Derivatives and Hedging

Transcription

1 Derivatives and Hedging Corporate Finance Ernst Maug University of Mannheim Tel: +49 (621)

2 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

3 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

4 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

5 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

6 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= Identical portfolios must have the same return: - F= /21

7 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= Identical portfolios must have same return: - F+ 2= , hence F= /21

8 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

9 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

10 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 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

11 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

12 Commodity futures: Convenience yield Convenience yield per barrel of Brent oil from 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/ /21

13 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) = /21

14 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

15 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

16 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

17 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

18 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

19 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

20 Margins requirements and marking to market (Cont.) Date Futures price Gain (loss) Cumulative gain (loss) Margin balance 500 3,000 Jan (600) (600) 2,400 Jan (500) 2,500 Margin call Jan (700) (1,200) 1,800 1,200 Jan (1,000) 3,200 Jan (900) 3,300 Jan (1,700) (2,600) 1,600 1,400 Jan (2,500) 3,100 Jan (100) (2,600) 3,000 20/21

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 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