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

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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.


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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.


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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.


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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

    where,

    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.


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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.


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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).


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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)

    then,

  • 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).


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Principles of Forward Pricing (cont.)

  • If FP0< P0 + FV(costs) – FV(benefits)

    then,

  • 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).


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FX Risk: Calculate the indirect quotations for euros and Swedish krona

  • Euro: 1 / 0.8000 = 1.25

  • Krona: 1 / 0.1000 = 10.00


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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.


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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.


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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


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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


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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.


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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.


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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.


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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.


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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.


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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).


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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.

ForwardT

U.S. $T

ColonesT

U.S. $0

Colones0

Spot0


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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

ColonesT

ForwardT=520.9

+1.00151/2

-1.08951/2

Spot0=499.4

U.S. $0

Colones0


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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.


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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.


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Currency Risk and Forward Pricing Examples

  • Link to Forward Pricing Excel file:

  • FM 12 Ch 26 Mini Case.xls (Brigham & Ehrhardt file)


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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.


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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)


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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.


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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).


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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.


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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)

    where,

    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.


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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.


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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.


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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.


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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


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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


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