Risk Management with Futures Contracts PDF 2021/22

RISK MANAGEMENT WITH FUTURES CONTRACTS D. LAUTIER - UE 109 - 2021/22 1 1 OBJECTIVE OF HEDGING OPERATIONS: PROTECTION AGAINST PRICE RISK Commodities example...

RISK MANAGEMENT WITH FUTURES CONTRACTS D. LAUTIER - UE 109 - 2021/22 1 1 OBJECTIVE OF HEDGING OPERATIONS: PROTECTION AGAINST PRICE RISK Commodities example Generalization to other assets D. LAUTIER - UE 109 - 2021/22 2 2 The use of hedging operations is very important for: - producers of agricultural or industrial commodities - traders and dealers - processors D. LAUTIER - UE 109 - 2021/22 3 3  The agent who possesses the goods does not fear a price increase, but fears a price fall The agent who undertakes the delivery of goods fears a price increase, but does not fear a price fall D. LAUTIER - UE 109 - 2021/22 4 4 GENERAL PRINCIPLE OF HEDGING OPERATION: TAKE OPPOSITE POSITIONS ON THE DERIVATIVE MARKET AND ON THE UNDERLYING ASSET D. LAUTIER - UE 109 - 2021/22 5 5 Section 1. The hedging mechanism Section 2. Basis management Section 3. Financial operations in organized derivative markets Section 4. The hedging ratio D. LAUTIER - UE 109 - 2021/22 6 6  Section 1. The hedging mechanism 1.1. Protection against rising prices 1.2. Protection against falling prices 1.3. Cross hedging operations 1.4. The mechanisms of deposit and margin calls D. LAUTIER - UE 109 - 2021/22 7 7 1.1. Protection against rising prices D. LAUTIER - UE 109 - 2021/22 8 8 A grain trader sells wheat to Russia for delivery in 6 months An international trader sells oil to a refiner for delivery in 6 months D. LAUTIER - UE 109 - 2021/22 9 9  Three possibilities: Buy now the physical products Postpone the purchase of the physical products Postpone the purchase of the physical products and undertake a hedging operation D. LAUTIER - UE 109 - 2021/22 10 10 t Sell oil to a refiner 105 - 35 t+6 Buy oil on the spot market 140 D. LAUTIER - UE 109 - 2021/22 11 11 t Sell oil to a refiner 105 Buy contracts 102 + 38 - 35 t+6 Sell contracts 140 Buy oil on the spot market 140 D. LAUTIER - UE 109 - 2021/22 12 12  t Sell contracts 102 - 38 t+6 Buy contracts 140 D. LAUTIER - UE 109 - 2021/22 13 13 t sell contracts 102 -3 t+1 buy contracts 105 t+1 sell contracts 105 t+1.5 buy contracts 107 -2 t+1.5 sell contracts 107 t+2 buy contracts 112 -5 ….. ….. t+5.6 sell contracts 138 t+6 buy contracts 140 -2 D. LAUTIER - UE 109 - 2021/22 14 14 t Sell oil to a refiner 105 Buy contracts 102 t+6 Sell contracts 139 Buy oil on the spot market 140 D. LAUTIER - UE 109 - 2021/22 15 15 t Sell oil to a refiner 105 Buy contracts 102 + 37 - 35 t+6 Sell contracts 139 Buy oil on the spot market 140 D. LAUTIER - UE 109 - 2021/22 16 16 t Sell oil to a refiner 105 Buy contracts 102 + 39 - 35 t+6 Sell contracts 141 Buy oil on the spot market 140 D. LAUTIER - UE 109 - 2021/22 17 17 t Sell oil to a refiner 105 Buy contracts 102 - 33 + 35 t+6 Sell contracts 69 Buy oil on the spot market 70 D. LAUTIER - UE 109 - 2021/22 18 18  t Buy contracts 102 + 33 t+6 Sell contracts 69 D. LAUTIER - UE 109 - 2021/22 19 19 Futures market : t buy contracts 102 -7 t+1 sell contracts 95 t+3 buy contracts 72 +28 t+4 sell contracts 100 Physical market t sell physical 105 t+6 buy physical 70 +35 D. LAUTIER - UE 109 - 2021/22 20 20 Prices of futures contracts 102.0 Quality differential -2.0 Transportation costs +2.3 Transportation funding +0.3 Insurance premium +0.2 Losses +0.2 Basis at maturity +0.5 Imperfection of the hedging +0.5 Profit +1.0 Forward price 105.0 Economic function of the futures market: efficiency of the transactions D. LAUTIER - UE 109 - 2021/22 21 21  1.2. Protection against falling prices D. LAUTIER - UE 109 - 2021/22 22 22 t Stock of fuel oil 100 Sell contracts 98 + 28 - 30 t+3 Buy contracts 70 Sell fuel oil 70 D. LAUTIER - UE 109 - 2021/22 23 23 t Buy contracts 98 - 28 t+3 Sell contracts 70 D. LAUTIER - UE 109 - 2021/22 24 24 t Stock of fuel oil 100 Sell contracts 98 - 32 + 30 t+3 Buy contracts 130 Sell fuel oil 130 D. LAUTIER - UE 109 - 2021/22 25 25 t Buy contracts 98 + 32 t+3 Sell contracts 130 D. LAUTIER - UE 109 - 2021/22 26 26 1.3. Cross hedging operations Commodities Interest rates Equities D. LAUTIER - UE 109 - 2021/22 27 27  D. LAUTIER - UE 109 - 2021/22 28 28 t Stock of kerosene 110 Sell fuel oil contracts 95 - 10 - 25 t+3 Buy fuel oil contracts 105 Sell kerosene 85 D. LAUTIER - UE 109 - 2021/22 29 29 D. LAUTIER - UE 109 - 2021/22 30 30  1.4. The mechanisms of deposit and margin calls D. LAUTIER - UE 109 - 2021/22 31 31 16/01 Buy an oil contract for March delivery Purchase price USD 85.50 USD 85,500 Deposit USD 4,000 Maintenance margin USD 2,800 Settlement price USD 83.80 USD 83,800 Daily loss USD 1,700 Cumulated loss USD 1,700 Margin account USD 2,300 17/01 Margin call paid: USD 1,700 Settlement price USD 82.70 USD 82,700 Daily loss USD 1,100 Cumulated loss USD 2,800 Margin account USD 2,900 D. LAUTIER - UE 109 - 2021/22 32 32 18/01 Margin call paid: USD 0 Settlement price USD 80.30 USD 80,300 Daily loss USD 2,400 Cumulated loss USD 5,200 Margin account USD 500 19/01 Margin call paid: USD 3,500 Settlement price: USD 82.50 USD 82,500 Daily gain USD 2,200 Cumulated loss USD 3,000 Margin account USD 4,000 D. LAUTIER - UE 109 - 2021/22 33 33 20/01 Margin returned: USD 2,200 Settlement price: USD 84.30 USD 84,300 Daily gain USD 1,800 Cumulated loss USD 1,200 Margin account USD 4,000 23/01 Margin returned: USD 1,800 Settlement price: USD 86.80 USD 86,800 Daily gain USD 2,500 Cumulated gain USD 1,300 Margin account USD 4,000 D. LAUTIER - UE 109 - 2021/22 34 34 Client’s account Purchase on the 16/01 at USD 85.50 USD 85,500 Sale on the 19/01 at USD 79.90 USD 79,900 Loss USD 5,600 Margins paid : 1,700 + 3,500 : USD 5,200 Available Capital USD 0 Balance - USD 400 Margin account USD 4,000 Net Balance USD 3,600 D. LAUTIER - UE 109 - 2021/22 35 35 Section 2. Basis management 2.1. Initiation of hedging position 2.2. Maturity shift 2.3. Application D. LAUTIER - UE 109 - 2021/22 36 36  2.1. Initiation of the hedging position D. LAUTIER - UE 109 - 2021/22 37 37 t Sale of oil available at t + 6 105 Purchase of contracts for t+6 115 + 25 - 35 t+6 Sale of contracts for t+6 140 Purchase of physical oil 140 D. LAUTIER - UE 109 - 2021/22 38 38 R. D. t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12 D. LAUTIER - UE 109 - 2021/22 39 39 t Sale of oil available at t + 6 105 t+1 Purchase of contracts for t+6 102 + 38 - 35 t+6 Sale of contracts for t+6 140 Purchase of physical oil 140 D. LAUTIER - UE 109 - 2021/22 40 40 R. D. t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12 D. LAUTIER - UE 109 - 2021/22 41 41 2.2. Introduction of a maturity gap D. LAUTIER - UE 109 - 2021/22 42 42 t Sale of oil available at t + 6 105 Purchase of contracts for t+6 115 + 25 - 35 t+6 Sale of contracts for t+6 140 Purchase of physical oil 140 D. LAUTIER - UE 109 - 2021/22 43 43 15 8 t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12 D. LAUTIER - UE 109 - 2021/22 44 44 15 8 t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12 D. LAUTIER - UE 109 - 2021/22 45 45  15 8 t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12 D. LAUTIER - UE 109 - 2021/22 46 46 20 17 15 8 t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12 D. LAUTIER - UE 109 - 2021/22 47 47 20 17 15 8 t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12 D. LAUTIER - UE 109 - 2021/22 48 48 t Sale of oil available at t + 6 105 Purchase of contracts for t+12 117 + 31 - 35 t+6 Sale of contracts for t+12 148 Purchase of physical oil 140 D. LAUTIER - UE 109 - 2021/22 49 49 20 17 15 8 t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12 D. LAUTIER - UE 109 - 2021/22 50 50 2.3. Application and analysis of an imperfect hedge The imperfection in hedging results from: the difference between the theoretical futures price F * and the observed futures price F the commissions the funding of deposit the financing of margin calls D. LAUTIER - UE 109 - 2021/22 51 51  Imperfect hedge against price risk: Example 1 On 26 November : A producer holds stocks and wants to protect himself against the risk of falling prices Length of hedge: 3 months Calculation of the theoretical futures price: S = 20 Cs = 4 F* = 20 + 4 – 0 = 24 Cy = 0 D. LAUTIER - UE 109 - 2021/22 52 52 On 26 November To hedge a stock worth 20, the producer: - Sells a futures contract at a price of 26 - Finances the stock for three months with a cost of 4 On 25 February The producer - Sells the stock at the price of 15 - Closes his/her futures position at the price of 15 The cost of imperfect hedge totals: (- 20 + 26 – 4) + (15 – 15) = + 2 D. LAUTIER - UE 109 - 2021/22 53 53 On 26 November To hedge a stock worth 20, the producer: - Sells a futures contract at the price of 26 - Finances its stock for three months with a cost of 4 On 25 February The producer - Sells the stock at a price of 15 - Closes his/her futures position at the price of 16 The cost of imperfect hedge totals: (- 20 + 26 – 4) + (15 – 16) = + 1 D. LAUTIER - UE 109 - 2021/22 54 54  Imperfect hedge against price risk: Example 2 On 15 January Sale of 10 wheat contracts for September delivery: USD 5 Commissions: USD 30 Deposit: USD 2,000 On 15 June Sale of 50,000 bushels: $ 3.25 Closing the futures position: $ 3.40 Interest rate: 12% D. LAUTIER - UE 109 - 2021/22 55 55 1. Effective selling price of 50,000 bushels? Transactions on the futures market: (5 – 3.4) x 5,000 x 10 = + USD 80,000 Sale in the physical market: 3.25 x 50,000 = + USD 162,500 Financing costs of the deposit: 2,000 x 10 x 12% x (5/12) = - USD 1,000 Placement of the margins: (1/2) x 80,000 x 12% x (5/12) = + USD 2,000 Commissions : 30 x 10 = - USD 300 Effective selling price: + 80,000 + 162,500 – 1,000 + 2,000 - 300 = USD 243,200 D. LAUTIER - UE 109 - 2021/22 56 56 Observed futures prices are identical to theoretical futures prices 2. What is the amount of the imperfection ? Deposit : - 1,000 Commissions : - 300 Margin calls : + 2,000 + 700 D. LAUTIER - UE 109 - 2021/22 57 57  Section 3. Financial transactions in the futures markets 1. Speculation 2. Arbitrage D. LAUTIER - UE 109 - 2021/22 58 58 3.1. Speculation The mechanism Examples 59 D. LAUTIER - UE 109 - 2021/22 59 Examples 1. Commodities 2. Interest rate 3. Individual stocks, equity D. LAUTIER - 60 UE 109 - 2021/22 60  1. Commodities In January, a speculator buys 5 coffee contracts for $ 2.45 / lb for delivery in the end of August Transaction costs are USD 200 In June, the speculator resells 5 coffee contracts for $ 2.65 / lb for August delivery The profit is equal to: 5 x 37,500 x (2.65 – 2.45) - 200 = USD 37,300 If prices had fallen to $ 2.10 / lb, the loss would have been: 5 x 37,500 x (- 2.45 + 2.10) - 200 = USD 65,425 D. LAUTIER - 61 UE 109 - 2021/22 61 3. Individual stocks 3.1. Speculation on a prices’ rise 3.2. Speculation on a price’s fall D. LAUTIER - 62 UE 109 - 2021/22 62 3.1. Speculation in anticipation of higher prices On 2 September : - SVega = GBP 10.40 - 3-month interest rate: 6% - Expected dividend rate: 3% 1. What is the theoretical price of the futures contract with a maturity of three months (simple interest rate)? D. LAUTIER - 63 UE 109 - 2021/22 63  Theoretical futures price: 10.40 + 10.40 x [(6% - 3%) x (90/360)] = GBP 10.48 Observed futures price GBP 10.85 2. How to benefit from the anticipated increase: - Purchase of the shares on the cash market - Purchase of futures contracts on the stock - Nominal of the contract: 100 shares - Purchase of 20 contracts - The deposit is GBP 120 / contract D. LAUTIER - 64 UE 109 - 2021/22 64 On the 23rd of September, SVega = GBP 11.65 FVega = GBP 11.90 3. What is the financial result of the speculation transaction? (11.90 – 10.85) x 100 x 20 = GBP 2,100 Annual profitability as a percentage of the amount invested : 65 D. LAUTIER - UE 109 - 2021/22 65 4. What would have been the financial result if, on September 2, the investor had purchased the shares on the spot market? (11.65 – 10.40) x 2,000 = GBP 2,500 Annual profitability as a percentage of the amount invested : D. LAUTIER - 66 UE 109 - 2021/22 66  5. On 23 September, SVega = GBP 9.50 FVega = GBP 9.72 On the futures market: (9.72 – 10.85) x 100 x 20 = - GBP 2,260 that is: This result is theoretical because the speculator will liquidate its futures position before realizing the loss On the spot market: (9.50 – 10.40) x 2,000 = - GBP 1,800 that is: D. LAUTIER - UE 109 - 2021/22 67 67 6. The amount of the deposit is GBP 240 On the futures market : D. LAUTIER - 68 UE 109 - 2021/22 68 3.2. Speculation in anticipation of falling prices On 13 August, STheta = € 45.20 FTheta = € 45.60 An investor anticipates a fall in the stock price. 1. Which are the strategies at his/her disposal? - Short selling of the securities: - Borrow the securities - Sell them on the cash market - Repurchase - Sell futures contracts on the stocks D. LAUTIER - 69 UE 109 - 2021/22 69  Sell 5 futures contracts on Theta’s stocks Deposit: € 450 On 21 August, STheta = € 38.70 FTheta = € 38.98 2. Financial result of speculation transaction? (45.60 – 38.98) x 100 x 5 = € 3,310 3. On 21 August, FTheta = € 48.20 (45.60 – 48.20) x 100 x 5 = - € 1,300 D. LAUTIER - 70 UE 109 - 2021/22 70 Deposit = € 450 Brokerage fees = € 8 Interest rate = 6% Funding of deposit: 450 x 5 x (8/360) x 6% = € 3 Brokerage fees: 8 x 5 = € 40 D. LAUTIER - 71 UE 109 - 2021/22 71 Result in case of falling prices: Placement of creditor margins : (1/2) x (45.60 – 38.98) x 100 x 5 x 6% x (8/360) = € 2.21 3,310 + 2.21 – 3 - 40 = € 3,269.21 Result in case of rising prices: Financing of debtor margins: (1/2) x (48.20 – 45.60) x 100 x 5 x 6% x (8/360) = € 0.87 1,300 + 0.87 + 40 + 3 = € 1,343.87 D. LAUTIER - 72 UE 109 - 2021/22 72  3.2. Arbitrage transactions Cash and carry arbitrage Intertemporal Arbitrage Spatial Arbitrage D. LAUTIER - UE 109 - 2021/22 73 73 3.2.1. Cash & carry arbitrage 31 December Index CAC 40 on the cash market: 4,530.12 Index CAC 40 for the January maturity: 4,571.35 r = 4% d = 0% Theoretical value of CAC 40 for January maturity: Possibility of cash and carry arbitrage D. LAUTIER - 74 UE 109 - 2021/22 74 December 31 Buy portfolio that replicates the index CAC 40 222,560 EUR Sell futures contracts D. LAUTIER - 75 UE 109 - 2021/22 75  January 31 Index CAC 40 spot: 4,500 Sell portfolio that replicates the index: EUR 220,690 D. LAUTIER - 76 UE 109 - 2021/22 76 January 31 1. Portfolio that replicates the index: 220,690 - 222,560 - 1,870 2. Financing of the portfolio: 222,560 x 4% x (31/360) = - 767 3. Result on the futures market: [4,571.35 - 4,500 ] x 10 x 5 = + 3,566 4. Interests: + (1/2) x 3,566 x 4% x (31/360) = + 6 D. LAUTIER - 77 UE 109 - 2021/22 77 January 31 Results of the arbitrage: + 3,566 + 6 - 1,870 - 767 + 935 D. LAUTIER - 78 UE 109 - 2021/22 78  3.2.2. Intertemporal Arbitrage on commodity markets January 3 February 1,200 March 1,250 April 1,300 May 1,350 June 1,400 July 1,260 D. LAUTIER - 79 UE 109 - 2021/22 79 Decisions taken on January 3 Sell a contract for May at 1,350 Buy a contract for July at 1,260 D. LAUTIER - 80 UE 109 - 2021/22 80 3 January 15 February February 1,200 1,200 March 1,250 1,250 April 1,300 1,300 May 1,350 1,350 June 1,400 1,400 July 1,260 1,450 D. LAUTIER - 81 UE 109 - 2021/22 81  On February 15 Buy a contract for May at 1,350 Sell a contract for July at 1,450 Consequences: The agent makes a profit of 190 on the July contract 82 D. LAUTIER - UE 109 - 2021/22 82 The prices may rise between the time the agent initiates the arbitrage and the time he/she unwinds his/her position D. LAUTIER - 83 UE 109 - 2021/22 83 3 January 15 February February 1,200 1,230 March 1,250 1,280 April 1,300 1,330 May 1,350 1,380 June 1,400 1,430 July 1,260 1,480 D. LAUTIER - 84 UE 109 - 2021/22 84  On February 15 Buy a contract for May at 1,380 Sell a contract for July at 1,480 Consequences: - The agent loses 30 on the May contract - The agent gains 220 on the July contract - The result is always equal to 190 D. LAUTIER - 85 UE 109 - 2021/22 85 The prices may fall between the time the agent initiates the arbitrage and the time he/she unwinds his/her position D. LAUTIER - 86 UE 109 - 2021/22 86 3 January 15 February February 1,200 1,150 March 1,250 1,200 April 1,300 1,250 May 1,350 1,300 June 1,400 1,350 July 1,260 1,400 D. LAUTIER - 87 UE 109 - 2021/22 87  On February 15 Buy a contract for May at 1,300 Sell a contract for July at 1,400 Consequences: - The agent profits 50 on the May contract - The agent profits 140 on the July contract -The result is always equal to 190 D. LAUTIER - 88 UE 109 - 2021/22 88 Section 4. Hedge Ratio 4.1. Theoretical approach 4.2. Empirical approach D. LAUTIER - UE 109 - 2021/22 89 89 Price of Light Sweet Crude, 2001-2017 D. LAUTIER - UE 109 - 2021/22 90 90  D. LAUTIER - UE 109 - 2021/22 91 91 4.1 Theoretical approach Let us note: - qS the position held in the physical market - qF the position held in the futures market - H the holding period for this position in the physical market - T the expiry date of the futures contract used to hedge this position - Hedging objective: Reduce the variability of the hedged position. D. LAUTIER - UE 109 - 2021/22 92 92 Value of the position held on the spot market at time t: qSS(t) The agent is long in the physical asset at time t He/She takes a short position in the futures market at time t Hedging to horizon H using a contract of maturity T (T > H) : Value of hedged position at time t to horizon H: D. LAUTIER - UE 109 - 2021/22 93 93  Objective of the agent: Min (Var[V(H)]) under qF With: where: D. LAUTIER - UE 109 - 2021/22 94 94 Hedge Ratio: D. LAUTIER - UE 109 - 2021/22 95 95 Hedge Ratio: Where: is the correlation coefficient between S and F The hedge ratio becomes: D. LAUTIER - UE 109 - 2021/22 96 96  4.2. Empirical approach Estimation of the correlation and the standard deviations on the basis of historical data An airline company purchases 200,000 barrels of kerosene and hedges with crude oil futures From the past prices, one can measure that: - The correlation is 0.92 - The volatility of the kerozene is 0.0256 - The volatility of crude oil is 0.0378 So that the hedge ratio is: h = 0.6231 D. LAUTIER - UE 109 - 2021/22 97 97 - The size of one crude oil contract is 1,000 barrels - Optimal number of contracts: 0.6231 x (200,000 / 1,000) = 124.62 which rounds to 125. D. LAUTIER - UE 109 - 2021/22 98 98 4.3. Hedging with equity index futures To hedge the risk of any portfolio, the number of contracts that should be shorted should be: where: - VA is the value of the portfolio A (or the stock) - VB is the value of one futures contract on the market index - the beta is the sensitivity of the portfolio (or the stock) to the market index D. LAUTIER - UE 109 - 2021/22 99 99  Εxample S&P500 index value is 3,000 Multiple on S&P500 futures contract : USD 250 Value of portfolio is USD 5 millions Beta of portfolio: 1.5 What position in futures contract on the S&P500 is necessary to hedge the portfolio? 1.5 x (5,000,000 / (3,000 x 250)) = 10 D. LAUTIER - UE 109 - 2021/22 100 100 What position is necessary to reduce the beta of the portfolio to 0.75 ? >5 What position is necessary to increase the beta of the portfolio to 2 ? > 13 D. LAUTIER - UE 109 - 2021/22 101 101