Derivatives and Hedging Corporate Finance Ernst Maug University of Mannheim http://cf.bwl.uni-mannheim.de maug@cf.bwl.uni-mannheim.de Tel: +49 (621) 181-1952
Overview Introduction - The use of hedge instruments Forward and futures contracts - Valuation - Arbitrage - Hedging Major categories of forwards and futures - Commodity risk - Foreign exchange risk - Stock market risk 2/21
Applications for hedge instruments A mining company expects to produce 1000 ounces of gold 2 years from now if it invests in a new mine: - Avoid that the loan for financing the investment cannot be repaid because the gold price moved 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 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 3/21
Forward contracts A forward contract is a contract made today for future delivery of an asset at a prespecified price. - no money or assets change hands prior to maturity. - Forwards are traded in the over-the-counter market. 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. 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 4/21
Forwards on securities The case of a security without income 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) Example: Only if you purchase it now, not if you buy forward - Share trades today at 25 - Pays no dividends during the next three months - The risk free rate for 3 months is 6% p. a. with quarterly compounding 5/21
What is the forward price? Consider the following two strategies: - Buy one share for 25 - Sell the share forward in three months for the forward price F What are the cash flows: - Today: Zero from forward, - 25 from buying share - 3 Months: from selling share forward: F - value of share + from owning share: value of share = F - Riskless investment of 25 yields F Investing 25 at riskless rate gives: - 25*1.015= 25.375 Identical portfolios must have the same return: - F= 25.375 6/21
Forwards on securities Now suppose the share pays a dividend at the end of three months of 2 What are the cash flows now: - Today: Zero from forward, - 25 from buying share - 3 Months: from selling share forward: F - value of share + from owning share: value of share + 2 dividend = F+ 2 - Riskless investment of 25 yields F+ 2 Investing 25 at riskless rate gives: - 25*1.015= 25.375 Identical portfolios must have same return: - F+ 2= 25.375, hence F= 23.375 7/21
The general formula Portfolio I: - Buy stock at S 0, Sell share forward at F Portfolio II: - Invest S 0 at risk free rate Cash flows from this are: Today 3 Months Portfolio I Stock -S 0 S T +D T Forward 0 F- S T Net -S 0 F+D T Portfolio II -S 0 S 0 (1+r T ) Hence we obtain: F= S 0 (1+r T )-D T 8/21
Forward price and arbitrage Case 1: F< S 0 (1+r T )-D T Then portfolio I has a lower payoff than portfolio II: - Buy portfolio II, (short) sell portfolio I Invest in bonds (short) sell stock buy stock forward at F Today Realize arbitrage profit -F+ S 0 (1+r T )-D T >0 3 Months Sell Stock S 0 -(S T +D T ) Buy Forward 0 S T -F Buy Bond -S 0 +S 0 (1+r) Total 0 -F-D T +S 0 (1+r) 9/21
The standard formula Previous formula unusual. - Assume you receive dividend up front: D 0 DT 1 r T - Rewrite dividend as dividend yield d: D d * S 0 0 - Then the previous formula can be rewritten: F S (1 r ) D 0 0 T S 1 d (1 r ) T T - The conventional way to express this is (use continuous compounding): F S e 0 ( r d ) T 10/21
Commodity forwards 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 - Summarized as cost of carry, usually written as constant annual percentage q of initial value. - Sometimes possession of commodity also provides benefits: Demand fluctuations Supply shortages (Oil) - Summarized as convenience yield, usually written as constant annual percentage y of initial value. 11/21
Commodity futures: Convenience yield Convenience yield per barrel of Brent oil from 1991-2006 in $US. During the same time period the price per barrel of fluctuated between $15 and $64. Convenience yield for Brent crude oil, from Knetsch (2006), Forecasting the price of crude oil via convenience yield predictions, Deutsche Bundesbank Discussion Paper 12/2006. 12/21
Example: Cost of carry You are considering taking physical delivery of live cattle in order to execute a commodity futures arbitrage. The cost of carry is assessed at 4% relative to the current spot price of 100. If the contract has 2 months to maturity, the up-front cost of storing and feeding the cattle is: - CC = S 0 ((1+q) T -1) = 100 ((1+0.04) 2/12-1) = 0.656 13/21
Hedging commodity risk Example: Wheat farmer - grows wheat in January - pays 20,000 for plant and equipment on January 1 - expects to harvest 10,000 bushels of wheat in September - hires labor for harvest costing 2,000 - can sell wheat forward at 3.50 per bushel by September 30 - can invest money in bank account that yields 6%, compounding monthly - can rent the land for 5,000 if not used by the farmer, rent payable in September 14/21
Hedging commodity risk Questions: - what is the net income in January Euros from this? - what are the terms of the forward contract that makes this riskless? 15/21
Commodity forwards example How do you set up the hedge: - sell 10,000 bushels forward per September 30 - receive 35,000 on September 30, risk free Calculate net income: - Receive 35,000 in September - Deduct 2,000 harvesting costs and 5,000 rent - Generate incremental cash flow of 28,000 - Present value of this is 28,000/1.005^9= 26,771 - Deduct costs today ( 20,000) to get: net income = 6,771 16/21
Futures contracts - 1 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. - The daily cash flows between buyer and seller are equal to the change in the futures price. Futures and forward prices must be identical if interest rates are constant. - Can use results on forward for futures - Hedging a little different 17/21
Futures contracts - 2 Futures contracts allow investors to: - Hedge - Speculate Futures contracts are available on commodities and financial assets: - Agricultural products and livestock - Metals and petroleum - Interest rates - Currencies - Stock market indices 18/21
Margin requirements and marking to market Margin account - initial margin with the broker - maintenance margin and margin call - adjust for gains or losses - marking to market Example: January 1, 2006, we buy a Gold futures contract. Contract size is 100 ounces. Current futures price is 500 per ounce. Assume initial margin is 3,000 per contract and maintenance margin is 2,000 per contract. 19/21
Margins requirements and marking to market (Cont.) Date Futures price Gain (loss) Cumulative gain (loss) Margin balance 500 3,000 Jan. 1 494 (600) (600) 2,400 Jan. 2 495 100 (500) 2,500 Margin call Jan. 3 488 (700) (1,200) 1,800 1,200 Jan. 4 490 200 (1,000) 3,200 Jan. 5 491 100 (900) 3,300 Jan. 6 474 (1,700) (2,600) 1,600 1,400 Jan. 7 475 100 (2,500) 3,100 Jan. 8 474 (100) (2,600) 3,000 20/21
Metallgesellschaft Corp. The implications of marking to market Possesses substantial refining capacity Marketing strategy: - sell heating oil at guaranteed prices up to 10 years short heating oil forwards Risk management strategy - buy crude oil futures on NY Mercantile Exchange September 1993 - oil price drops sharply - margin calls on futures, no offsetting gains realized on forwards Problems - overhedged (too many futures relative to forwards) - other risks: imperfect hedge, marking to market, credit risk 21/21