Financial Risk Management

1. Financial Risk Management Session 2 Forward Contracts and Futures Contracts

2. Hedging with FX forwards • Major corporates attempt completely hedge (cover) their FX exposure. • All divisions involved in foreign trade usually hedge FX risk under the centralized control of HQ or regional office. • Hedging conducted on quarterly basis many times. • Example, four quarters: April-June, July-Sept., Oct.-Dec., Jan.-March N. Takezawa (ICU) Spring 2001

3. Assuming shipment in the period Oct-Dec. • 1)June-Aug.: June some hedging takes place. End of July official shipment figures are sent in. End of Aug.-internal FX rate is set by averaging forward rates. • 2) Sept. Pricing is determined based on the internal rate set in the previous quarter. N. Takezawa (ICU) Spring 2001

4. July-Sept Oct-Dec April-June Shipment FX forward N. Takezawa (ICU) Spring 2001

5. Organized Exchange (取引所): Futures, some options, options on futures • Bank (inter-bank、店頭取引): forward FX contracts, forward rate agreement (FRA), options, swaps, structured products. • Structured products=A financial instrument designed to meet the needs of one or a small number of investors. They are often a combination of swaps, forwards, options (packaged to provide customized payout profile). N. Takezawa (ICU) Spring 2001

6. Investment Banks/Securities Front Office Trading, Sales, Marketing (research, data gathering, etc.) Middle Office Book Keeping, Profit/Loss Risk Management Back Office Legal, Computer Support (IT), HR N. Takezawa (ICU) Spring 2001

7. Client Corporate Front Office Marketing/Sales Front Office Trading (Quote, Hedge out Risk) N. Takezawa (ICU) Spring 2001

8. inter-bank flexibility in contract terms No price movement restriction Delivery of good at settlement organized exchange standardized contracts Could have limits Daily Marking to Market （毎日値洗い） Forward vs Futures Contracts N. Takezawa (ICU) Spring 2001

9. Notes on Futures • Selling futures: taking a short position • Buying futures: taking a long position • A future position is the individual’s total contracts purchased less contracts sold. Net positions can be long or short. • Total of long positions is open interest. • Futures price equals spot price at maturity. N. Takezawa (ICU) Spring 2001

10. Standardized Contracts • Amount of the underlying asset is fixed per contract. • wheat (20 metric tons, Winnipeg), gold (100 troy oz, NY), soybeans (5000 bu, CBOT), etc. • Maturity or delivery date fixed: March, June, September, December most often. • Relative to today – April 2001: June contract is a nearby contract. September is a deferred contract. N. Takezawa (ICU) Spring 2001

11. Futures Trading Pit Each pit is usually for a particular commodity or financial instrument Deferred Nearby Contracts PHONE DESK Pit is divided into slices according to maturity date or upper steps for nearby and inside for deferred. N. Takezawa (ICU) Spring 2001

12. Cost of Carry • Storage costs • insurance costs • transportation costs • financing costs N. Takezawa (ICU) Spring 2001

13. Cash and Carry Cash　(現物取引） Futures　（先物取引） t=0 Borrow S @ 10% Sell futures @ F(0,T) Buy gold @ S t=1 Repay loan S with interest Deliver gold Profit = F(0,T) - S(1+cc) F(0,T)=<S(1+cc) to rule out arbitrage　 (裁定取引) N. Takezawa (ICU) Spring 2001

14. Reverse Cash and Carry Cash Futures t=0 Short Sell gold @ S Buy futures @ F(0,T) Lend S @ 10% t=1 Collect S(1+0.1) Receive gold Deliver gold (from futures) and repay Profit = S(1+cc)- F(0,T) F(0,T)>=S(1+cc) to rule out arbitrage　(裁定取引) N. Takezawa (ICU) Spring 2001

15. Futures Price From the cash and carry & reverse cash and carry conditions, we arrive at the following conclusion: F(0,T)=S (1+cc) Notice, this is similar to the covered interest rate parity condition we discussed last week. N. Takezawa (ICU) Spring 2001

16. Convenience yield r is interest rate u is storage costs y is convenience yield convenience yield reflects market expectations of demand-supply of the underlying asset. If restricted supply(supply shortage) is expected, then the convenience yield is higher. In other words, there is greater value in holding the underlying asset - a premium for holding the commodity. N. Takezawa (ICU) Spring 2001

17. Margins　(証拠金制度) • Initial margin　(当初証拠金): The minimum initial deposit required by the futures exchange when a contract is opened. • Maintenance margin: The minimum equity (cash) a futures exchange requires in the customers account to continue trading futures. If the equity position falls below this margin, then funds must be added to bring the equity level up to the initial level.　This additional funding is referred to as variation margin (変動証拠金). N. Takezawa (ICU) Spring 2001

18. Cont. • The margin amounts differ according to contract (underlying asset), exchange and type of trade. N. Takezawa (ICU) Spring 2001

19. initial maintenance time N. Takezawa (ICU) Spring 2001

20. Margin requirements International Money Market (IMM): Chicago Mercantile Exchange(CME) yen contract, initial margin is US$2700, maintenance margin is US$2000, Face value is 12,500,000 yen Lower margin for hedging purposes, day trades, and spread trades Price is in (US$/yen): gain/loss in long position is determined by looking at the settlement price. P(1)-P(0)x face = gain/loss at t=1 P(2)-P(1)x face= gain/loss at t=2 so on…. N. Takezawa (ICU) Spring 2001

21. Simple hedging example • An airline company needs ten million gallons of jet fuel in three months. Since fuel price variability is expected to be substantial, the airline decides to hedge by using heating oil futures contracts. If each heating oil futures contract is for 42,000 gallons, how many contracts should the airline purchase? N. Takezawa (ICU) Spring 2001

22. Number contracts=ten million gallons divided by 42,000 gallons. • Note, the underlying asset price and futures price do not move together perfectly. This is especially the case here since we want to hedge the jet fuel position with heating fuel futures. Need to make adjustments=hedge ratio. N. Takezawa (ICU) Spring 2001

23. Minimum Variance Hedge Ratio(for your reference) • P is the portfolio value of holding long position in the underlying (cash market) asset and short the futures contract. • h is the number short futures contracts. • Obtain the variance (total risk) of P. • Minimize the risk (variance) by changing the number contracts you hold, h. • The optimal h, is the number contracts which minimizes the total risk of the portfolio. N. Takezawa (ICU) Spring 2001

24. N. Takezawa (ICU) Spring 2001

25. Even if the correlation is one, the min. variance hedge ratio is not necessarily equal to one. The hedge ratio still depends on the relative volatility of the underlying vs Futures. N. Takezawa (ICU) Spring 2001

26. notation • Covariance (共分散)　sij • Variance　(分散) s2 • Standard deviation　(標準偏差) s • Correlation　 (相関係数) r N. Takezawa (ICU) Spring 2001

27. Backwardation • When the nearby futures price exceeds the distant (deferred) futures price. • Or, when the spot price exceeds the futures price. price Contract maturity N. Takezawa (ICU) Spring 2001

28. Normal Backwardation and Contango • Normal backwardation: futures prices tend to rise over the life of the contract. • Contango: futures prices tend to fall over the life of the contract. N. Takezawa (ICU) Spring 2001

29. Price Contango Expected Future Spot Price Normal backwardation Time N. Takezawa (ICU) Spring 2001