Characteristics of futures and forward contracts

Futures and forward contracts are contracts for the purchase or sale of specific underlying instruments at a specified time in the future and on the terms specified in the contract. The underlying asset of the contract may be one of the following:

  • commodities,
  • stocks,
  • indices,
  • interest rates or fixed income instruments,
  • currrncies,
  • cryptocurrencies,

The counterparty issuing of the contract opens a short position and is obliged to deliver (unless there is a financial settlement) the underlying within the defined deadline. The buyer of the contract opens a long position and is obliged to pay the agreed price upon delivery for the underlying of the contract. The purchase (sale) of a forward contract is defined as the opening of a long (short) position.

Comparison of forward and futures contracts

forward futures
Private contract between two parties Traded on an exchange
Not standardized Standardized contract
Usually one specified delivery date Range of delivery dates
Settled at the end of contract Settled daily, marking to market procedure
Delivery or final cash settlement usually takes place Contract is usually closed out prior to maturity
Some credit risk Virtually no credit risk because of Clearing Houses

Source: Options, futures and other derivatives. John C. Hull

Prices of futures contracts

There are three prices characterizing futures / forward contracts:

  •  (K or X) the price of the contract (delivery price) - it is fixed, i.e. determines the price at which the transaction will be executed in the future,
  •  (F) forward price of the contract (futures / forward price) - the price determined by the two parties on the market, defines the price of delivery that would be negotiated if the contract was signed at a given moment; it changes on the market every day.
  •  (S) spot price of the subject of the contract, i.e. the underlying instrument.

Base = forward price of the contract (F) - spot price (S)

The difference between the current spot price and the price of the futures contract is called the basis. As the delivery time approaches, the value of the base should approach zero, as the forward prices are close to the spot price.

Profit and loss profile

Long position

  • profit of the buyer of a futures contract: when the current price of the underlying instrument is higher than the price of the instrument on the trade date,
  • loss of a futures contract buyer: when the current price of the underlying instrument is lower than the price determined in the contract.

Short position

  • profit of the futures contract seller: when the current price of the underlying instrument is lower than the price set in the contract, then the investor earns income equal to the difference between the two prices,
  • loss of a futures contract seller when the price of the underlying instrument on the day of delivery is higher than the price set in the futures contract.

Contracts pay-off

Margin and leverage

  • Margin - the amount that is deposited on the investor’s account in order to secure the settlement in case of default of the investor (counterparty risk)
  • Margin account - an account where investor deposits required margin (deposit)
  • Initial margin - the amount that must be deposited at the time the contract is entered into. It is ususlly higher than the maintenance margin.
  • Maintenance margin - the amount that is required to be kept on the margin account during the cotract period. It is usually lower than initial margin.
  • Marking to market - daily settlement of the P&L of the contract and margin account adjustment.
  • Margin call - the action which is initiated when the balance in the margin account falls below the maintenance margin. The investor is usually requested to top up the margin account to the initial margin level by the end of the next day.

Marking to market

Example: FW20 futures contract Initial margin: 8.1% Maintenence margin: 5.8% - please seee excel file for detailed formulas for the table http://coin.wne.uw.edu.pl/gzakrzewski/materials/financeII/fin-II_marking-to-market.xls.
day Underlying_price PnL initial_margin margin_account_day_t margin_call margin_account_day_t1 maintenance_margin
1 3000 0 2430.00 2430.0 0.0 2430.0 1740.0
2 3015 150 2442.15 2580.0 0.0 2580.0 1748.7
3 3050 350 2470.50 2930.0 0.0 2930.0 1769.0
4 3010 -400 2438.10 2530.0 0.0 2530.0 1745.8
5 2975 -350 2409.75 2180.0 0.0 2180.0 1725.5
6 2920 -550 2365.20 1630.0 735.2 2365.2 1693.6
7 2900 -200 2349.00 2165.2 0.0 2165.2 1682.0
8 2910 100 2357.10 2265.2 0.0 2265.2 1687.8
9 2870 -400 2324.70 1865.2 0.0 1865.2 1664.6
10 2920 500 2365.20 2365.2 0.0 2365.2 1693.6
11 2940 200 2381.40 2565.2 0.0 2565.2 1705.2
12 2890 -500 2340.90 2065.2 0.0 2065.2 1676.2
13 2870 -200 2324.70 1865.2 0.0 1865.2 1664.6
14 2820 -500 2284.20 1365.2 919.0 2284.2 1635.6
15 2770 -500 2243.70 1784.2 0.0 1784.2 1606.6
  • simplified example for single contract, as in practice there is more sophisticated method of margin calcualtion for portfolio of derivatives

Main incentive of derivative trader

Speculators
Speculators are risk takers, who take the position in the market. They assume that the price will behave in line with theirs expectations.

  • bull speculation
  • bear speculation
  • intracontract spread
  • intermarket spread

Arbitrageurs
Arbitrageurs are looking for inefficiences in market prices. They usually enter simultaneously trasactions in two or more markets in underlying and derivative contract. Arbitrage will deliver “riskless” profit. In liquid markets space for arbitrage is very limited if any.

Hedgers
Hedgers use derivatives to reduce the risk they face from possible future market behaviour. Depending on the expectations they try to limit the risk to the acceptable level or to avoid the risk at all.

Hedging

The purpose of hedging is to transfer the risk from a person who wants to limit or get rid of it to a person who accepts this risk in the hope of making a speculative profit. On the other hand, by entering into a futures contract in order to protect against the risk of changing the price or value of a particular good, the institution or person resigns from any profits that might arise in the event of the reverse price development. An excellent hedging strategy does not cause losses or profits on either side (the base is zero when the contract is executed).
Optimal number of contracts:
\[N^{*} = \frac{h^{*}Q_{A}}{Q_{F}}\] \(Q_{A}\) - Size of position being hedged
\(Q_{F}\) - Size of one futures contract
\(N^{*}\) - Optimal number of futures contracts for hedging
\(h^*\) - minimum variance hedge ratio \[h^* = \rho\frac{\sigma_s}{\sigma_f}\] \(\sigma_s\) - standard deviation of changes in spot price
\(\sigma_f\) - standard deviation of changes in future price
\(\rho\) - coefficient of correlation between the changes in spot and future prices

Prices of future contracts

Indices and stocks

\[F = S * e ^ {(r - d) * T}\] \(F\) - futures price
\(S\) - spot price
\(r\) - risk-free rate (usualy 52 week treasury bill yield is taken as risk-free rate)
\(d\) - dividend rate
\(T\) - time to maturity in years

Currencies

\[F = S * e ^ {(r - r_f) * T}\] \(F\) - forward FX
\(S\) - spot FX
\(r\) - risk-free rate
\(r_f\) - foreign risk-free interest rate
\(T\) - time to maturity in years

FRA (forward rate agreement)

A forward rate agreement (FRA) is a transaction designed to fix the interest rate in the period between two future dates. One side of the contract lend certain amount of money (principal) to the other. As a result of the transaction if the agreed fixed rate is greater than the actual reference (variable) rate for the period, the borrower pays the lender the difference between the two applied to the principal. Otherwise the lender pays the borrower adequate amount.

Rationale for FRA transactions: Various expectations of FRA, traders concerning future evolution of interest rates

Valuation Define:
\(T_1\) - start of the lending period
\(T_2\) - end of the lending period
\(r_r\) - reference rate (The forward, usually LIBOR, interest rate for the period between times T1 and T2
\(r_c\) - contract rate (the fixed rate of interest agreed to in the FRA)
\(FV\) - principal of the underlying contract

If in the maturity \(r_r\) > \(r_c\) then seller pays to the buyer the amount:
\[C = FV * \frac{(r_r - r_c) * (T_2 - T_1) }{1+r_r * (T_2 - T_1)}\]
If in the maturity \(r_r\) < \(r_c\) then buyer pays to the seller the amount:
\[C = FV * \frac{(r_c - r_r) * (T_2 - T_1) }{1+r_r * (T_2 - T_1)}\]

Other future contracts

Treasury bond futures

  • long term
  • short term
  • quotes
  • prices

Eurodolar futures

  • short term interest rate
  • basis instruments
  • prices
  • eurodolar
  • eurodolar interest rate

Excercise 1

An American farmer - a supplier of wheat to the market, assesses his future harvest, which will be collected in September at 50,000 tones. On April 1st, the futures contract for 10,000 tones of wheat and expiration in September was $ 300 per ton. Assume there is no transactions’ fees.
a) Did the farmer choose the correct hedging strategy by selling in April 5 contracts covering 50 000 tons with expiry in September? The settlement price of wheat in September was $ 400 per ton?
b) What are the consequences of his decision?
c) What would have been the consequences if the settlement price in September had fallen to $ 250 per ton?

Excercise 2

The American speculator predicts that the corn price will rise from the current $3 per bushel in June to $4 per bushel over the next three months. September contracts for corn currently cost $3.25. The speculator buys 10 contracts for 5 000 bushels of corn each, the initial deposit is 15% and the commission is $40 for the contract. Please describe the investor’s situation in these two cases below.
a) The American speculator is unlucky: three months later the price of corn futures falls to the price of $2.75 per bushel. How much did the speculators loose?
b) The American speculator is lucky: three months later, the price increases to $3.90 per bushel. How much did the speculator earn?

Excercise 3

The speculator tries to evaluate the forward price of a three-month futures contract issued for the stock index, if the dividend rate of all stocks included in the index is 4% per annum, the current value of the index is 1233, and the continuously capitalized risk-free rate is 6% p.a. What should he do if the market price is higher (\(F_1\) = 1250), and what if it is lower (\(F_2\) = 1230)? Please provide a detailed description of the arbitrage strategy.

Excercise 4

The Bloomberg Money Desk analyst calculates the forward price of a 9-month forward contract for shares of the ABC Bank, listed on the London Stock Exchange. The share price is currently GBP 94. The analyst assumes that the risk-free interest rate (capitalized on a continuous basis) is equal to 7% and that after 3, 6 and 9 months Bank ABC will pay a dividend of GBP 1.25 per share, and after 12 months will not pay dividends. Calculate the contract price.

Excercise 5

The novice investor opens a short position in a futures gold contract for the delivery of 1000 ounces. The 1-month price of one-ounce is $ 550. The security deposit is $ 5000. What is the profit / loss of the novice analyst if the spot price price is: a) 520 $, b) 555 $ when the contract expires? One way shipping costs are $ 10.

Excercise 6

The novice investor is considering the arbitrage of one-year futures contract for crude oil. How to make the arbitrage if: the futures price is: a) F1 = $21 per barrel, b) F2 = $19 per barrel, the spot price is $19 per barrel, the risk-free interest rate is 3% per annum, and the annual storage price is $0.4 per barrel payable in advance. Please provide a detailed description of the arbitrage strategy.

Excercise 7

The level of the WIG20 index equals 1233 points, the risk-free rate is 4% p.a. (continuous capitalization), the dividend rate equals 2%. At what future price will a long position be opened for a six-month contract? What is the theoretical price of the contract?

Excercise 8

On 1 January, the company purchased a FRA contract. On this day the reference rate was 6.5%, the contract rate is 7%. The notional is PLN 100,000 The contract is to be settled on April 1. What price the dealer will pay to the company if:
a) the reference rate on the settlement day is 7.6%,
b) 6.75%?

Excercise 9

Mr. Shorter has a portfolio of shares of companies listed on the NYSE with a total value of USD 60 million. He anticipates a downward trend and therefore plans to secure its assets. The three-month S&P500 index is traded at 1200. How many position should he open on the S&P500 to protect against an unfavorable fall in the index? We assume that the S&P500 falls to 960. What is the value of his assets if:
a) the value of the fully secured portfolio falls in 3 months to the level of 48 million, and the hedge ratio is 1?
b) the value of the fully secured portfolio falls in 3 months to the level of 48 million, and the hedge ratio is 1.5?
The multiplier of S&P500 contract is 250 USD per 1 point.

Excercise 10

It is 10th of June. Carla Morris manages a short-term portfolio of US Treasury bills with a face value of $ 4 million and an expiry date of 91 days and a discount rate of 8%. On September 10 Carla will exchange her papers for a new issue of treasury bills. Carla believes that the discount of treasury bill will fall during these three months. For this purpose, she opens a long position on the forward market in interest rate contracts to secure her position on the cash market. Please provide the list of Carla’s operations and cash flows if:
- the long positioni opened at the course F1 = 92,00,
- the value of one contract is $ 1 million,
- the value of 1 bp = $ 25.
We assume that the discount actually falls to d2 = 7% on 10th Septtember, and the price of contracts reaches F2 = 93.00.
T = 91/360,
d1 = 8%,
N = $4mln.

Excercise 11

The bank offers the institutional client two options:
a) a cash loan at 11 percent per annum and
b) a gold loan at 2 percent per annum (interest must be paid in gold, which means that loans of 100 ounces should be returned at the level of 102 ounces a year later).
The risk-free interest rate is 9.25 percent per annum and the cost of gold storage is 0.5 percent per year. Analyse whether the interest rate on the gold loan is too high or too low in relation to the interest rate on the cash loan. The interests on both loans are calculated based on annual capitalization, the risk-free interest rate and the cost of storing of gold are presented with the assumption of continuous capitalization.

Excercise 12

The standard deviation of the monthly change in the cash price of cattle is 1.2 cents per pound. The standard deviation of the monthly change in futures contracts for cattle with the nearest expiration date is 1.4 cents per pound of weight. The correlation between the change in the forward price and the change in the cash price is 0.7. On 15th October, the beef producer plans to buy 200,000 pounds of livestock on November 15 and wants to use the strategy to secure December contracts for slaughter, each of which is for a supply of 40,000 pounds. Describe the beef producer’s strategy.