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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.

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

- 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 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.

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

- 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.)

- 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).

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).

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?

- 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.

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

- 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)

- 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?

- 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

- 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

- 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

- 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…

- 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:

- 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”

- 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

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

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

- 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

- Link to Forward Pricing Excel file:
- FM 12 Ch 26 Mini Case.xls (Brigham & Ehrhardt file)

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.)

- 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 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

- 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

- 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 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.

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

- “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-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)

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

- 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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