2 Forward pricing Some prelims Forward contracts on assets that Pay no income Pay a lumpy income Pays continuously Financial Derivatives 3 Forward pricing Some prelims Pay no income Easiest type of contract to value ID: 1008186
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1. Forward/Futures Pricing
2. Financial Derivatives2Forward pricing: Some prelimsForward contracts on assets thatPay no incomePay a lumpy incomePays continuously
3. Financial Derivatives3Forward pricing: Some prelimsPay no incomeEasiest type of contract to value:Underlying asset has no intermediate cash flows.
4. Financial Derivatives4Forward pricing: Some prelimsTwo ways to own an art piece at time T:Buy it todayGo long a forward contract that expires at TBoth ways should cost the same today.Assuming no benefits
5. Financial Derivatives5Forward pricing1. You want to present your spouse a painting on his/her birthday 1 yr from now. Suppose an art dealer offers to sell you a painting today for INR 100,000 or INR 120,000 in one year’s time. Would you buy it today or in one year?? (assume your banker will pays/finance it at 10%)2. Suppose an art dealer offers to sell you a painting today for INR 100,000 or INR 108,000 in one year’s time. Would you buy it today or in one year?? (assume your banker will pays/finance it at 10%)
6. Financial Derivatives6Forward pricing3. Now suppose you have an opportunity to buy a property worth INR 1Mn now or at INR 1.1 Mn after one year. The property can be leased at INR 220,000 pa (payable at the end of the year). Our banker will finance at 15%.
7. Financial Derivatives7Some relationshipsF = forward priceS = spot pricer = int. rate to fwd datet = no. of days to fwd expirySo an asset that pays no income
8. Financial Derivatives8F = forward priceS = spot pricer = int. rate expressed as % pat = no. of days to fwd expiryq = asset income expressed as % paan asset that pays constant incomeSome relationships
9. Financial Derivatives9an asset that pays lumpy incomeF = forward priceS = spot pricer = int. rate expressed as % pat = no. of days to fwd expiry
10. Financial Derivatives10Our learningReplicationFair priceInterest effectIncome effectThe relationship between Forwards and spotFwd. Price = spot price + cost of carryAny violations??? interest paid – income recd.
11. Financial Derivatives11ViolationsPrice a 4-month forward contract on a non-dividend paying stock with following data: Stock price = Rs. 130interest rate = 6%The theoretical price of the forward contract on a financial asset that pays no income:F0,t = S0ert
12. Financial Derivatives12Cash and carry arbitrageThis gives us a forward price of Rs. 132.6What if F0,4/12 = Rs. 135 rather than Rs. 132.6? Free lunch!!Today:Borrow 130 at a rate of 6% (will owe Rs. 132.6 in 4 months).Buy stock for Rs. 130.Short a 4-month forward contract at Rs. 135.WAIT 4 MONTHS!
13. Financial Derivatives13Cash and carry arbitrage4 months later:Deliver stock under forward contract at Rs. 135Repay loan of Rs.132.6Keep the profit of Rs. 2.4 (135 -132.6)
14. Financial Derivatives14Reverse cash and carry arbitrageWhat if the fwd is available at 129.95 rather 132.63?See whether you arrive at a minimum arbitrage profit of Rs. 2.65.
15. Financial Derivatives15Cash and carry arbitrage1Borrow money to buy shares2Buy the shares3Simultaneously sell forward contract4Hold shares5Deliver shares as fulfillment of fwd. obligation and collect money = Fwd price6Repay the loan along with interestTodayFWD expiry day
16. Financial Derivatives16Reverse cash and carry1Sell shares short2Lend proceeds from sale3Simultaneously buy the forward contract4Wait until expiry5Encash the deposit, 6Pay the money under fwd. take delivery of shares from fwd counterparty7And deliver these shares against the short saleTodayFWD expiry day
17. Financial Derivatives17Arbitrage StepsCompute the fair forward price that can be replicated in the cash market ( Asset + Borrowing)Compare the fair forward price with market price of the forwardIFFWDm < FWDF Market price of fwd < fair fwd price -------- Reverse Cash & Carry ArbFWDm > FWDF Market price of fwd > fair fwd price -------- Cash & Carry ArbPut up the trades as mentioned in the earlier slides
18. Financial Derivatives18Fwd Pricing PhilosophyPreclude Arb Opps
19. Financial Derivatives19Is there an Arb oppty?4. Spot gold sells for $600/oz. You can risklessly borrow or lend any amount of money at an annual rate of 10%. What is the forward price of gold that calls for delivery of 100oz. of gold 5 months from today? Suppose that F = $627/oz. Explain how you would arbitrage.5. Spot gold sells for $600/oz. You can risklessly borrow or lend any amount of money at an annual rate of 10%. What is the forward price of gold that calls for delivery of 100oz. of gold 5 months from today? Suppose that F = $622/oz. Explain how you would arbitrage.
20. Financial Derivatives20Value of a forward prior to maturityLet S0 = 400; t = 1; r = 10%.Now consider six months have gone by and the spot rate is 450 other things remaining the same.Is the old forward an asset or liab for the buyer? seller?
21. Financial Derivatives21But in practiceAbsence of perfect marketsDifferential lending and borrowing ratesRestrictions on short salesThe net effect of all these complexities is that there will be a band around fair value within which arbitrage will not be profitable
22. Financial Derivatives22CC, RCC with imperfections6. Assume 1% transaction costs (only in spot market) in Q. No. 4 and determine whether there is an arbitrage opp?7. Assume 50% short-sale proceeds in Q. No. 5 and determine whether there is an arbitrage opp?
23. Financial Derivatives23In summaryThe net effect of all these complexities is that there will be a band around fair value within which arbitrage will not be profitableCC ArbRCC Arb
24. Financial Derivatives24Value of a Fwd ContractIf one already holds a position, valuation means the amount of money one would either have to pay or expect to receive in order to get out of the position.
25. Financial Derivatives25ExampleSuppose you entered in to a fwd contract on Dec 1 2009 to buy Crude oil at $75/bbl on Jan 28, 2010.On Jan 28, 2010 if the spot price of crude oil is $78/bbl your forward contract is worth/value $3/bbl.In other words $3 is the value of contract.At expiry (T) value of the forward is given as:VT = ST - F
26. Financial Derivatives26Example8. Suppose you buy a one-year forward contract at $65. At expiration, the spot price is $73. The risk-free rate is 10 percent. What is the value of the contract at expiration?
27. Financial Derivatives27Value of the Fwd contd..What is the value of the fwd at inception?What is the value of the Fwd at any other point of time prior to expiry?
28. Financial Derivatives28Value of the Fwd contd..9. Suppose you bought a three-month forward contract at $35. One month later, new forward contracts are selling for $40. The risk-free rate is 10 percent. What is the value of your contract?
29. Financial Derivatives29Forwards and FuturesSo far we had not distinguished between futures pricing and fwd pricingDo futures prices equal fwd prices?Consider the case of copper futures traded on LME
30. Forward Price at expiryDistinction between Price and Value
31. Assume Ft = 403 and St = 400 what happens?
32. Legal aspects
33. Financial DerivativesLegal aspects...Governed by SC(R) Act, 1956, the SEBI Act, various rules, regulations and bye laws of the concerned exchanges
34. Financial DerivativesLegal frameworkSCRA, 1956 Act does not include derivatives as securitiesIndian Contracts Act 1872
35. Financial DerivativesLegal framework contd…Securities Laws (amendment) Act, 1999The derivatives formally defined under the said Act, 1999 includeA security from a debt market, share, loan, risk instrument or contract for differences or any other form of securityA contract which derives its value from the prices or index of prices underlying securitiesAnd….
36. Financial DerivativesThe Act also clarified that ‘not with standing in any other law for the time being in force, contracts shall be legal and valid only if such contracts are traded on a recognized exchanges in accordance with the rules and bye laws of stock exchange, thus precluding OTC derivatives”.Legal framework contd…
37. Financial DerivativesMarch 1, 2000 NotificationThe contracts for sale and purchase of Gsecs, securities related to gold, money market securities and debt market related securities will be regulated by RBISuch securities if traded on stock exchanges will be regulated by SEBILegal framework contd…
38. Financial DerivativesProvisions affecting legality of OTC deri..Section 30 of Contracts Act, 1872 which renders all wagering contracts as unenforceable and void.Section 2(aa) of Securities Contract (Regulation) Act, 1956, defining “derivatives” and Section 18A of Securities Contract (Regulation) Act, 1956 which makes only the exchange traded derivatives legal.