ch 5 determination of forward and future prices

Question 1

Investment assets vs Consumption assets

Answer 1

Investment assets:

Held solely for investment purposes by at least some traders.

Examples: stocks, bonds, gold, and silver.
They do not have to be held exclusively for investment, but they have to be held by some traders solely for investment.

Consumption assets:

Held primarily for consumption, not for investment.
Examples: commodities such as copper, crude oil, corn, and pork bellies.

Question 2

Arbitrage and Forward/Futures prices

Answer 2

Arbitrage arguments can be used to determine the forward and futures prices of an investment asset from its spot price and other observable market variables. However, we cannot do this for consumption assets.

Question 3

What is short selling?

Answer 3

Short selling, or simply “shorting”, is the practice of selling an asset that is not owned, with the expectation of buying it back at a lower price in the future to make a profit. Shorting involves borrowing the asset from someone who owns it, selling it in the market, and then buying it back later to replace the borrowed shares and close out the position.

Question 4

What is the margin account in short selling?

Answer 4

The margin account in short selling consists of cash or marketable securities deposited by the investor with the broker to guarantee that the investor will not walk away from the short position if the share price increases. It is similar to the margin account for futures contracts. An initial margin is required and if there are adverse price movements, additional margin may be required. The proceeds of the sale of the asset belong to the investor and normally form part of the initial margin.

Question 5

What is the uptick rule and why was it introduced?

Answer 5

The uptick rule was introduced in 1938 and allowed shares to be shorted only on an “uptick” – that is, when the most recent movement in the share price was an increase. It was introduced to prevent short sellers from exacerbating market downturns by driving prices down further. The SEC abolished the uptick rule in July 2007, but introduced an “alternative uptick” rule in February 2010, which restricts short selling when the price of a stock has decreased by more than 10% in one day.

Question 6

What determines the relationship between forward and spot prices?

Answer 6

The trading activities of the key market participants and their eagerness to take advantage of arbitrage opportunities as they occur determine the relationship between forward and spot prices.

Question 7

What is the relationship between forward and spot prices for an investment asset with no income?

Answer 7

The relationship between the forward price (F0) and spot price (S0) for an investment asset with no income is F0 = S0e^rT, where T is the time to maturity and r is the risk-free rate. The forward price is higher than the spot price due to the cost of financing the spot purchase during the life of the forward contract.

Question 8

What is the relationship between short sales and forward contracts?

Answer 8

Short sales are not necessary for the derivation of the forward price equation. Market participants holding the asset purely for investment can sell it and take a long position in a forward contract if the forward price is too low.

Question 9

What is the strategy an investor can adopt if F0 < S0erT?

Answer 9

An investor can borrow S0 dollars, buy 1 unit of the asset, and enter into a forward contract to sell 1 unit of the asset if F0 < S0erT.

Question 10

What is the profit made by an investor who follows the strategy when F0 < S0erT?

Answer 10

The profit made by an investor who follows the strategy when F0 < S0erT is F0 - S0erT.

Question 11

What types of investment assets provide a perfectly predictable cash income to the holder?

Answer 11

Stocks paying known dividends and coupon-bearing bonds.

Question 12

What is the difference between a forward contract on an investment asset with a predictable cash income and one with a known yield?

Answer 12

A forward contract on an investment asset with a predictable cash income involves an investment asset that provides a known cash income, while a forward contract with a known yield involves an investment asset that provides a known yield expressed as a percentage of the asset’s price at the time the income is paid.

Question 13

Variables in Forward Contracts

Answer 13

K: delivery price for a contract negotiated in the past, which remains constant throughout the life of the contract.
F0: forward price applicable if the contract were negotiated today, which changes as time passes.
f: value of the forward contract today, which is close to zero at the beginning of the contract and may become positive or negative as time passes. The contract is marked to market each day.

Question 14

What is the arbitrage argument

Answer 14

The arbitrage argument shows that, when the short-term risk-free interest rate is constant or is a known function of time, the forward price for a contract with a certain delivery date is theoretically the same as the futures price for a contract with that delivery date.

Question 15

When are forward and futures prices theoretically no longer the same?

Answer 15

Forward and futures prices are theoretically no longer the same when interest rates vary unpredictably, as they do in the real world.

Question 16

Are forward and futures prices always the same?

Answer 16

While it is reasonable to assume that forward and futures prices are the same for most purposes, there are several factors, such as taxes, transactions costs, margin requirements, and the risk of counterparty default, that may cause forward and futures prices to differ in practice. Additionally, interest rate futures are an exception to the rule that forward and futures contracts can be assumed to be the same.

Question 17

What is a stock index and how are futures prices for stock indices determined?

Answer 17

A stock index can be considered the price of an investment asset that pays dividends, and the investment asset is the portfolio of stocks underlying the index. Futures prices for stock indices are determined by factors such as the current price of the underlying stocks, the interest rate, and the time remaining until the delivery date. Dividends are assumed to provide a known yield rather than a known cash income.

Question 18

What is index arbitrage?

Answer 18

Index arbitrage is a trading strategy that involves making profits by simultaneously buying or selling the stocks underlying an index and taking an opposite position in futures contracts on the same index. It is used to take advantage of temporary misalignments between the futures price and the spot price of the index, with the aim of making riskless profits. It is typically implemented through program trading using computer systems.

Question 19

What is program trading in the context of index arbitrage?

Answer 19

Program trading in the context of index arbitrage involves using a computer system to generate trades that simultaneously short futures contracts and sell the underlying stocks of an index (or buy the stocks and take a long position in futures contracts) to profit from any difference between the futures price and the spot price.

Question 20

What are forward and futures foreign currency contracts?

Answer 20

A forward or futures foreign currency contract is an agreement between two parties to buy or sell one unit of a foreign currency at a specified price on a future date. The spot price is the current price of the currency, while the forward or futures price is the price agreed upon in the contract.

Question 21

How are the spot and forward exchange rates quoted for major exchange rates?

Answer 21

For major exchange rates other than the British pound, euro, Australian dollar, and New Zealand dollar, a spot or forward exchange rate is normally quoted as the number of units of the currency that are equivalent to one U.S. dollar.

Question 22

What is the cost of carry in futures contracts?

Answer 22

The cost of carry is the storage cost of the underlying asset plus the cost of financing it minus the income received from it.

Question 23

How does the correlation between the return on the asset and the return on the stock market affect the futures price?

Answer 23

If the return on the asset is positively correlated with the return on the stock market, the theoretical futures price will be lower than the expected future spot price. If the return on the asset is negatively correlated with the return on the stock market, the theoretical futures price will be higher than the expected future spot price. Only when the correlation is zero will the theoretical futures price be equal to the expected future spot price, assuming the capital asset pricing model is true.

Question 24

What is the convenience yield in futures pricing?

Answer 24

The convenience yield is a parameter that measures the extent to which users of a commodity feel that ownership of the physical asset provides benefits that are not obtained by the holders of the futures contract.

Question 25

How does the correlation between asset returns and stock market returns affect futures pricing?

Answer 25

If the return on the asset is positively correlated with the return on the stock market, the futures price tends to be lower than the expected future spot price. If the correlation is negative, the futures price tends to be higher than the expected future spot price. Only when the correlation is zero will the theoretical futures price be equal to the expected future spot price.