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Forwards, Futures, and their Applications

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

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Forwards, Futures, and their Applications

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  1. Forwards, Futures, and their Applications

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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).

  8. 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).

  9. 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).

  10. FX Risk: Calculate the indirect quotations for euros and Swedish krona • Euro: 1 / 0.8000 = 1.25 • Krona: 1 / 0.1000 = 10.00

  11. 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.

  12. 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.

  13. 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

  14. 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

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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).

  21. 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

  22. 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

  23. 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.

  24. 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.

  25. Currency Risk and Forward Pricing Examples • Link to Forward Pricing Excel file: • FM 12 Ch 26 Mini Case.xls (Brigham & Ehrhardt file)

  26. 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.

  27. 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)

  28. 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.

  29. 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).

  30. 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.

  31. 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.

  32. 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.

  33. 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.

  34. 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.

  35. 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

  36. 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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