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Lecture 10

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Purchase of shares April: Purchase 500 shares for $120-$60,000 May: Receive dividend +500 July: Sell 500 shares for $100 per share +50,000 Net profit = -$9,500 Short Sale of shares April: Borrow 500 shares and sell for $120+60,000 May: Pay dividend -$500 July: Buy 500 shares for $100 per share -$50,000 Replace borrowed shares to close short position. Net profit = + 9,500

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Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 Futures Price Notation S0:S0:Spot price today F0:F0:Futures or forward price today T:T:Time until delivery date r:r:Risk-free interest rate for maturity T

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The price of a non interest bearing asset futures contract. The price is merely the future value of the spot price of the asset.

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Example IBM stock is selling for $68 per share. The zero coupon interest rate is 4.5%. What is the likely price of the 6 month futures contract?

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Example - continued If the actual price of the IBM futures contract is selling for $70, what is the arbitrage transactions? NOW Borrow $68 at 4.5% for 6 months Buy one share of stock Short a futures contract at $70 Month 6Profit Sell stock for $ Repay loan at $ $0.45

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Example - continued If the actual price of the IBM futures contract is selling for $65, what is the arbitrage transactions? NOW Short 1 share at $68 Invest $68 for 6 months at 4.5% Long a futures contract at $65 Month 6Profit Buy stock for $ Receive 68 x e.5x $4.55

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The price of a non interest bearing asset futures contract. The price is merely the future value of the spot price of the asset, less dividends paid. I = present value of dividends

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Example IBM stock is selling for $68 per share. The zero coupon interest rate is 4.5%. It pays $.75 in dividends in 3 and 6 months. What is the likely price of the 6 month futures contract?

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If an asset provides a known % yield, instead of a specific cash yield, the formula can be modified to remove the yield. q = the known continuous compounded yield

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Example A stock index is selling for $500. The zero coupon interest rate is 4.5% and the index is known to produce a continuously compounded dividend yield of 2.0%. What is the likely price of the 6 month futures contract?

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The profit (or value) from a properly priced futures contract can be calculated from the current spot price and the original price as follows, where K is the delivery price in the contract (this should have been the original futures price. Long Contract ValueShort Contract Value

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Example IBM stock is selling for $71 per share. The zero coupon interest rate is 4.5%. What is the likely value of the 6 month futures contract, if it only has 3 months remaining? Recall the original futures price was

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Commodities require storage Storage costs money. Storage can be charged as either a constant yield or a set amount. The futures price of a commodity can be modified to incorporate both, as in a dividend yield. Futures price given constant yield storage cost Futures price given set price storage cost u =continuously compounded cost of storage, listed as a percentage of the asset price

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Example The spot price of copper is $3.60 per pound. The 6 month cost to store copper is $0.10 per pound. What is the price of a 6 month futures contract on copper given a risk free interest rate of 3.5%?

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Example The spot price of copper is $3.60 per pound. The annual cost to store copper is quoted as a continuously compounded yield of 0.5%. What is the price of a 6 month futures contract on copper given a risk free interest rate of 3.5%?

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Shortages in an asset may cause a lower than expected futures price. This lower price is the result of a reduction in the interest rate in the futures equation. The reduction is called the convenience yield or y.

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Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull The Cost of Carry (Page 117) The cost of carry, c, is the storage cost plus the interest costs less the income earned For an investment asset F 0 = S 0 e cT For a consumption asset F 0 S 0 e cT The convenience yield on the consumption asset, y, is defined so that F 0 = S 0 e (c–y )T c can be thought of as the difference between the borrowing rate and the income earned on the asset. C = r - q

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