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Arbitrage and other issues in the Gold futures markets

Question 1: Arbitrage and other issues in the Gold futures markets
Q.1 Assume that today is 5/11/2020 and that you can lend/borrow at interest rates of 1% p/a (monthly compounding)
Below is the table with gold prices for May 2020 and May 2021
DATA : May 11,2020-
closing prices
Month Price
May-20 1723
May-21 1750

1. Find an arbitrage opportunity using the spot and future prices of Gold .
2. How would your answer to previous question change if you can lend/borrow at interest rates of 2% p/a (monthly compounding)
3. How would your answer to question Q.1.1 change if you can lend/borrow at interest rates of 2% p/a (monthly compounding)
and you have to pay for borrowing Gold a lending fee of 2% p/a (monthly compounding).
4. (HARD)Assuming that there are no arb. Opportunities, calculate the interval of lending rates as implied by the futures prices.
Remember , you pay a 2% p/a lending fee (monthly compounding) if you borrow Gold.
Q.2 Oil Futures
Read the quote from an article (see below). Attached is a clickable excel spreadsheet with futures oil prices for Feb 2007 and Oct 2007.
Assume that spot oil was sold on Feb7, 2007 for $57.96 per barrel and it was sold at $82 per barrel on Oct 7, 2007
Q. 2.1 Draw the future oil curves for Feb. and Oct.2007
Q. 2.2 Explain why so much oil was stored in Cushing in Feb but no oil was stored after mid-July; Are the “reasons for Cushing’s crude …disappearing are surprisingly complex…”
Q. 2.3 Why “some financial firms involved in oil trading got into the storage business”?
Q. 2.4 Given: on February 7 the spot one-year interest rate was 4%.
Using the table below, show that on February 7 the cost of one-year storage was higher than $3.68 per barrel.

Where Has All The Oil Gone? WSJ Ann Davis Oct. 6, 2007
After Sitting on Crude, Speculators Unload It. The World’s Eyes Fall on Cushing , Oklahoma .
“Since summer, one of North America’s most important oil towns (Cushing, Okla. ) has witnessed a disappearing act. The mammoth storage tanks that blanket the rolling grasslands around this remote prairie town had been filled to the brim with crude oil. (But now these tanks disappeared). Until mid-July, unprecedented conditions in the oil market had given oil companies and speculators alike a financial incentive to sock away oil in storage tanks for sale later. These days, the steel oil tankers on the outskirts of town stretch to the horizon, covering more than nine square miles. The biggest held 575,000 barrels.
… some financial firms, (that had been) involved in oil trading, got into the storage business. That gave them the means to set aside oil when the market wasn’t ripe to sell it profitably, and to take a cut as middlemen.
But the steel oil tankers … aren’t there anymore. Since May, millions of barrels of crude have been sold off, and Cushing’s inventory has fallen by nearly 35%.
The reasons Cushing’s crude has been disappearing are surprisingly complex…”

Q. 3
The article in WSJ form June 4, 2020 tells that “Yields on the China’s 10-year sovereign bonds, denominated in yuan, this week hit their highest levels since late February at about 2.83%”
Assume that on June 4, 2020 a China’s 10-year sovereign bond has a coupon rate of 4.5( with two coupon payments in a year). What is the price of the bond?
Q. 4
Find the technical details about the delivery quality standards for the Chinese hog markets futures