate of return do you earn on your
gold if you sell it after one year?
How could you take your $250 and instead invest in a synthetic
form of gold (from an investment perspective)? (What actions would
you need to take, including...

Suppose the spot price of gold is $300 per ounce and the
one-year forward price is $350. Assume the riskless interest rate
is 7%. (4 pts.)
What is the implied cost of carrying the gold?
What is the implied storage cost of the gold?

Assume that the only cost (or opportunity cost) associated with
gold is the “interest on the money” if you own gold. There are no
storage costs and the convenience yield is zero. Suppose you can
borrow or lend money at 10 percent per annum (continuous
compounding) if you buy / sell gold. Today's price of gold is
$1,320 per ounce, and there are also gold futures contracts
available. The 6-month gold futures is trading at $1,370 and the
12-month gold...

Suppose that the spot price for gold is $300 per ounce. If the
storage costs are 0.02 per year and the riskless rate is 0.07 per
year: (4 pts.)
What is the forward price of gold after one year?
What would happen if the price of gold were greater than what
you calculated in section (a)?

38. Suppose the current price of gold is $250 per ounce and that
the future spot price one year from now is projected to be $350. (7
pts.)
a. If storage costs are 3%, what rate of return do you earn on
your gold if you sell it after one year?
b. How could you take your $250 and instead invest in a
synthetic form of gold (from an investment perspective)? (What
actions would you need to take, including in...

Consider a forward contract on gold. Each contract covers 100
ounces of gold and matures one year from now. Suppose it costs $2
per ounce per year to store gold with the payment being made at the
end of the year. Assume that the spot price of gold is $1300 per
ounce, the continuously compounded risk-free interest rate is 4%
per annum for all maturities.
a) In the absence of arbitrage, find the current forward price.
Show your calculations.
b)...

Consider a forward contract on gold. Each contract covers 100
ounces of gold and matures one year from now. Suppose it costs $2
per ounce per year to store gold with the payment being made at the
end of the year. Assume that the spot price of gold is $1300 per
ounce, the continuously compounded risk-free interest rate is 4%
per annum for all maturities.
a) In the absence of arbitrage, find the current forward price.
Show your calculations.
b)...

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