Futures and Forwards Finance 100 Prof. Michael R. Roberts Copyright © Michael R. Roberts 1 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 Copyright © Michael R. Roberts 2 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 Copyright © Michael R. Roberts 3 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 Copyright © Michael R. Roberts 4 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 Copyright © Michael R. Roberts 5 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.” Copyright © Michael R. Roberts 6 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 Copyright © Michael R. Roberts 7 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 Copyright © Michael R. Roberts 8 4 4 What is the Delivery Price? Example z Consider the replicating the payoff of the forward contract: z No arbitrage implies: Copyright © Michael R. Roberts 9 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. Copyright © Michael R. Roberts 10 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: Copyright © Michael R. Roberts 11 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 Copyright © Michael R. Roberts 12 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 ? Copyright © Michael R. Roberts 13 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? Copyright © Michael R. Roberts 14 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 Copyright © Michael R. Roberts 15 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 Copyright © Michael R. Roberts 16 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? Copyright © Michael R. Roberts 17 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 ? Copyright © Michael R. Roberts 18 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. Copyright © Michael R. Roberts 19 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. Copyright © Michael R. Roberts 21 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 ⎦⎥ Copyright © Michael R. Roberts 22 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? Copyright © Michael R. Roberts 23 Commodity Forwards Example (Cont.) z What is the implied delivery price? z Arbitrage table Copyright © Michael R.