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DERIVATIVES MBA Finance “Hedging using Futures” Mrs Elsie Kambala MSc Investment Analysis Operations Manager: Finance (Lending) Old Mutual Namibia , 061 299 3555 [email protected] / [email protected] 2020 PROFILE Currently employed by Old Mutual Namibia as an Operations Manager: Finance (Lending). Previously worked for the Bank of Namibia as a Senior Portfolio Analyst in the Risk & Analytics Division (Middle Office) in the Financial Markets Department. From a Corporate Governance perceptive, I am currently serving as a Director on the Boards for the Orion Namibia Pension & Provident Funds (Investment Committee & Claim Committee member) and Rivera Asset Managers (Shareholder & Director). I served as a Director on the Retirement Funds Institute of Namibia Board and was a member of the Audit, Finance & Risk Committee. Was an Employee-Elect Trustee and an Investment Committee member as well as a Claim Committee member for the Bank of Namibia Provident Fund. Likewise, I was a voting member of the BoN Credit Risk Committee responsible for Credit Risk Management. Similarly, I also served on the Board of Directors for the Iththus Fishing Company which is solely owned by the Evangelical Lutheran Church (ELCIN). Academic: Obtained a Master of Science in Investment Analysis with Distinction (Cum Laude) from the University of Stirling, Scotland, United Kingdom and a holder of a Bachelor of Technology (Economics) from the Namibia University of Science & Technology. Additionally, I hold an Advanced Diploma in Banking, Finance and Credit from the Institute of Bankers as well as a Trading & Financial Market Analysis Certificate: Amplify Trading, University of Stirling Management School, UK. Others: Was an Employee-Elect Trustee and an Investment Committee member as well as a Claim Committee member for the Bank of Namibia Provident fund. Likewise, I was a voting member of the BoN Credit Risk Committee responsible for Credit Risk Management. I was awarded the Best Overall Trader: Amplify Trading (trading in multiple asset classes such as Fixed Income, Equities, Derivatives & Alternative Investments) by the University of Stirling. Similarly, the Bank of Namibia awarded me the Most Outstanding Individual Performer award within the Financial Markets Department. Worked in Germany at Daimler AG the Mercedes Benz Cars Company in the Revenue Controlling & Pricing Department. Worked at the National Planning Commission Secretariat in the Sub-Division: Productive & Economic Infrastructure as a Development Planner. My Leadership and Management skills were enhanced through participation in the Stirling Management School’s Flying Start Leadership and the HP-GSB / B360 Leading Change programmes. 2 “HEDGING USING FUTURES” Introduction to futures hedging Arguments for and against hedging Basis risk Minimum variance hedge Stock index futures Hedging equity portfolios Why Hedge Equity portfolios? Liquidity Issues Capital Asset Pricing Model (CAPM) Rolling a hedge forward Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 3 4 “HEDGING USING FUTURES” Hedging in general means cover or neutralize the risk of transaction by doing a transaction with just the opposite risk profile – reverse position. If the original investments leads to a loss it is covered by a profit of the same amount in the hedge position. A futures contract is a standardized forward contract, a legal agreement to buy or sell something at a predetermined price at a specified time in the future, between parties not known to each other. The asset transacted is usually a commodity or financial instrument. 5 Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 6 7 INTRODUCTION TO FUTURES HEDGING Types of hedging using futures Two types of hedge: Long vs Short Long hedge: When you know you will purchase an asset in the future and you desire to lock-in a favorable price. E.g.: A Company has to buy copper as input material in 2 months. Short hedge: When you know you will sell an asset in the future and you desire to lock-in a favorable price. Simply put…when the hedger already owns an asset and expects to sell it at some time in the future. E.g.: Farmer who owns cattles. Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 8 Long Hedges Company knows that in 6 months they have to buy one ton copper. Copper price today S1= $320; Q: What is the risk position? If the copper price in 6 mo (S2) is much higher the company makes a loss. Hedge: Buy Future (long Future) Future price today F1 If in 6 mo copper price increased - > increase in Future price F2 > F1 = profit Profit Future covers Loss Spot Optimal hedge, if profit in Future position exactly compensates the loss in the spot position Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 9 INTRODUCTION TO FUTURES HEDGING Short hedge example Example 1: A producer is planning to sell 1 million barrels of crude oil in 3 months from now. The spot price is $100 per barrel and the 3-month futures price is $98 per barrel. Each contract is for delivery of 1,000 barrels. Q: How can the producer hedge the risk of an unexpected decrease in crude oil prices in the next 3 months? Answer: Sell (go short) 1,000,000/1,000 = 1,000 crude oil futures contracts for delivery 3 months later. Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 10 Types of hedging using futures Long hedge example A farmer knows he will need to buy 20,000 bushels of corn in 2 months from now to feed his animals. The spot price of corn is N$400 cents/bushel and the futures price for delivery 2 months later is N$395 cents/bushel. Each contract is for N$5,000 bushels. Q: What can the farmer do to avoid the risk of an increase in the price of corn over the next 2 months? Answer: Buy (go long) 20,000/5,000 = 4 corn futures contracts for delivery 2 months later. Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 11 Arguments in favor of & Against hedging Arguments in favor of hedging Companies should focus on the main business they are in and take steps to minimize risks arising from interest rates, exchange rates, and other market variables. Arguments against hedging Shareholders are usually well diversified and can make their own hedging decisions. It may increase risk to hedge when competitors do not. Explaining a situation where there is a loss on the hedge and a gain on the underlying can be difficult. Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 12 Hedging can lead to a worse outcome In the example of the oil producer above, a decrease the price of crude oil leads to a loss in the spot market that is offset by a gain from the futures position. Thus, the company is better off with than without hedging. However, if the price of oil goes up the producer gains from selling the oil spot, but suffers a loss because of the position in futures. Therefore, the producer would be better of without the hedge. The hedging decision is absolutely logical, but it should be justified and clear to the Board of the company. Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 13 BASIS & BASIS RISK Convergence of spot to futures price Spot price above the Futures price. S1: Spot price at time t1 S2: Spot price at time t2 F1: Future price at time t1 F2: Future price at time t2 b1: Basis at time t1 (b1=S1-F1) b2: Basis at time t2 (b2=S2-F2) Variation of Basis over time. Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 14 Futures basis Basis: The difference between spot and contemporaneous futures price. b t = S t − F t,T where: b t is the basis at time t, S t is the spot price at t and F t,T is the price at time t of a futures contract maturing at T. During the life of the futures contract the futures basis changes (since spot and futures prices both change). An increase in the basis is referred to as strengthening of the basis, whereas a decrease in the basis is called weakening of the basis. Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 15 BASIS RISK Perfect hedge is rarely feasible in practice. The main reasons are: The asset we are trying to hedge may not be exactly the same as the asset underlying the futures. The hedger might not be sure about the exact time the asset has to be purchased or sold. There might be no futures contract with the specific maturity. There might be no contract available on asset that needs to be hedged. Therefore, there is uncertainty about the value of the basis at the time the asset will be bought/sold. This is called “basis risk”. Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 16 BASIS RISK : Long hedge for Purchase of an Asset Suppose the hedge is put in place at time t 1 and closed at time t 2. F 1 : Futures price at the time the hedge is set up. S1 S2 F1 F2 F 2 : Futures price at time asset is purchased. S 2 : Asset price at time of purchase. b 2 : Basis at time of purchase. S1: Spot price at time t1 S2: Spot price at time t2 F1: Future price at time t1 F2: Future price at time t2 b1: Basis at time t1 (b1=S1-F1) b2: Basis at time t2 (b2=S2-F2) Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 17 BASIS RISK : Short hedge for Sale of an Asset F1: Futures price at the time hedge is set up. F 2 : Futures price at time asset is sold. S 2 : Asset price at time of sale. b 2 : Basis at time of sale. The basis b 2 collects all the uncertain terms and so collects all the risk into one number. Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 18 Choice of futures contract Which contract to choose? What underlying? What delivery date? Choose a delivery month that is as close as possible to, but later than, the end of the life of the hedge. When there is no futures contract on the asset being hedged, choose the contract whose futures price is most highly correlated with the asset price. This is known as “cross-hedging”. Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 19 MINIMUM VARIANCE HEDGE RATIO: FUTURES HEDGING; CROSS-HEDGING Hedge ratio: The ratio of the size of the position in futures over the size of the exposure in the spot market. More simply, the number of units of asset in futures contracts per unit of asset being hedged. If the asset being hedged is the same as the underlying asset, the hedge can be perfect and the hedge ratio is equal to 1. However, in practice this is rarely the case. Thus, the hedger should use the value of the hedge ratio that minimizes the variance of the hedged position. 20 Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. How many Futures contracts do you have to buy to get a optimal hedge ? Change in basis depends on: volatility of spot price volatility of Future price how price changes are correlated (correlation) Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 21 Computing the minimum variance hedge ratio The minimum variance hedge ratio is computed as: where: 𝜎S (𝜎F ) is the volatility of changes in spot (futures) prices during a period equal to the life of the hedge. ρ is the correlation coefficient between the changes in spot and futures prices during the hedging period. If the correlation is positive they are changing in the same direction. Meaning if the Future rate increases the spot rate increases as well. The minimum variance hedge ratio depends on the relationship between changes in the spot price and changes in the futures Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. price. 22 Optimal number of contracts Define the following: QA : Size of position being hedged (units) QF : Size of one futures contract (units) VA : Value of position being hedged (=spot price × QA) VF : Value of one futures contract (=futures price × QF ) Optimal number of contracts: Or with tailing adjustment to allow for the impact of daily settlement: Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 23 Optimal hedge example Assume It’s now January 2021. A wheat producer knows that he will need to sell 240,000 bushels of wheat in February 2021. The wheat producer wants to hedge this risk using March futures contracts. Each futures contract is for delivery of 20,000 bushels of wheat. The standard deviation of monthly changes in the spot price of corn is 𝜎S ( N$ 12 per bushel) while the standard deviation of monthly changes in the futures price of wheat for the nearest to maturity contract is 𝜎F( N$ 18 per bushel). The correlation between the futures price changes and the spot price changes is 0.6. Q: Compute the optimal hedge ratio and specify the Optimal number of contracts ? ℎ∗=0.6*12/18 = 0.40 𝑁=0.4*(240,000/20,000)= 5 Optimal number of contracts Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 24 Tailing the hedge Adjustment to take the daily settlement into consideration. e.g., the spot price and the futures price are N$14 and N$20 per bushel, respectively. Then VA = 240, 000 *14 = 3 360 000 and VF = 20,000 *20 = 400 000. So the optimal number of contracts is: N* = 0.4*3 360 000/400 000 = 3.36 = 3 Contracts Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 25 HEDGING USING INDEX FUTURES: Hedging equity portfolios Stock index is a broad equity portfolio (e.g., DJIA, S&P 500, FTSE 100). Futures contracts on equity indices are widely traded. These futures can be employed to hedge the return of a stock portfolio. A stock portfolio will usually have a beta different from 1 (if stock portfolio perfectly tracks index, its beta equals 1). Hedging ensures that the return you earn is the risk-free return plus the excess return of your portfolio over the market. Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 26 Reasons for choosing to hedge an equity portfolio The hedger feels that the stocks in the portfolio have been chosen well. Hedger might be uncertain about the performance of the market, but confident that the stocks in the portfolio will outperform the market. Hedge using index futures removes the risk from market moves and leaves the hedger exposed only to the performance of the portfolio relative to the market. Another reason for hedging may be that the hedger is planning to hold a portfolio for a long period of time and requires short-term protection in an uncertain market situation. 27 Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. LIQUIDITY ISSUES In any hedging situation there is a danger that losses will be realized on the hedge while the gains on the underlying exposure are unrealized This can create liquidity problems. Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 28 Capital Asset Pricing Model (CAPM) In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio. i.e. CAPM is used to calculate expected return from an asset during a period in terms of the risk of the return. Risk of Return is divided into two parts: systematic risk and nonsystematic risk. Systematic risk is related to the return from the market as a whole and can’t be diversified away. Nonsystematic risk is unique to that asset and can be diversified away by choosing a large portfolio of different assets. Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 29 30 Capital Asset Pricing Model (CAPM) Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 31 Capital Asset Pricing Model (CAPM) Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 32 33 Capital Asset Pricing Model (CAPM) Expected return on Asset =Rf+ β (RM-Rf) Where Rf is the Risk free rate, RM is the expected return on the market, usually estimated as a return on a well diversified stock index such as the S&P500. β measures the sensitivity of its returns from the market. Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 34 CAPM: BETA β can be estimated from historical data as the slope when regressing excess returns on the asset over the risk-free rate against the excess returns on the market over the risk-free rate. When β =0, an asset’s returns are NOT sensitive to returns from the market and its expected return is the freerisk rate. When β =0.5, the excess return on the asset over the riskfree rate is on average half of the excess return of the market over risk-free rate. When β =1, the excess return on the asset equals the return on the market Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 35 CAPM Example Total market return S&P500 was RM = 10% in 2012, Beta =1, Risk free rate (US-treasury bills) Rf = 3%, Beta = 0 Q: What should be the expected return of a stock with a beta of 1.5? Expected Return =0.03+1 (0.10-0.03) =10% Expected Return =0.03+0 (0.10-0.03) =3% Expected Return =0.03+1.5 (0.10-0.03) =13.5% If the historical return in 2012 was lower than 13.5% sell or don’t buy stock as in this case the return is not an adequate compensation for the given market risk (beta). Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 36 Changing portfolio beta To reduce the beta of a portfolio from β to β’ (β > β’) we need to take a short position in: futures contracts If we need to increase beta from β to β’ (β < β’) then: futures contracts Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 37 Hedging using index futures To hedge the risk in a portfolio the number of contracts that should be shorted is: Where: VA is the current value of the portfolio, β is its beta (CAPM), and VF is the current value of one futures contract (=futures price × contract size). Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 38 Hedging using index futures • Example 1:Hedging using index futures Value of FTSE 100 index today is N$4,000.One futures is for N$10*Index. Value of Portfolio is N$400,000. Beta of portfolio is 1.5. Q: What position in futures contracts on the FTSE 100 is necessary to hedge the portfolio? What should the company do if it wants to reduce the beta of the portfolio to 0.9? Answer: VF = 4000*10 = 40,000 N = 1.5 * (400, 000/40, 000) = 15 contracts. Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 39 Example: Changing portfolio beta We have the portfolio of the previous example: Index value is N$4,000, Futures price N$4,100, Portfolio value: N$400,000, β =1.5 1. What position is necessary to reduce the beta of the portfolio to 0.9? To reduce the beta to 0.9, a short position in 6 contracts, is required; β to β’ (β > β’); (1.5-0.9) = (400,000/40,000) =6 contracts 2. What position is necessary to increase the beta of the portfolio to 2?To increase the beta from β to β’ (β < β’) then: (2-1.5) = (400,000/40,000) =5 contracts Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 40 Rolling the hedge forward We can use a series of futures contracts to increase the life of a hedge. For example, if we need to hedge a 3-year position in N$ and only 6-months futures are available. Take a position in a 6-months contract and as it expires, close this position and take one in a new 6months contract. Repeat 5 times. Each time we switch from one futures contract to another we incur a type of basis risk. Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 Investments 10th Edition , Copyright © Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2014. 41 Thank You 42