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Financial Derivatives 4 Forward pricing: Some prelims Two ways to own an art piece at time T:
Buy it today
Go long a forward contract that expires at T
Both ways should cost the same today.
Assuming no benefits<br>
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Financial Derivatives 5 Forward pricing 1. 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%)<br>
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Financial Derivatives 6 Forward pricing 3. 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%.<br>
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Financial Derivatives 7 Some relationships F = forward price
S = spot price
r = int. rate to fwd date
t = no. of days to fwd expiry So an asset that pays no income<br>
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Financial Derivatives 8 F = forward price
S = spot price
r = int. rate expressed as % pa
t = no. of days to fwd expiry
q = asset income expressed as % pa an asset that pays constant income Some relationships<br>
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Financial Derivatives 9 an asset that pays lumpy income F = forward price
S = spot price
r = int. rate expressed as % pa
t = no. of days to fwd expiry<br>
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Financial Derivatives 10 Our learning Replication
Fair price
Interest effect
Income effect The relationship between Forwards and spot
Fwd. Price = spot price + cost of carry Any violations??? interest paid – income recd.<br>
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Financial Derivatives 11 Violations Price a 4-month forward contract on a non-dividend paying stock with following data:
Stock price = Rs. 130
interest rate = 6%
The theoretical price of the forward contract on a financial asset that pays no income:
F0,t = S0ert<br>
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Financial Derivatives 12 Cash and carry arbitrage This gives us a forward price of Rs. 132.6
What 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!<br>
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Financial Derivatives 13 Cash and carry arbitrage 4 months later:
Deliver stock under forward contract at Rs. 135
Repay loan of Rs.132.6
Keep the profit of Rs. 2.4 (135 -132.6)<br>
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Financial Derivatives 14 Reverse cash and carry arbitrage What if the fwd is available at 129.95 rather 132.63?
See whether you arrive at a minimum arbitrage profit of Rs. 2.65.<br>
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Financial Derivatives 15 Cash and carry arbitrage Today FWD expiry day<br>
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Financial Derivatives 16 Reverse cash and carry Today FWD expiry day<br>
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Financial Derivatives 17 Arbitrage Steps Compute the fair forward price that can be replicated in the cash market ( Asset + Borrowing)
Compare the fair forward price with market price of the forward
IF
FWDm < FWDF
Market price of fwd < fair fwd price -------- Reverse Cash & Carry Arb
FWDm > FWDF
Market price of fwd > fair fwd price -------- Cash & Carry Arb
Put up the trades as mentioned in the earlier slides<br>
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Financial Derivatives 18 Fwd Pricing Philosophy Preclude Arb Opps<br>
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Financial Derivatives 19 Is 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.<br>
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Financial Derivatives 20 Value of a forward prior to maturity Let 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?<br>
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Financial Derivatives 21 But in practice Absence of perfect markets
Differential lending and borrowing rates
Restrictions on short sales
The net effect of all these complexities is that there will be a band around fair value within which arbitrage will not be profitable<br>
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Financial Derivatives 22 CC, RCC with imperfections 6. 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?<br>
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Financial Derivatives 23 In summary The net effect of all these complexities is that there will be a band around fair value within which arbitrage will not be profitable CC Arb RCC Arb<br>
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Financial Derivatives 24 Value of a Fwd Contract If 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.<br>
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Financial Derivatives 25 Example Suppose 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<br>
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Financial Derivatives 26 Example 8. 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?<br>
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Financial Derivatives 27 Value 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?<br>
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Financial Derivatives 28 Value 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?<br>
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Financial Derivatives 29 Forwards and Futures So far we had not distinguished between futures pricing and fwd pricing
Do futures prices equal fwd prices?
Consider the case of copper futures traded on LME<br>
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Forward Price at expiry Distinction between Price and Value<br>
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Assume Ft = 403 and St = 400 what happens?<br>
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Financial Derivatives Legal aspects... Governed by SC(R) Act, 1956, the SEBI Act, various rules, regulations and bye laws of the concerned exchanges<br>
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Financial Derivatives Legal framework SCRA, 1956 Act does not include derivatives as securities
Indian Contracts Act 1872<br>
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Financial Derivatives Legal framework contd… Securities Laws (amendment) Act, 1999
The derivatives formally defined under the said Act, 1999 include
A security from a debt market, share, loan, risk instrument or contract for differences or any other form of security
A contract which derives its value from the prices or index of prices underlying securities And….<br>
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Financial Derivatives The 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…<br>
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Financial Derivatives March 1, 2000 Notification
The contracts for sale and purchase of Gsecs, securities related to gold, money market securities and debt market related securities will be regulated by RBI
Such securities if traded on stock exchanges will be regulated by SEBI Legal framework contd…<br>
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Financial Derivatives Provisions 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.<br>
