Chapter 14 Future Prices Objective Copyright Prentice Hall

Chapter 14: Future Prices Objective Copyright © Prentice Hall Inc. 1999. Author: Nick Bagley • How to price forward and futures • Storage of commodities • Cost of carry • Understanding financial 1 futures

Chapter 14: Contents 1 Distinction Between Forward & Futures Contracts 2 The Economic Function of Futures Markets 3 The Role of Speculators 4 Relationship Between Commodity Spot & Futures Prices 5 Extracting Information from Commodity Futures Prices 6 Spot-Futures Price Parity for Gold 8 The “Implied” Risk-Free Rate 9 The Forward Price is not a Forecast of the Spot Price 10 Forward-Spot Parity with Cash Payouts 11 “Implied” Dividends 12 The Foreign Exchange Parity Relation 13 The Role of Expectations in Determining Exchange Rates 7 Financial Futures 2

14. 1 Distinction Between Forward & Futures Contracts • parties agree to exchange some item in the future at a delivery price specified now • the forward price is defined as the delivery price which makes the current market value of the contract zero • no money is paid in the present by either party to the other – the face value of the contract is the quantity of the item specified in the contract multiplied by the forward price – the party who agrees to buy the specified takes the long position, and the party who agrees to sell the item takes the short position 3

Terms – Open, High, Low, Settle, Change, Lifetime high, Lifetime low, Open interest – Mark-to-market – Margin requirement – Margin call 4

Characteristics of Futures • Futures are: – standard contracts – immune from the credit worthiness of buyer and seller because • exchange stands between traders • contracts marked to market daily • margin requirements 5

14. 2 The Economic Function of Futures Markets • The futures markets facilitate the reallocation of exposure to commodity price risk among market participants • But: 6

– by providing a means to hedge the price risk associated with storing a commodity, futures contracts make it possible to separate the decision of whether to physically store a commodity from the decision to have financial exposure to price changes 7

The Economic Function of Futures Markets (Continued) • A distributor, j, may hedge by – selling the commodity on the spot market now at a price S – selling short a futures contract at a price F and deliver the commodity at a specified time in the future • there will be a carrying cost Cj for distributor j, and she will store only if Cj < F - S 8

The Economic Function of Futures Markets (Continued) • The difference between the futures price and the spot price, F - S, is called the spread, and governs how much wheat will be stored, and by whom 9

The Economic Function of Futures Markets (Continued) • Suppose the commodity is wheat, and next year’s crop is expected to be much higher than average, then futures prices may be lower than the spot, (the spread may be negative, ) nobody will store wheat 10

The Economic Function of Futures Markets (Continued) • The existence of the futures market for wheat conveys information to all producers, distributors, and consumers; and this eliminates the necessity for market participants to gather and process information in order to forecast the future spot price 11

14. 3 The Role of Speculators – Hedger • anyone using a futures market to reduce risk – Speculator • anyone who takes a position in the market (increasing his risk) in order to profit from his forecasts of future spot prices – (A producer, distributor or consumer who chooses not to hedge her risk may be considered to be a speculator) 12

The Role of Speculators: Example – Suppose that the current 1 -month futures in wheat is $1. 5/bushel, and a farming family with stored wheat believes that the price will rise to $2. 00 – Not hedging the stored wheat results in the family being exposed to the vagrancies of the wheat market, and it becomes, in effect, a wheat speculator (just like their cobbler cousins who are long wheat futures) 13

The Role of Speculators: Gamblers and Wasters • Critic: “Speculators have no social value” • Answer: – Successful speculators make the market • more efficient as an information resource • provide liquidity when it is needed, which is when producers, distributors, and consumers can’t or won’t hedge • more efficient by contributing towards recovering the fixed costs of providing a futures exchange 14

14. 4 Relationship Between Commodity Spot and Futures Prices • Arbitrageurs place an upper bound on futures prices by locking in a sure profit on futures prices if the spread between the futures price and spot price becomes greater than the cost of carry, F - S £ C – the cost of carry varies as a function of time and warehousing organization 15

14. 5 Extracting Information from Commodity Futures Prices • Case 1 If (Futures Price < Current Spot) – Then the futures price is an indicator of the expected future spot price • The futures price is a biased estimate because there are risk premiums and discounts associated with holding the commodity 16

Extracting Information from Commodity Futures Prices • Case 2 If (Futures Price > Current Spot) – Then the futures price is not an indicator of the expected future spot price • The spread cannot exceed the cost of carry 17

14. 6 Spot-Futures Price Parity for Gold • In the case of gold futures, arbitrage establishes an upper- and lower-bound on the spread between the futures and spot prices, resulting in the spotfutures price-parity relationship 18

Spot-Futures Price Parity for Gold • There are two ways to invest in gold • buy an ounce of gold at S 0, store it for a year at a storage cost of $h/$S 0, and sell it for S 1 • invest S 0 in a 1 -year T-bill with return rf, and purchase a 1 -ounce of gold forward, F, for delivery in 1 -year 19

Spot-Futures Price Parity for Gold • A contract with life T: • This is not a causal relationship, but the forward and current spot jointly determine the market • If we know one, then the rule of one market determines that we know the other 20

Spot-Futures Price Parity for Gold • The following diagram shows how to create synthetic gold, T-bills, or gold forward contract from the other two • All prices are predetermined, – except the price of the one year of the forward and the price in one year of the gold, but the difference between them is equal to the known financing and storage costs 21

Rule of One Price: No Arbitrage Profits Purchase Actual Au Sell T-Bill Sell Actual Au Settle T-Bill Sell Au Forward Settle Au Forward • Au = Gold 22

Implied Cost of Carry • As a consequence of the forward-spot price parity relationship, you can’t extract information about the expected future spot price of gold (unlike one wheat case) from futures prices • The implied cost of carry (per $spot) is h = (F - S 0)/S 0 - r f 23

14. 7 Financial Futures • We now focus on financial futures – standardized contracts for future delivery of stocks, bonds, indices, and foreign currency – they have no intrinsic value, but represent claims on future cash flows – they have very low storage costs – settlement is usually in cash 24

Financial Futures • With no storage cost, the relationship between the forward and the spot is • Any deviation from this will result in an arbitrage opportunity 25

Financial Futures: Example • Consider shares in Bablonics, Inc, trading at $50 each, ($5, 000 for a round lot); assume 6 -month T-bills yield 6% (compounded semiannually) 26

Bablonics, Inc (Continued) • 1 Purchase one round lot of stock at spot – This results in a negative cash flow today of $5, 000 (out), and will generate a cash flow of 100*Spot 6 m (in) in six months 27

Bablonics, Inc (Continued) • 2 Cover today’s negative cash flow by selling short $5, 000 worth of 6 -month Tbills with a face value of 5000 (1+ 0. 06/2)^0. 5 = $5, 150 • The cash flow today is $5, 000 (in), and the cash flow in six months time will be $5, 150 (out) 28

Bablonics, Inc (Continued) • 3 Cover the risk exposure by selling 100 shares forward at the equilibrium price of 5000*(1+0. 06/2)^0. 5 = $5, 150 – There is no cash flow today, but the value of this forward contract in six months time will be $(Spot 6 m - 5, 150) 29

Bablonics, Inc (Continued) • -$5, 000 (long stock) + $5, 000 (short bond) + $0 (short forward) = $0 30

Bablonics, Inc (Continued) • Cash Flow in 6 -Months + $Spot 6 m (settle long stock) - $5, 150 (settle short bond) +($5, 150 - $Spot 6 m) (settle forward) = $0 31

Bablonics, Inc (Conclusion) • If your net risk-free investment was zero, – and you receive nothing • that is what you should expect – and you expect to: • received positive value with no risk, then the rule of one price has been violated • lose value with no risk, then reverse the direction of all transactions, and again you profit with no risk 32

14. 8 The “Implied” Risk-Free Rate • Rearranging the formula, the implied interest rate on a forward given the spot is • This is reminiscent of the formula for the interest rate on a discount bond 33

14. 9 The Forward Price is not a Forecast of the Spot Price • Following the diagrams in Chapter 12 we might suppose that the expected price of a stock is • If this is indeed correct, then the forward price is not an indicator of the expected spot price at the maturity of the forward 34

The Forward Price is not a Forecast of the Spot Price • The forward price is obtained without risk from the current spot and riskless bond • The spot value at a future date is obtained by investing in the security and accepting (market) risk, and this risk must be rewarded 35

14. 10 Forward-Spot Parity with Cash Payouts • So far we have assumed that there is no dividend – Now suppose that everybody expects an uncertain dividend in 1 year of D – It is not possible to replicate D because of this uncertainty – We will treat D as if it were known with certainty, and only deal with 1 -year forwards 36

Forward-Spot Parity with Cash Payouts • The S 0 - F relationship becomes • Note: (forward price > the spot price) if (D < r S) • Because D is not known with certainty, this is a quasi-arbitrage situation 37

14. 11 “Implied” Dividends • From the last slide, we may obtain the implied dividend 38

14. 12 The Foreign Exchange Parity Relation • Recall from Chapter 2 the following diagram: 39

Exchange Rate Example Time Japan 15000 ¥ (Borrowed) U. K. • 150 ¥/£ 3% ¥/¥ (direct) 3% ¥/£/£/¥ 15450 ¥ (Repaid) £ 100 (Invested) 9%£/£ Forward ¥/£ £ 109 (Matures)

The Foreign Exchange Parity Relation • We used the diagram to show that • Recall there is a time structure of interest, and the appropriate risk free rate should be used 41

14. 13 The Role of Expectations in Determining Exchange Rates – Consider a world in which there are two countries, Domestic & Foreign, and conditions are such in each country that the yield curves are flat, with yields of 5% and 10% respectively – Further assume that the exchange rate is 1 today – The 1 -year forward is 1*1. 05/1. 10=0. 9545 42

The Role of Expectations in Determining Exchange Rates – If the interest rate in Foreign is higher than in Domestic, one explanation may be that the rate of inflation is higher. – Assume no taxes, and the interest rate difference is the result inflation being 5% and 10% respectively – Then the price dynamics of both countries will result in an exchange rate of 0. 9545 next year, which is also the forward rate 43

The Role of Expectations in Determining Exchange Rates – In real life, things are not so simple, but several mechanisms may be postulated that support the expectations hypothesis – International investor confidence, and their forecasts of inflation, place price pressure on both spot and forward exchange rates through the international bond market 44