*Question 1a: Open** interest tends to be low when a contract with a new expiration is first listed for trading, and it tends to be small after the contract has traded for a long time. Explain.*

When the agreement is initially listed for exchange or trading, open interest is virtually zero. As investors take positions, free interest develops. Therefore, at the end of the trading, public interest returns to zero. Each contract would have been realized by offset, provision, or an EFP. Thus, as the agreement approaches the end of the month or period, several traders would offset their locations to escape delivery. This significantly reduces or minimizes open interest. At the end of the trading, deliveries that happen further decrease open interest. Additionally, EFPs usually minimize public interest. This develops a series of each low open interest in the agreement’s initial days of doing business, followed by rises, then diminution, and lastly, contract termination.

*Question 1b: Explain** why the futures price converges to the spot price and discuss what would happen if this convergence failed.*

The description for the convergence at the extension or expiration relies on whether the market presents cash settlement or deliveries, but in every incidence, convergence relies on common arbitrage arguments. Traders consider every type of the agreement in turn; however, for a deal with real delivery, future convergence provides increase to an arbitrage chance at delivery. Nonetheless, the cash price may either be below or above the next value, if the two are not same. If the cash value is higher than the future price, the investor or business person purchase the future, leaving the delivery, and resells the product in the cash market at a slightly higher price. However, if the price is more than the cash price, the trader acquires goods on the cash market, markets futures, and provides the cash item in the realization of prospects. To isolate both kinds of cash markets together, the future price should be equal as the cash price at the end. Small differences may exist. This is because of the transaction costs and the idea that the short business person owns chances linked with starting the delivery pattern.

For the contract with cash settlement, shortfall of convergence means arbitrage. Before delivery, in case the future value becomes higher than the cash price, a business person can dispose of the future costs, wait for the end of the business period, and the future prices would be set to be same as cash price. This provides a profit, which is same as the difference between the futures and cash. On the other hand, if the cash price is more than future value, and end if imminent, the entrepreneur may purchase the future and hold on for the costs to rise to equate cash price. Therefore, regardless of whether future expenses if below or above the cash price, the profit opportunity would be accessible instantly. In summary, the cash and coming price convergence at the end of the business to exclude arbitrage, and failure of the convergence means there is arbitrage chances or opportunities.

*Question 2. Suppose that the Jewellery Company is planning to sell twenty thousand ounces of platinum at some future date. The standard deviation of changes in the futures price per ounce sd (F) is 11.86% that for changes in the spot price per ounce sd (S) is 12.38%, and the correlation coefficient between the spot and futures price changes corr(S, F) is 0.60.*

*a. **Compute the optimal hedge ratio for Jewellery Co. *

Standard deviation SD= 12.38%

Standard deviation of futures SD (f) = 11.86%

Correlation coefficient c = 0.6

Optimal hedge ratio (H) = x s SD/ SD (f) = 0.6 x 12.38 / 11.86 = 0.63

*b. **How many contracts do they need to hedge their position? *

H = 0.63

A = 20,000

Size of contract S = 50

Number of contracts needed

= (A x H )/ S

= 0.63 x 20,000 / 50

= 250.53

*c. Will this be a buying or a selling hedge? Why? *

The company is planning to dispose of the jeweler in the future. This indicates that the item, jewelry, would experience a loss in case the price of silver reduces hence implying that the entity would focus on silver. To hedge the spot (silver) position, the company needs to follow the opposite side in the future of the market. Therefore, the jeweler will increase in future markets. Any shortfall in the spot’s original price would be reimbursed by similar earnings in the next position.

*Question 3: *Gamma Corporation’s pension assets

*How much of the portfolio should Fisher have hedged? Justify your answer. *

Fisher Black should have hedged 100 percent portfolio, $ 60 million, even though the payment is for $ 10 million which is used a risk of reduction in the price of asset for the entire stock thus whatever the amount of loss Fisher Black experienced in the spot equal returns (profit) can be realized in the future market so that Fisher Back would sell his futures at the end of August or start of September according to the workings. (Refer the calculations below in part b).

*Design a hedge based on your answer to part a) above*.

The future price = sixe of investment x beta (value of index future x size of the contract)

The future price = $ 60 x 1.2 / 522125 (250 x 2,088.5)

The future price = $ 137.90 (this is the price at which Fisher black would be sold.

Note: The schedule of four months is ignored as data of the contract period.

*Question 4. **Using zero-coupon bond prices (maturing every six months) given below, compute the value of this swap.*

The formula is price = M / (1 + i) ^n where: M = maturity value or face value. i = required interest yield divided by 2

Item

AMERICANA(USD)

BRITANIA (GBP)

Face value U

200

200

maturity

4%

6%

number of years

3

3

bond value

USD 240 million

BGP 260 million