Chapter 14: Forward & Futures Prices Objective •How to price forward and futures •Storage of commodities •Cost of carry •Understanding financial Copyright © Prentice Hall Inc 2000 Author: Nick Bagley, bdellaSoft, Inc futures Chapter 14: Contents Distinction Between Forward & Futures Contracts The Economic Function of Futures Markets The Role of Speculators Relationship Between Commodity Spot & Futures Prices Extracting Information from Commodity Futures Prices Spot-Futures Price Parity for Gold Financial Futures The “Implied” Risk-Free Rate 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 Terms – Open, High, Low, Settle, Change, Lifetime high, Lifetime low, Open interest – Mark-to-market – Margin requirement – Margin call 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 Spot-Futures Price Parity for Gold • There are two ways to invest in gold • buy an ounce of gold at S0, store it for a year at a storage cost of $h/$S0, and sell it for S1 • invest S0 in a 1-year T-bill with return rf, and purchase a 1-ounce of gold forward, F, for delivery in 1-year S1 − S S1 − F − h = rAu = rAu ( syn ) = + rf ⇒ F = (1 + rf + h ) S S0 S0 Spot-Futures Price Parity for Gold ( ) T • A contract with life T: F = + r f + h S • 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 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 •Au==Gold Gold 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 - S0)/S0 - r f Financial Futures • With no storage cost, the relationship between the forward and the spot is F S= T (1 + rf ) • Any deviation from this will result in an arbitrage opportunity 14.8 The “Implied” Risk-Free Rate • Rearranging the formula, the implied interest rate on a forward given the spot is T F F − S0 r = − 1; if T = 1, r = S0 S0 • This is reminiscent of the formula for the interest rate on a discount bond 10 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 σ S2 µ s = S0e rf + t t ≠ S0e rf t =F • If this is indeed correct, then the forward price is not an indicator of the expected spot price at the maturity of the forward 11 Forward-Spot Parity with Cash Payouts • The S0 - F relationship becomes D+F S0 = ⇒ F = S + rS − D 1+ r • Note: (forward price > the spot price) if (D < r S) • Because D is not known with certainty, this is a quasi-arbitrage situation 12 14.11 “Implied” Dividends • From the last slide, we may obtain the implied dividend D = (1 + r ) S − F 13 Exchange Rate Example Time Japan 15000 ¥ (Borrowed) U.K •150 ¥/£ 3% ¥/¥ (direct) 3% ¥/£/£/¥ 15450 ¥ 15450 ¥ (Repaid) £100 (Invested) 9%£/£ Forward ¥/£ £109 (Matures) The Foreign Exchange Parity Relation • We used the diagram to show that $ denominated Forward on Yen $ Denominated Spot for Yen = t (1 + r$ ) (1 + rY ) t • Recall there is a time structure of interest, and the appropriate risk free rate should be used 15 [...]...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 σ S2 µ s = S0e rf + t 2 t ≠ S0e rf t =F • If this is indeed correct, then the forward price is not an indicator of the expected spot price at the maturity of the forward 11 Forward- Spot Parity with Cash Payouts... D 1+ r • Note: (forward price > the spot price) if (D < r S) • Because D is not known with certainty, this is a quasi-arbitrage situation 12 14.11 “Implied” Dividends • From the last slide, we may obtain the implied dividend D = (1 + r ) S − F 13 Exchange Rate Example Time Japan 15000 ¥ (Borrowed) U.K •150 ¥/£ 3% ¥/¥ (direct) 3% ¥/£/£/¥ 15450 ¥ 15450 ¥ (Repaid) £100 (Invested) 9%£/£ Forward ¥/£ £109... (Repaid) £100 (Invested) 9%£/£ Forward ¥/£ £109 (Matures) The Foreign Exchange Parity Relation • We used the diagram to show that $ denominated Forward on Yen $ Denominated Spot for Yen = t (1 + r$ ) (1 + rY ) t • Recall there is a time structure of interest, and the appropriate risk free rate should be used 15