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Forwards, Futures, and their Applications. The Oldest Derivative: Forward Contracts.

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the oldest derivative forward contracts
The Oldest Derivative: Forward Contracts
  • Forward Contracts – Obligates its owner to buy (if in a “long” position) or sell (if in a “short” position) a given asset on a specified date at a specified price (the “forward price”) at the origination of the contract.
  • Two Key Features:
    • Credit risk is two-sided (i.e., both buyer and seller of the forward can default on the deal).
    • No money is exchanged until the forward’s maturity date.
  • The above features increase default risk and restricts the availability and liquidity of these contracts.
futures contracts
Futures Contracts
  • Futures Contracts – Similar to Forwards. Obligates its owner to buy (if in a “long” position) or sell (if in a “short” position) a given asset on a specified date at a specified price (the “futures price”) at the origination of the contract.
  • Key Features:
    • Credit risk is two-sided but is reduced substantially because of two mechanisms:

1) marking-to-market (daily settling up of the account), and

2) margin requirements (i.e., a good-faith deposit).

    • Standardized contract specifies exact details of term, asset, contract size, delivery procedures, place of trading, etc.
    • Clearinghouse reduces transaction costs and de-couples buyer from seller by providing anonymity.
forward contract characteristics
Forward Contract Characteristics
  • Forwards can be created on all types of financial assets (FX, interest rates, commodities, stock prices).
  • Can require physical delivery or cash-settled.
  • The expected NPV of an at-market forward is zero.
  • Notional principal is used to determine cash flows but is not paid/received at maturity.
  • Most liquid within 1-2 year maturities.
  • Most frequently used with FX transactions by larger corporations with international exposures.
profit calculations on a forward contract
Profit Calculations on a Forward Contract
  • Profit on a forward contract is related to the difference between the price of the underlying asset at the forward’s maturity (time = T) and the forward price (initially specified at the onset of the contract at time = 0).
  • Profit = L/S Indicator * (PT – PF0) * Number of units


L/S indicator = +1 if in a long position or

-1 if in a short position.

  • The objective is to use the forward’s profit to offset any losses in the underlying asset’s position.
hedging strategies
Hedging Strategies
  • If you are long the underlying asset (i.e., increases in the asset’s price increase firm value), then you can enter into a forward contract to sell (or “short”) the asset at the forward price. This can hedge changes in the asset’s price.
  • A classic example is a farmerproducing an agricultural commodity. He/she is long wheat and is worried about price declines so he/she hedges by selling wheat in the forward market.
  • Conversely, if you are short the underlying asset, then you should buy (or “go long”) the asset. For example, a baker consumes wheat and is worried about increases in wheat prices. So, should buy wheat at the forward price.
principles of forward pricing
Principles of Forward Pricing
  • A cynic: “Someone who knows the price of everything but the value of nothing”.
  • There are costs and benefits to all derivatives and underlying assets.
  • Storage and insurance costs of the underlying asset.
  • Opportunity costs (forgone interest, missed opportunities).
  • Benefits such as income generation (e.g., dividends on a stock) and having the asset on-hand (e.g., a “convenience yield” for commodities).
principles of forward pricing cont
Principles of Forward Pricing (cont.)
  • Forward Price = FP0 = P0 + FV(cost of asset ownership) – FV(benefits of asset ownership)
  • Forward prices must be arbitrage-free.
  • If FP0> P0 + FV(costs) – FV(benefits)


  • Sell the forward at FP0,
  • Borrow proceeds equal to P0 and buy asset in spot market (at P0),
  • Receive income on long position in the asset.
  • At maturity, you reverse your actions to lock in a riskless profit (receive income, pay back loan, and sell asset at FP0).
principles of forward pricing cont9
Principles of Forward Pricing (cont.)
  • If FP0< P0 + FV(costs) – FV(benefits)


  • Buy/go long the forward at FP0,
  • Borrow the asset (and pay any interest on this borrowing),
  • Sell the asset immediately in the spot market (at P0) and invest proceeds equal to P0 in riskless asset,
  • At maturity, reverse your actions to lock in a riskless profit (recoup investment in riskless asset, pay for underlying asset at FP0, and return borrowed asset with interest).
fx risk calculate the indirect quotations for euros and swedish krona
FX Risk: Calculate the indirect quotations for euros and Swedish krona
  • Euro: 1 / 0.8000 = 1.25
  • Krona: 1 / 0.1000 = 10.00
what is a cross rate
What is a cross rate?
  • A cross rate is the exchange rate between any two currencies not involving U.S. dollars.
  • In practice, cross rates are usually calculated from direct or indirect U.S. rates. That is, on the basis of U.S. dollar exchange rates.
calculate the two cross rates between euros and krona
Euros Dollars Dollar Krona

Cross Rate =


= 1.25 x 0.1000= 0.125euros/krona

Krona Dollars Dollar Euros

Cross Rate =


= 10.00 x 0.8000= 8.00 krona/euro

Calculate the two cross ratesbetween euros and krona.
example of international transactions
Example of International Transactions
  • Assume a firm can produce a liter of orange juice in the U.S. and ship it to Spain for $1.75.
  • If the firm wants a 50% markup on the product, what should the juice sell for in Spain?

Target price = ($1.75)(1.50)=$2.625

Spanish price = ($2.625)(1.25 euros/$)

= € 3.28

example continued
Example (continued)
  • Now the firm begins producing the orange juice in Spain. The product costs 2.0euros to produce and ship to Sweden, where it can be sold for 20krona.
  • What is the dollar profit on the sale?

2.0 euros* (8.0 krona/euro) = 16krona

20 - 16 = 4.0kronaprofit.

Dollar profit = 4.0 krona * (0.1000 $ per krona)

= $0.40

what is exchange rate risk
What is exchange rate risk?
  • Exchange rate risk is the risk that the value of a cash flow in one currency translated from another currency will decline due to a change in exchange rates.
currency appreciation and depreciation
Currency Appreciation and Depreciation
  • Suppose the exchange rate goes from 10krona per dollar to 15kronaper dollar.
  • A dollar now buys morekrona, so the dollar is appreciating, or strengthening.
  • The kronabuys less dollars, so the krona is depreciating, or weakening.
affect of dollar appreciation
Affect of Dollar Appreciation
  • Suppose the profit in kronaremains unchanged at 4.0krona, but the dollarappreciates, so the exchange rate is now 15krona/dollar.
  • Dollar profit = 4.0 krona/ (15 kronaper dollar) = $0.267
  • Strengthening dollar hurts profits from international sales.
forward fx rate contracts
Forward FX rate contracts
  • FX forward contract – agree on an exchange rate today to exchange one currency (e.g., the Japanese yen) for another currency (e.g., the U.S. dollar) at some time in the future.
  • Interest Rate Parity determines the forward FX rate that makes the E(NPV) = 0.
  • Covered Interest Arbitrage ensures that Interest Rate Parity holds.
  • Conceptually equivalent to a pair of zero coupon bonds.
fx forward rates
FX forward rates…
  • Forward exchange rate determined by the current spot FX rate and the riskless interest rates in the two countries.
  • The interest rate parity relation can be summarized by:
  • Where, r1 = interest rate for the country that has its currency in the denominatorof the FX rate (e.g., U.S. dollar if FX rate is expressed as Yen / dollar).
  • r2 = interest rate for country whose currency is in the numerator of the FX rate.
application for 6 month colon u s dollar fx forward rate
Application for 6-month Colon / U.S. Dollar FX forward rate:
  • To synthesize the current Colon / Dollar 6-month forward exchange rate, we must use the current spot FX rate and the (near) riskless interest rates of the two countries.
  • This interest rate parity relation can be summarized by:
  • Where, r1 = the U.S. dollar interest rate because the FX rate is expressed as Colones / U.S. Dollar).
  • r2 = the interest rate in Colones).
interest rate parity and the box
Interest Rate Parity and the “Box”
  • Forward FX rates can be replicated by following the lines around a box that links spot rates, forward rates, and interest rates.


U.S. $T


U.S. $0



application of how to synthesize a short colon dollar forward fx rate
Application of how to synthesize a Short Colon / Dollar Forward FX Rate
  • A ShortColonesposition can be synthesized by: 1) borrowing in Colones at 8.95% for 6 months, 2) investing in U.S. Dollars at 0.15% for 6 months at the Spot FX rate of 499.4.

U.S. $T






U.S. $0


forward interest rates fras
Forward Interest Rates (FRAs)
  • Forward Interest Rate Agreement – agree on an interest rate today to receive (or pay) at some time in the future.
  • Forward Interest Rates are implicit in spot yield curves.
  • This is due to a “no arbitrage” argument that says that the return on, say, a two-year bond must be equivalent to the return on a “roll-over” strategy of investing in a 1-year bond and rolling it over into another 1-year bond at the beginning of the second year.
fra pricing
FRA pricing
  • You can use interest rates from the spot yield curve to derive forward rates as follows:
  • Where, R’s with a prefix of “0” are spot rates andj= the term of the FRA and k= the start date of the FRA.
currency risk and forward pricing examples
Currency Risk and Forward Pricing Examples
  • Link to Forward Pricing Excel file:
  • FM 12 Ch 26 Mini Case.xls (Brigham & Ehrhardt file)
futures contracts26
Futures Contracts
  • Similar to Forward contracts but are more structured and standardized than forwards.
  • Futures contract is a legally binding obligation to buy or sell a specified quantity of a specific asset at a specified date in the future.
  • Standardization features: contract specifies a homogeneous asset, maturity date, contract size, delivery mechanism, and minimum “tick” size.
futures contracts cont
Futures Contracts (cont.)
  • Institutional Features that:
    • Reduce credit risk, and
    • Improve liquidity
  • Five key elements:
    • Standardized contract on homogeneous asset
    • Daily settlement of positions (like a series of forwards)
    • Margin requirements (good faith deposit that reduces credit risk)
    • Price limits (restricts daily movement in futures price to be within margin requirement)
    • Clearinghouse (de-couples buyer and seller by providing anonymity and reduces counterparty risk)
pricing of futures contracts
Pricing of Futures Contracts
  • Pricing reflects the spot price, P0, plus the “cost of carry”, c, (which includes the risk-free rate, rf).
  • F0 = P0 + c = P0 * (1 + rf)T

if the only component of c is a constant risk-free rate.

  • No arbitrage requirement enforces the above relation
  • Other factors can affect the cost of carry, c, such as storage and insurance costs, as well as interest/dividend income on the underlying asset.
features of futures prices
Features of Futures Prices
  • The concept of Basis is a key factor when determining the effectiveness of a hedge:

Basist = Ft - PtSee Spreadsheet File.

  • According to the cost-of-carry model, the basis should correspond to the cost of carry variable, c.
  • Over time, futures prices will tend to converge toward the price implied by c.
  • Also, the futures price will converge to the spot price at the futures contract’s expiration (FT = PT).
basis risk
Basis Risk
  • Perfect hedges are difficult to construct due to basis risk.
  • Basis Risk is the risk that the payoff profile of the hedging instrument is not exactly equal to the firm’s risk profile associated with a specific financial asset.
  • Four primary sources of basis risk:
    • Changes in the convergence rate of FTto PT
    • Changes in the factors affecting c,
    • Random deviations in c,
    • Mismatches between the hedging instrument and the underlying asset exposure (cross-hedge basis risk)
  • Note: basis risk goes to zeroif hedge’s maturity exactly equals the underlying asset’s purchase/sale date.
cross hedge basis risk
Cross-hedge Basis Risk
  • Cross-hedge is used when there is no hedging instrument that is identical to the underlying asset exposure (e.g., use T-bond futures to hedge a corp. bond portfolio).
  • Cross-hedge Basist = (Ft,X – Pt,X) + (Pt,X - Pt,Y)


X = asset that is used for hedging purposes,

Y = underlying asset exposure to the firm.

  • Three factors that affect the above basis risk:

1) Maturity mismatch, 2) Liquidity, 3) Credit risk.

hedging applications of forwards and futures
Hedging Applications of Forwards and Futures
  • Forward contracts are normally best for situations where the contract details (size, maturity, underlying asset) need to be tailored to a specific set of firm cash flows.
  • Forwards are usually more cost-effective for larger firms with good credit ratings and special needs that suit “custom-tailoring”.
  • Futures are less flexible than forwards in terms of tailoring the payoffs to fit a firm’s exposures.
  • However, futures are much more liquid than forwards and have much less credit risk.
hedging prerequisites
Hedging Prerequisites
  • “Appropriates” – specifies the details of the financial exposure that the firm plans to hedge (e.g., What security?, What time/maturity?, How much?).
  • Hedging Strategies:
    • Do Nothing – easiest strategy (but can be very costly!).
    • Lock in price today – use forwards or futures to hedge exposure fully (100% of exposure is covered).
    • Lock in price today for some of the exposure - less than 100% coverage can be cheaper.
    • Cross-hedge – when derivative is not available for the firm’s underlying financial exposure.
  • Note: hedging substitutesBasis Risk for Price Risk.
cross hedging example
Cross-Hedging Example
  • Cross-hedge: Use New Mexican Peso Futures to hedge against changes in Colon / U.S. Dollar rate).
  • Find Futures Contract with closest correlation to underlying exposure – Usually use a regression:

PC.R. Exchange Rate = a + b * PMexican Exchange Rate + e

(choose the future that has the highest adj. R2,

e.g., our R2 = .333 and b = 0.023 for the peso)

  • Divide total exposure by standard futures contract size (0.5M pesos) to get “raw” number of contracts needed.

e.g., {[400M colones x 0.023] / 0.5M} = 18.4 19.

cross hedging example continued
Cross-Hedging Example (continued)

Assume: Peso devalues from 11.1 to 12.3 per U.S. dollar and Colon devalues from 513 to 570 per U.S. dollar.

Initial Value of 400M Sale: $0.780M = 400M / (513 / $1)

Ending Value of Sale: $0.702M = 400M / (570 / $1)

Loss due to Devaluation: $0.078M (-10.0%)

Initial SHORT Futures: $0.856M = (19 x 0.5M) / 11.1

Ending SHORT Futures: $0.772M = (19 x 0.5M) / 12.3

Gain due SHORT Futures: $0.084M (+9.8%)

Net Change in Total Value:+$0.006M = +0.084 – 0.078

calculating the overall effect of a hedge
Calculating the Overall Effect of a Hedge
  • Calculate Change in Underlying Asset Position – Multiply the spot price at maturitytimes quantity of the underlying position

– Then subtract initial asset value (at t=0) from the above figure.

  • Calculate the Hedge’s Profit/Loss

Hedging Profit/Loss = L/S Indicator * (FT – F0) * Number of Futures Contracts * Futures Contract size

Note: must replace FT with PT if there is no basis risk

  • Add the two figures together to get net effect:

Net Change in Value = D Underlying + D Hedge