电子科技大学：《金融学基础》（英文版）Chapter14: Forward& Futures Prices

Finance School of management Chapter 14: Forward Futures prices Objective How to price forward and futures Storage of commodities st of carry Understanding financial uesTc futuris

1 Finance School of Management Chapter 14: Forward & Futures Prices Objective •How to price forward and futures •Storage of commodities •Cost of carry •Understanding financial futures

Finance School of management Chapter 14: Contents Distinction between forward The " Implied Risk-Free Rate Futures Contracts The forward Price is not a The economic Function of Forecast of the Spot Price Futures markets The role of speculators Forward-Spot Parity with Cash Payouts Relationship between Commodity Spot futures Implied" Dividends Prices The foreign exchange parity Extracting Information from Relation Commodity Futures prices The role of expectations in Spot-Futures Price Parity for Determining Exchange Rates Gold Financial futures uesTc

2 Finance School of Management 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 ❖ Forward-Spot Parity with Cash Payouts ❖ “Implied” Dividends ❖ The Foreign Exchange Parity Relation ❖ The Role of Expectations in Determining Exchange Rates

Finance School of management Features of forward Contracts Two parties agree to exchange some item on a specified future date 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 .s The face value of the contract is the quantity of the item specified in the contract times the forward price The party who agrees to buy the specified item is said to take a long position, and the party who agrees to sell the item is said to take a short position uesTc

3 Finance School of Management ❖ Two parties agree to exchange some item on a specified future date 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 times the forward price ❖ The party who agrees to buy the specified item is said to take a long position, and the party who agrees to sell the item is said to take a short position Features of Forward Contracts

Finance School of management Features of Forward Contracts Customization", difficulty of closing out positions, low liquidity The risk of contract default credit risk uesTc

4 Finance School of Management Features of Forward Contracts ❖ “Customization”, difficulty of “closing out” positions, low liquidity ❖ The risk of contract default, credit risk

Finance School of management 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 dail margin requirements(enough collateral uesTc

5 Finance School of Management 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 (enough collateral)

Finance School of management Terms Open, High, LoW, Settle, Change, Lifetime high Lifetime low, Oper en interest Mark-to-market Margin requirement Margin call uesTc

6 Finance School of Management Terms ❖ Open, High, Low, Settle, Change, Lifetime high, Lifetime low, Open interest ❖ Mark-to-market ❖ Margin requirement ❖ Margin call

Finance School of management An lllustration You place an order On August 5, the futures price closes 7/4 cents per to take a long bushel lower position in a You have lost 7 /4 cents*5,000 bushels=$362.50 September wheat that day futures contract on The broker takes that amount out of your account August 4, 1991 and transfers it to the future exchange, which The broker requires transfers it to one of the parties who was on the short side of the contract (marking to market) you to deposit an initial margin of o If you do not have enough money in your account to meet the margin requirement (variation $1, 500 in your maintenance margin), you'll receive a margin call account from the broker asking you to add money If you do not respond immediately then the broker liquidates your position at the prevailing market price uesTc

7 Finance School of Management An Illustration ❖ You place an order to take a long position in a September wheat futures contract on August 4, 1991 ❖ The broker requires you to deposit an initial margin of $1,500 in your account ❖ On August 5, the futures price closes 71 /4 cents per bushel lower ❖ You have lost 71 /4 cents*5,000 bushels=$362.50 that day ❖ The broker takes that amount out of your account and transfers it to the future exchange, which transfers it to one of the parties who was on the short side of the contract (marking to market) ❖ If you do not have enough money in your account to meet the margin requirement (variation / maintenance margin), you ’ll receive a margin call from the broker asking you to add money ❖ If you do not respond immediately, then the broker liquidates your position at the prevailing market price

Finance School of management Spot-Futures Price Parity for Gold There are two ways to invest in gold buy an ounce of gold at so, store it for a year at a storage cost of sho, and sell it for S invest so in a 1-year T-bill with return rs and purchase a 1-ounce of gold forward, F, for delivery in 1-year 0-h=r F gold =1 gold(syn) F=(1+r+h)s 0 uesTc

8 Finance School of Management 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 $hS0 , 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 ( ) 0 0 1 ( ) 0 1 0 r F 1 r h S S S F h r r S S S gold gold syn + f  = + f + − − = = = −

Finance School of management Arbitrage Opportunity when Forward Price of Gold Is Too High The spot price of gold is $300, the storage costs is 2% per year, and the risk-free rate is 8% The forward price is $340 Arbitrage Immediate Cash Cash Flow 1 Year Position Flow From now Sell a forward contract $340-S Borrow $300 $300 ($324) Buy an ounce of gold ($300) Pay storage costs ($6) Net cash flows 0 $340-$330=$10 uesTc

9 Finance School of Management – The spot price of gold is $300, the storage costs is 2% per year, and the risk-free rate is 8% – The forward price is $340 Arbitrage Opportunity when Forward Price of Gold Is Too High Arbitrage Immediate Cash Cash Flow 1 Year Position Flow From Now Sell a forward contract 0 $340-S1 Borrow $300 $300 ($324) Buy an ounce of gold ($300) S1 Pay storage costs ($6) Net cash flows 0 $340-$330=$10

Finance School of management Arbitrage Opportunity when Forward Price of gold Is Too low The forward price is $320 Arbitrage Immediate Cash Cash Flow 1 Year Position Flow From now Sell short an ounce of gold $300 0-S1 buy a forward contract 0 S1-$320 Invest $300 in 1-year pure ($300) 324 discount bond Receive storage costs $6 Net cash flows 0 330320=10 uesTc 10

10 Finance School of Management Arbitrage Opportunity when Forward Price of Gold Is Too Low Arbitrage Immediate Cash Cash Flow 1 Year Position Flow From Now Sell short an ounce of gold $300 0-S1 Buy a forward contract 0 S1 -$320 Invest $300 in 1-year pure ($300) $324 discount bonds Receive storage costs $6 Net cash flows 0 $330-$320=$10 – The forward price is $320