Futures and Forwards Finance

Futures and Forwards

Finance 100

Prof. Michael R. Roberts

Topic Overview z Forward contracts » Valuation z Futures contracts » Valuation z Using futures to hedge in practice »Stock market risk » Foreign exchange risk » Interest rate risk

1 1 Forward Contracts z A forward contract is a contract made today for future delivery of an asset at a prespecified price (delivery price). » no money or assets change hands prior to maturity. » Forwards are traded in the over-the-counter market. z The buyer (long position) of a forward contract is obligated to: » take delivery of the asset at the maturity date. » pay the agreed-upon price at the maturity date. z The seller (short position) of a forward contract is obligated to: » deliver the asset at the maturity date. » accept the agreed-upon price at the maturity date

Forward Contracts (Cont.) z Forwards can be used for hedging » Commodity price risk – for a buyer (miller) – for a seller (farmer) » Foreign exchange risk – Sell Swiss Francs (buy $) if you are a US company – Buy Swiss Francs (sell $) if you are a Swiss company z Further issues » Risk analysis »Stock market risk » Interest rate risk

2 2 Institutional Details z Futures contracts traded on CBOT, MYCE, CME » Commission brokers and local traders » Market and limit orders z Most contracts do not end in delivery of asset! » Positions “closed out” by executing opposite trade z Purpose of exchanges » Create an organized and efficient market in the security » Minimize default risk (margin requirements) z Regulation »CFTC » Daily Price Movement & Position Limits z Exchange Clearinghouse

Contract Details

z Asset Specification » Orange Juice Futures: “US Grade A, with Brix value of not less than 57 degrees, having a Brix value to acid ratio of not less than 13 to 1 nor more than 19 to 1, with factors of color and flavor each scoring 37 points or higher and 19 for defects, with a minimum score of 94.” z Contract size z Delivery » Random length lumber futures “On track and shall either be unitized in double-door boxcars or, at no additional cost to the buyer, each unit shall be individually paper-wrapped and loaded on flatcars. Par delivery of hem-fir in CA, ID, MO, NE, OR, and WA, and in the province of British Columbia.”

3 3 Applications for Hedge Instruments z A mining company expects to produce 1000 ounces of gold 2 years from now if it invests in a new mine: » Concern about the impact of future gold price movements on the revenue stream used for loan payments. z A bank expects repayment of a loan in 1 year, and wishes to use proceeds to redeem 2-year bond » Lock in current interest rate between 1 and 2 years from now in order to avoid shortfall if interest rates have changed z A hotel chain buys hotels in Switzerland, financed with a loan in US-dollars: » Make sure that the company can repay the loan, even if Swiss franc proceeds diminished because of exchange rate movement

Forwards on Securities The Case of Securities without Income z What is the difference between buying a security today, and between buying a security forward? » If you purchase the security forward, you do not have to pay the purchase price today: – Can invest the money somewhere else » Securities pay income (dividends, coupons) – Only if you purchase it now, not if you buy forward Example: » Share trades today at $25 » Pays no dividends during the next year » The annual risk free rate is 6% p. a. with annual compounding

4 4 What is the Delivery Price? Example z Consider the replicating the payoff of the forward contract:

z No arbitrage implies:

A Payoff Diagram

Replicating Portfolio 70 Future Spot Own Own 60 Long Forward Price Forward Asset Borrow Total 50 Own Stock 0 -26.5 0 -26.5 -26.5 Borrow 40 5 -21.5 5 -26.5 -21.5

30 10 -16.5 10 -26.5 -16.5 15 -11.5 15 -26.5 -11.5 f 20 20 -6.5 20 -26.5 -6.5 Payof 10 25 -1.5 25 -26.5 -1.5 0 30 3.5 30 -26.5 3.5 0 10203040506070 -10 F 35 8.5 35 -26.5 8.5 40 13.5 40 -26.5 13.5 -20 45 18.5 45 -26.5 18.5 -30 50 23.5 50 -26.5 23.5 -40 55 28.5 55 -26.5 28.5 Future Spot Price 60 33.5 60 -26.5 33.5

Borrowing + Owning the underlying asset results in a payoff identical to buying a forward contract.

5 5 The Effect of a Dividend z Now suppose the share pays a $2 dividend at the end of the year » Same approach (and strategy) as before.

z No arbitrage implies:

General Formula – Dividend at end of Period z The examples above can be generalized to: » Arbitrary asset price S » Arbitrary payout, D (received at end of position, T) » Arbitrary interest rate

Time Period (Year) 0T

Buy Forward 0 ST-K

Buy Share S0 ST+D Borrow (K+D)(1+r)-T -K-D -T Portfolio (K+D)(1+r) - S0 ST-K z Implies a general formula for the forward price: T K = S0(1+r) -D

6 6 Computing the Delivery Price Example z Find the delivery price on an 18 month equity forward contract where the current share price is $100, the risk-free rate is 6% compounded semi- annually and no dividends are expected. T » Start with the general formula: K = S0(1+r) -D

» What is S0 ?? r T ? D ? » What is K ?

Forward Arbitrage Example z What if the delivery price in the market is $111 for the contract considered in the previous example?

» Is there an arbitrage? What strategy would you use to take advantage of the arbitrage?

7 7 Using a Dividend Yield z Standard fare is to express dividend payouts in terms of a yield (d) as opposed to a lump sum (D). z The approach to valuation is unchanged but we get a slightly different equation for the delivery price

Time Period (Year) 0T

Buy Forward 0 ST-K -T Buy Share -S0(1+d) ST Borrow K(1+r)-T -K -T -T Portfolio K(1+r) -S0(1+d) ST-K

T ⎛⎞1+ r z New formula is: KS= 0 ⎜⎟ ⎝⎠1+ d

Delivery Price & Continuous Compounding z Same exercise but assume interest and dividends are compounded continuously Time Period (Year) 0T

Buy Forward 0 ST-K -dT Buy Share -S0e ST Borrow Ke-rT -K -rT -dT Portfolio Ke -S0e ST-K z New formula is: (rdT− ) KSe= 0

8 8 Delivery Price Example z The current price per share of IBM is $100 with a continuously compounded dividend of 2%. If the risk-free rate, assuming continuous compounding, is 6%, what is the delivery price of a 18-month forward contract on IBM stock?

Delivery Price Example (Cont.) z If the delivery price in the market is 105, is there an arbitrage opportunity and if so, how would you exploit it ?

9 9 What is a Forward Price?

z The Forward Price (Ft) is the price such that the present value of the contract payoff at time t equals zero. » At inception of the contract the forward price equals the

delivery price, F0=K » As time passes, K never changes but F changes with the value of underlying asset in order to make PV of contract = 0. (rd− )( Tt− ) FSett=

Value of a Forward Contract

z Thus, the value (Vt) of a forward contract at time t is given by:

− r (T −t ) Vt = (Ft − K )e

» where Ft is the current forward price in the market, and r is the (T-t)-year risk-free rate. z At time 0, the value of the contract is 0 since F0=K, which implies V0 = 0. z As time passes, Ft changes so Vt changes according to above formula

10 10 Forwards on Commodities

z Commodities are similar in many ways to securities, but some important differences: » Storage costs can be significant: – Security (precious metals) – Physical storage (grain) – Possibility of damage

z Summarized as cost of carry, usually written as constant annual percentage c of initial value. » Sometimes possession of commodity also provides benefits: – Demand fluctuations – Supply shortages (Oil)

z Summarized as convenience yield, usually written as constant annual percentage y of initial value.

Commodity Forwards Impact on Prices z Storage costs are a “negative dividend” z Convenience yield is a “positive dividend” z The net result and impact on the forward price is summarized in the arbitrage table below Time Period (Year) 0T

Buy Forward 0 ST-K (c-y)T Buy Share -S0e ST Borrow Ke-rT -K -rT (c-y)T Portfolio Ke -S0e ST-K z The new delivery price equation is: T ()rcyT+− ⎡()()11++rc⎤ KSe==00 (or KS⎢ ⎥ ) ⎣⎢ ()1+ y ⎦⎥

11 11 Commodity Forwards Example z As an electricity generator, you are concerned about your exposure to oil price volatility, since oil is a major input in the production process. How could you hedge your risk exposure? z In going to the market, you estimate the storage cost and convenience yield to be 5% and 4%, respectively, relative to the current spot price of $35 per barrel. z The risk-free rate is 6% and the current forward price in the market is $36 per barrel for a contract maturing in 6 months. z Is there an arbitrage opportunity here?(assume continuous compounding) If so, how would you take advantage of it?

Commodity Forwards Example (Cont.) z What is the implied delivery price? z Arbitrage table

12 12 Futures Contracts

z A futures contract is identical to a forward contract, except for the following differences: » Futures contracts are standardized contracts and are traded on organized exchanges. » Futures contracts are marked-to-market daily. z Futures contracts allow investors to: » Hedge » Speculate z Futures contracts are available on commodities and financial assets: » Agricultural products and livestock » Metals and petroleum » Interest rates » Currencies » Stock market indices

Futures Contracts Marking to Market z Futures Marking to Market: » Buy 1 March S&P500 Future @$300 = 500 x $300 = $150,000 exposure – Initial Margin = $15,000 (10% of exposure) – Maintenance Margin = $7,500 (5% of exposure) » *Contracts are now for 250 times the index, which is around 1400. z Cash Flows and Margin Account due to Marking-to-the-Market Deposit / Account Time Futures Price Action Cash Flow Withdrawal Equity 0 $300 Buy Contract $0 $15,000 $15,000 1 $301 Seller pays buyer $500 $15,500 2 $303 Seller pays buyer $1,000 -$500* $16,000 3 $297 Buyer pays seller -$3,000 $13,000 4 $283 Buyer pays seller -$7,000 $9,000** $15,000 5 $285 Seller pays buyer $1,000 $16,000

13 13 Foreign Exchange Risk: Foreign Currency Futures z Foreign currency futures are z Delivery Months: March, traded on the CME. June, Sept., Dec. z Foreign currency futures are z Prices are quoted as USD per traded on: unit of the foreign currency. » Euro: 125,000ECU » British Pound: 62,500GBP 2000 2008__ » Canadian Dollar: 100,000CAD » USD/CHF = 0.5682 (0.9768) » Japanese Yen: 12,500,000JPY » USD/EURO = 0.4379 (1.5718) » Swiss Franc: 125,000CHF » USD/GBP = 1.4536 (1.9758) » Australian Dollar: 100,000AUD » USD/AUD = .4379 (0.9523) » Mexican Peso: 500,000MP » Israeli Shekel: 1,000,000IS

Foreign Currency Futures Price

z A currency future is a contract guaranteeing the buyer a prespecified amount of foreign currency for a pre-specified domestic price. z Now the underlying variable, X, is the foreign currency exchange rate » E.g. $/L for a US investor buying British pounds » E.g. Eur/Yen for French investor buying Yen Time Period (Year) 0T

Buy Foreign Currency Forward 0 XT-K -(rf)T Loan Foreign Currency (Buy Foreign Bond) -X0e XT Borrow Domestic Currency Ke-rT -K -rT -(rf)T Portfolio Ke -X0e XT-K

14 14 Hedging with Foreign Currency Futures

z An American company sells 20 machines to a German company at a sale price of 50,000ECU per machine. The money will be collected at the end of the year and your concerned that the exchange rate ($/ECU) may go down. z Construct an appropriate hedge using a futures contract. » What’s our exposure ?

» What futures position should we take to hedge the risk ? z What happens if the exchange rate changes?

Hedging with Foreign Currency Futures (Cont.) z Assume current futures price for a Euro is $1.57 (I.e. exchange rate is $1.57/ECU) » Scenario 1: Exchange rate falls to $1.00/ECU – Profits from futures position = ?

– Profits from sale of machines = ? – Total profit in $US = ? » Scenario 2: Exchange rate rises to $2.00/ECU – Profits from futures position = ?

– Profits from sale of machines =? – Total profit in $US = ? z Punch line:

15 15 Hedging Considerations

z Account for natural hedges » If you can pass on the risk to consumers, no need to hedge – Gas stations don’t need to hedge oil prices z Liquidity Risk » Hedging with futures may entail margin calls in the interim – Metallgesellschaft Refining and Marketing (MGRM) – Hedged against rising oil prices with long futures contracts to supply oil to its customers – Oil prices dropped Æ margin call came Æ MGRM had no cash… – Shut down in 1993 with $1bil in oil futures losses z Basis Risk » Futures contracts are very specific Æ may not be a perfect hedge

Summary z Forwards and futures are redundant instruments: » Can be replicated through transactions in spot markets and borrowing or lending » Futures and forwards are derivatives: – Value depends on value of other asset z Forwards and futures can be used to hedge risks: » Foreign exchange rate risk » Stock market risk » Commodity price risk » Interest rate risk z Forwards and futures are very volatile instruments due to leverage. They increase risk unless: » they are used for hedging » the portfolio includes sufficient investments in riskfree assets

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