Reading 52 - Futures Markets and Contracts

Question 1

What does it mean that futures contracts are said to be fungible?

***Critical Concept****

Answer 1

That futures contract with any counterparty can be offset by an equivalent futures contract with another counterparty.

Question 2

What are 3 ways that Futures contracts are similar to Forwards contracts?

Answer 2

1. Deliverable contracts obligate the long to buy and the short to sell a quantity of an asset for a certain price on a specified future date.
2. Cash settlement contracts are settled by paying the contract value in cash on the expiration date.
3. Both forwards and futures are priced to have zero value at the time the investor enters into the contract.

Question 3

What are the important differences between Futures contracts and Forward contracts?

**Critical Concept****

Answer 3

1. Futures are marked to market at the end of every trading day. Forwards are not marked to market
2. Forwards are private contracts and do not trade on exchanges. Futures trade on exchanges
3. Forwards are customized to the parties involved needs. Futures are highly standardized
4. Forwards are with a counterparty, futures the counterparty is the exchange
5. Forwards are not regulated, Futures are.

Question 4

Why must futures prices converge to the spot price at expiration?

Answer 4

At expiration, the arbitrage price must equal the futures price or there will be an arbitrage opportunity.

Question 5

How is the value of a futures contract calculated?

Answer 5

= current futures price - previous mark-to-mark price

Question 6

What are some of the “real-world’ complications that will cause futures and forward prices to be different?

Answer 6

1. Higher reinvestment rates for gains and lower borrowing costs to fund losses lead to a preference for the mark-to-market feature of futures
2. A preference to avoid mark-to market cash flows will lead to a higher price for the forward relative to the future if interest rates and asset values are negatively correlated.

Question 7

If the correlation between the underlying asset value and interest rate is positive, will investors prefer a Futures Contract or a Forward Contract?

Answer 7

Futures Contract.

Question 8

If the correlation between the underlying asset value and interest rate is negative, will investors prefer a Futures Contract or a Forward Contract?

Answer 8

Forward contract.

Question 9

What is a cash-and-carry arbitrage?

***Critical Concept****

Answer 9

Occurs when the futures contract is overpriced

Consists of buying the asset, storing/holding the asset and selling the asset at the futures price when the contract expires

Question 10

What are the steps involved in creating a cash-and-carry abitrage?

***Critical Concept****

Answer 10

At Initiation:

1. Borrow money for the term of the contract at market interest rates
2. Buy the underlying asset at the spot price
3. Short a futures contract at the current futures price

At expiration:

1. Deliver the asset and receive the futures contract price
2. Repay the loan plus interest.

Question 11

What are the steps in a reverse cash-and-carry arbitrage?

Answer 11

At initiation:

1. Sell the asset short
2. Lend the short sale proceeds at the market interest rates
3. Go long the futures contract at the market price

At expiration:

1. Collect the loan proceeds
2. Take delivery of the asset for the futures price and cover the short sale commitment.

Question 12

What is normal backwardation?

***Critical Concept****

Answer 12

When the futures price is lower than the expected spot price

Question 13

What is normal contango?

***Critical Concept****

Answer 13

If the futures price is greater than the expected spot price.

Question 14

Calculate the no-arbitrage futures price of a 1.2 yr futures contract calling for the delivery of a specific bond, a 7% T-bond with exactly 10 yrs remaining to maturity and a price of $1,040, when the annual risk-free rate is 5%…

Answer 14

Question 15

What is the conversion factor (CF) in regards to fixed income futures contracts?

Answer 15

When the Futures settle, the short seller on a T-bond contract has the option of delivering any one of a number of different bonds. A CF is a multiplier for the futures price on the “contract” bond, to adjust the settlement payment for delivery of higher or lower coupon bonds.

*Is used to adjust the no-arbitrage price for the “cheapest to deliver” of all permitted bonds

Question 16

What is the formula to adjust the futures price of a bond with the identical face value that needs to be delivered?

***Critical Concept***

Answer 16

Question 17

Previous example:

Calculate the no-arbitrage futures price of a 1.2 yr futures contract calling for the delivery of a specific bond, a 7% T-bond with exactly 10 yrs remaining to maturityy and a price of $1,040, when the annual risk-free rate is 5%…

Now:

Now suppose the futures contract allows many different bonds to be delivered. The conversion factor of the 10yr 7% T-bond is 1.13. Calculate the appropriate no-arbitrage futures price.

The futures price previously calculated to be $1,031.15

Answer 17

Question 18

Calculate the no-arbitrage price for a 120 day future on a stock that is currently priced at $30 and is expected to pay a dividend of $0.40 in 15 days and $0.40 in 105 days. Assume the annual risk free rate is 5% and the yield curve is flat.

Answer 18

Question 19

What is the equation used to calculate the futures price of an equity index whose dividends are paid continuously?

***Critical Concept***

Answer 19

Question 20

The current value of the Nasdaq index is 1,780. The continuous dividend yield is 1.1% and the continuously compounded risk free rate is 3.7%. Calculate the no-arbitrage futures price of an 87 day futures contract on the Nasdaq index…..

Answer 20

Question 21

What is the equation to calculate the no arbitrage futures price of a currency contract?

***Critical Concept****

Answer 21

Question 22

The risk free rates are 5% in US $’s and 6.5% in British pounds. The current spot exchange rate is $1.7301 / £. Calculate the no-arbitrage price of a 6-month £ futures contract…

Answer 22

Question 23

How do you create a riskless arbitrage for Eurodollar futures contracts?

Answer 23

You cannot

**b/c Eurodollars do not discount back the interest cash flow to your futures expiry point, whereas the T-bills futures do

Question 24

A Cash-and-carry arbitrage will generate a riskless profit if the futures contract is underpriced or overpriced?

Answer 24

Overpriced

Question 25

A Reverse Cash-and-carry arbitrage will generate a riskless profit if the futures contract is underpriced or overpriced?

Answer 25

Underpriced

Question 26

What is the equation to solve for the futures price when there are storage costs involved in holding an asset?

Answer 26

***This is because the futures price should be higher by enough to cover the storage costs when a trader buys the asset and sells a futures contract to create a risk-free position

Question 27

What is the equation to solve for the futures price when there are cash flows (ie dividends or coupons) involved in holding an asset?

Answer 27

***because when cash is generated from holding the assets it results in a lowe futures price

Question 28

What is the equation to calculate the futures price when there are storage costs and nonmonetary benefits (ie convenience yield)?

Answer 28

***This is referred to as the cost-of-carry model****

Question 29

Are futures contract homogenous or heterogeneous?

Answer 29

Homogenous means: of the same kind or nature; essentially alike

Heterogeneous means: different in kind; unlike

Since all futures can be offset, they are homogenous!