Hedging Strategies To Manage Commodity Price Risk
Karen Ósk Finsen
Thesis of 30 ECTS credits Master of Science in Financial Engineering
June 2018
Hedging Strategies To Manage Commodity Price Risk
by
Karen Ósk Finsen
Thesis of 30 ECTS credits submitted to the School of Science and Engineering at Reykjavík University in partial fulfillment of the requirements for the degree of Master of Science (M.Sc.) in Financial Engineering
June 2018
Supervisor: Dr. Sverrir Ólafsson, Supervisor Professor, Reykjavík University, Iceland
Examiner: Dr. Sigurur Pétur Magnússon, Examiner Arion Banki, Reykjavík, Iceland
i Copyright Karen Ósk Finsen June 2018
ii Hedging Strategies To Manage Commodity Price Risk
Karen Ósk Finsen
June 2018
Abstract
Price fluctuations in commodity markets can have a significant impact on potential profits, both for those who use and produce that commodity. Commodity prices, which are based on the supply and demand of a market, are very volatile and it is nearly impossible to predict exactly which way a price will move in the future. Companies that are impacted by unexpected commodity price movements should consider managing these risks and minimizing their e ects through the use of financial market instruments. The purpose of this thesis is to use risk management strategies and derivatives to hedge risks faced by an Icelandic manufacturer that uses gold as an input. Fluctuating gold prices and foreign exchange rates are causing changes in cash flows and a ecting the company’s profitability. To reduce these risks, the company can hedge its exposure through the use of derivatives, such as futures contracts, forward contracts, options and swaps. Historical data on gold prices and foreign exchange rates are used to predict future prices and to calculate Value at Risk. Black Scholes model and Monte Carlo simulation are used for option pricing. In conclusion, risk management strategies and derivatives reduce price uncertainty and stabilize future cash flow. But considerable risk can also accompany the use of risk management, whereby the price of the underlying asset can develop in a di erent direction to what was predicted.
iii Áhættuvarnir Gegn Versveiflum á Hrávörumarkai
Karen Ósk Finsen
júní 2018
Útdráttur
Versveiflur á hrávörumörkuum geta haft veruleg áhrif á fjárhagslegan ávinning fyrirtækja sem stunda viskipti mehrávörur. Mikil óvissa ríkir almennt á essum mörkuum og getur ví áhættan verimikil bæi fyrir au fyrirtæki sem nota og framleia hrávörur. Til ess averjast essum óvæntu versveiflum á markai er hægt anota aferir áhættust˝ringar og tryggja ar af leiandi stöugra tekjustreymi í framtíinni. Markmi essara ritgerar er as˝na hvernig íslenskt fyrirtæki sem notar gull í framleislu sinni getur notaáhætt- urvarnir og afleiusamninga til ess averja sig fyrir áhættum sem a astendur frammi fyrir. Helstu áhættu ættir sem hafa áhrif á tekjustreymi fyrirtækisins eru verbreytingar á gulli, gjaldeyrishreyfingar og vaxtabreytingar. Skoaer hvernig fyrirtækigetur n˝tt sér framvirka samninga, valrétti og skiptasamninga til ess adraga úr essum helstu áhættu- áttum. Notast var visöguleg gögn um verá gulli og gengis róun krónunnar gagnvart bandaríkjadal til aspá fyrir um framtíarverog til ess areikna áhættuviri sem segir til um hugsanleg tap fyrirtækisins á ákvenu tímabili í framtíinni. Black-Scholes aferin og Monte Carlo hermun eru notaar til ess averleggja valréttina. Helstu niurstöur eru ær aáhættust˝ring og notkun afleiusamninga dregur úr helstu áhættum me ví a stula astöugum tekjum og minnka verulega óvæntar versveiflur í rekstri fyrirtækisins. En agetur líka fylgt ví töluveráhætta anotast viáhættust˝ringu ar sem veriá undirliggjandi eign getur róast í ara átt en búivar aspá fyrir um.
iv Hedging Strategies To Manage Commodity Price Risk
Karen Ósk Finsen
Thesis of 30 ECTS credits submitted to the School of Science and Engineering at Reykjavík University in partial fulfillment of the requirements for the degree of Master of Science (M.Sc.) in Financial Engineering
June 2018
Student:
Karen Ósk Finsen
Supervisor:
Dr. Sverrir Ólafsson
Examiner:
Dr. Sigurur Pétur Magnússon
v The undersigned hereby grants permission to the Reykjavík University Library to reproduce single copies of this Thesis entitled Hedging Strategies To Manage Commodity Price Risk and to lend or sell such copies for private, scholarly or scientific research purposes only. The author reserves all other publication and other rights in association with the copyright in the Thesis, and except as herein before provided, neither the Thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author’s prior written permission.
date
Karen Ósk Finsen Master of Science
vi vii Acknowledgements
I would like to thank my supervisor Dr. Sverrir Ólafsson for all his help and guidance through this research. I would also like thank my family and friends for all the support over the last years.
viii Contents
Acknowledgements viii
Contents ix
List of Figures xi
List of Tables xiii
List of Abbreviations xiv
1 Introduction 1
2 Risk and risk management 2 2.1 What is risk? ...... 2 2.2 Financial risk ...... 2 2.3 Risk management ...... 2 2.4 Why manage risk? ...... 3
3 Types of risk faced by corporations 4 3.1 Foreign exchange risk ...... 4 3.2 Interest rate risk ...... 4 3.3 Commodity price risk ...... 4
4 How to quantify risk? 6 4.1 Risk as spread in returns ...... 6 4.2 Value at Risk ...... 7 4.3 Risk from foreign investment ...... 7 4.4 Monte Carlo ...... 8
5 Instruments available for risk management purpose 9 5.1 Forward contracts ...... 9 5.2 Futures contracts ...... 9 5.2.1 Payo s from forward and future contracts ...... 10 5.2.2 Forward contracts on currencies ...... 10 5.3 Vanilla options ...... 11 5.3.1 Options positions ...... 11 5.4 Asian options ...... 12 5.5 Swaps ...... 12 5.6 Hedging strategies using derivatives ...... 13
ix 6 Valuing and pricing derivatives 14 6.1 Valuing European options ...... 14 6.2 Valuing currency options ...... 14 6.3 Implied volatility ...... 15 6.4 Monte Carlo methods ...... 15 6.5 Ornstein-Uhlenbeck process ...... 16 6.6 Valuing a commodity swap ...... 16 6.7 Valuing a fixed-floating currency swap ...... 17
7 Description of the risks the firm faces 19 7.1 Description of the firm to be discussed ...... 19 7.2 Commodity price risk ...... 19 7.3 Instruments available to manage commodity price risk ...... 27 7.3.1 Commodity futures ...... 27 7.3.2 Commodity options ...... 27 7.3.3 Commodity swaps ...... 27 7.4 Foreign exchange risk ...... 27 7.5 Instruments available to manage foreign exchange risk ...... 31 7.5.1 Forward exchange contract ...... 31 7.5.2 Currency options ...... 31 7.5.3 Currency swaps ...... 31 7.6 Comparison of the two risk types ...... 31
8 Implementation of risk management strategies 35 8.1 Hedging gold price with a future contract ...... 35 8.2 Hedging foreign exchange rate with a forward contract ...... 36 8.3 Pricing a European call option ...... 38 8.4 Pricing Asian call option ...... 41 8.5 Pricing a currency call option ...... 42 8.6 Pricing a gold swap ...... 44 8.7 Pricing a currency swap ...... 46 8.8 Summary ...... 48
9 Discussion and Conclusion 52
Bibliography 53
x List of Figures
2.1 Risk management planning process ...... 3 2.2 Risk management implementation process ...... 3
5.1 Payo from a long position at maturity...... 10 5.2 Payo from a short position at maturity...... 10 5.3 Payo from a long position in a call option...... 12 5.4 Payo from a short position in a call option...... 12 5.5 Payo from a long position in a put option...... 12 5.6 Payo from a short position in a put option...... 12
7.1 Historical data of gold prices between 4 December 2015 and 4 December 2017. 20 7.2 The daily gold price change ...... 21 7.3 Probability density function for the returns...... 22 7.4 Cumulative probability function for daily gold price changes ...... 23 7.5 VaR as a function of time ...... 24 7.6 Simulated 10,000 price paths for gold using the Ornstein-Uhlenbeck process. . 25 7.7 Profit loss probability density function for June 2018 ...... 26 7.8 Profit-and-loss probability density function for December 2018 ...... 26 7.9 Historical data of the foreign exchange rate...... 28 7.10 Daily change in exchange rate ...... 29 7.11 Probability density function for daily rate returns ...... 30 7.12 Cumulative probability function for daily rate change ...... 30 7.13 Daily gold price in ISK/oz...... 32 7.14 VaR calculations for given months ...... 34
8.1 The profit diagram for the long Gold futures contract with maturity in June 2018. 36 8.2 The profit diagram for the long foreign exchange rate forward contract with maturity in June 2018...... 37 8.3 10,000 simulated price paths 252 days into the future...... 38 8.4 The profit from a long position in a call option with strike 1280 in June 2018. . 40 8.5 Simulated price paths for foreign exchange rate ...... 43 8.6 Payo from a long currency call option ...... 44 8.7 The present value of the swap contract at di erent maturities...... 46
xi 8.8 The present value of the currency swap contract at di erent maturities...... 48 8.9 The probability density function for the present value of option payments . . . . 50
xii List of Tables
7.1 The USD Libor rates, required quantities of gold, the future price and the expected exposure for gold based on information on 4 December 2017...... 20 7.2 Theoretical and Empirical probabilities ...... 22 7.3 The 95% VaR risk for the gold price...... 23 7.4 Gold price forecast from January 2018 and December 2018...... 25 7.5 The 95% VaR for the gold price...... 27 7.6 The calculated forward exchange rate ...... 28 7.7 Theoretical and Empirical probabilities ...... 29 7.8 Forward exchange rate and gold future price in USD per oz and ISK per oz. . . 32 7.9 Correlation between the return of gold price and foreign exchange rate . . . . . 33 7.10 The 95% VaR risk for the gold price in ISK...... 33
8.1 The future price for gold ($/oz)...... 35 8.2 Calculated forward exchange rate ...... 37 8.3 Valuation of call options ...... 39 8.4 Valuation of call options ...... 39 8.5 Valuation of call options ...... 39 8.6 Valuation of call options ...... 40 8.7 Probabilities for monthly gold price to be greater than the strike price . . . . . 41 8.8 Valuations of Asian call options ...... 41 8.9 Valuations of Asian call options ...... 41 8.10 Valuations of Asian call options ...... 42 8.11 Calculated Monte Carlo price and Black Scholes price for currency call option . 43 8.12 The Swap Contract ...... 45 8.13 The Currency Swap Contract ...... 47 8.14 Compared hedging strategies for gold prices ...... 49 8.15 Compared hedging strategies for exchange rate ...... 51 8.16 Compared hedging strategies for exchange rate ...... 51
xiii List of Abbreviations
VaR Value at Risk OTC Over the counter SDE Stochastic di erential equation PV Present Value pdf Probability density function cdf Cumulative density function
xiv Chapter 1
Introduction
Uncertainty in commodity prices poses a huge risk to producers, manufactures and con- sumers, who are all a ected by fluctuations in the market prices. Prices are based on supply and demand of a market and therefore it can be di cult to predict future price movements. A business operating in the commodity markets should consider managing these risks where fluctuations in commodity prices may impact business profitability.
Companies that are exposed to commodity risk may also be exposed to foreign exchange risk, since most commodities are quoted in US dollars. Managing only commodity risk will leave the company exposed to adverse movements in foreign exchange rates. When locking the price in US dollars, the foreign exchange risk remains. With fluctuating commodity prices, foreign exchange rate risk can be complicated to manage. By using appropriate risk management strategies, the risk of unexpected price movements can be reduced.
Risk management is not always profitable because there can be risk and potential loss if the price of the underlying asset develops in a di erent direction to what was predicted or if the company chooses an inappropriate risk management tool. Therefore, a risk management plan must be appropriately implemented if it is to be successful.
The objective of this research is to reduce market price risk and foreign exchange risk of a company operating in the jewelry industry by implementing risk management strategies. The aim is to find the best way for the company to manage these risks. This thesis will answer the following main questions:
• What is the purpose of implementing risk management strategies?
• What are the reasons firms seek to manage risk?
The outline of this thesis is as follows. Chapter 2 begins with a description of risk and risk management. Chapter 3 discusses the description of risks faced by corporations, commodity price risk, foreign exchange risk and interest rate risk. Chapter 4 introduces methods to quantify risks. Derivatives are introduced as instruments available for risk management in Chapter 5 while Chapter 6 demonstrates methods for valuing and pricing these derivatives. Chapters 7 describe the firm and the risks the firm faces. In Chapter 8, implementation of risk strategies for the firm is described. Finally, Chapter 9 presents discussion and conclusions. Chapter 2
Risk and risk management
2.1 What is risk?
Risk is the possibility of something unexpected happening which can lead to a loss of any type. Everything we do in our daily lives involves some kind of risk. Most people want to avoid taking more risks in daily life than necessary, which is why high risk exposure or the possibility of something unexpected happening require us to take corrective action, for instance insuring our life, home, car and other possessions. Risk is essentially received as negative but risk can also provide an business opportunities.
2.2 Financial risk
Financial risk is caused by movements in financial variables and involves financial loss to corporations. Financial risk can be classified as following types of risk, such as market risk, credit risk, liquidity risk and operational risk. Market risk arises from the unexpected changes in stock prices, commodity prices, foreign exchange rates, interest rates and so on. Credit risk is the risk of loss arising from the failure of a counterparty to make a promised payment. Liquidity risk is the risk that arises when transactions cannot be undertaken at prevailing market prices due to insu cient market activity. Operational risk is the risk of loss arising from the failure of management or technology [1].
2.3 Risk management
Risk management involves procedure for becoming aware of risks and the methods used to analyze risks, asses their impact and minimize them. An objective needs to be defined in deciding how and when to manage risks and what to do about them. When measuring risk, it is important to identify all the key risk factors for the company to help identify a company’s exposure to uncertainty. Measuring these risks requires analysis of the potential exposure and an understanding of how these risks can a ect the company. Financial risk management is the activity of monitoring financial risk and managing their impact. Risk can be reduced or even eliminated through hedging and diversification [1]. . . WHY MANAGE RISK 3
Do nothing
Identify risk Quantify risk Optimize exposure to risk Diversify
Hedge
Figure 2.1: Risk management planning process
Successful implementation of risk management requires the following:
Actual outcome
How we plan to manage risk Implement plan Monitor implementation
Target outcome
Figure 2.2: Risk management implementation process
Whenever there is an opportunity there is also a risk. If risk is removed entirely there is little scope for gains. Risk and opportunity are intrinsically related: risk management is about understanding the relationship between these [1].
2.4 Why manage risk? Although risk management provides significant advantages, it does entail some costs and risks. The cost of risk management relates to the price to be paid for risk control. There can also be potential loss if the price of the underlying asset or commodity changes against the expectations of the risk management strategies used. Why would a firm use these strategies to manage risks? There are a number of di erent reasons why firms might seek to manage risk. The firm’s profitability may be sensitive to changes in commodity market prices, interest rates, foreign exchange rate and other factors. Managing these risks can increase the value of the firm, i.e. risk management increases the expected value of the firm. The firms might need to manage risk if losses might be more harmful than profits are beneficial [2]. Chapter 3
Types of risk faced by corporations
There are many di erent types of risks that corporations and financial institutions might face and need to overcome. Identifying and managing these risks has become a focus point within most corporations to minimize their losses and maximize their profit. Before understanding the techniques to control risk and perform risk management, it is very important to realize what risk is and what the types of risks are.
3.1 Foreign exchange risk
Foreign exchange risk is the risk that the value of one currency changes against another. Fluctuations in exchange rates will a ect companies that export or import their goods and services and can have a big impact on company income. Companies importing their goods and services may end up paying more than expected. Companies that export their goods and services may be at risk of getting paid less than planned. This is a big risk factor for businesses that deal in more than one currency but other businesses can also be exposed to foreign exchange risk if for example their business relies on imported products or services [3].
3.2 Interest rate risk
Interest rate risk is the risk of fluctuations in interest rates on borrowed or invested money that can have a big impact on company’s profitability. Cash flows of the borrower or lender are a ected by the changes in interest rates whereby the borrower can face increased costs when interest costs fluctuate according to interest rate movements during the life of a loan. An adverse movement in interest rate may potentially increase borrowing costs for borrowers and reduce returns for investors. When borrowers are generally concerned about rising interest rates, investors are concerned about falling rates [4].
3.3 Commodity price risk
Commodity price risk is the risk arising from changes in commodity prices that impact the firms that both use and produce a commodity. Commodities is a term for a basic good which can generally be classified into three categories: soft commodities, metals and energy commodities. Soft commodities include agricultural products such as wheat, co ee, sugar and fruit. Metals include gold, silver, copper and aluminum. Energy commodities . . COMMODITY PRICE RISK 5 include gas, oil and coal. Commodity price risk is a significant problem for some firms that use commodities in their manufacturing process and for consumers in general, both because consuming firms that use raw materials for their production may face increased production costs due to fluctuations in commodity prices and because producing firms that sell commodities are exposed to price falls which mean they will receive less revenue for the commodities they produce [5]. Chapter 4
How to quantify risk?
Measuring risk is important and helps the company to recognize the impact of the risks involved in the business. When measuring risk, a company can identify which risk factors are most important and can therefore prepare for the damage these can cause. By identifying the amount of risk involved, the company can make a decision to either accept or mitigate the risk. The firms then need to make a decision about how much risk may be acceptable and how much exposure can be tolerated. This should lead the firm to make strategic choices about what risks to accept and how risks are to be managed. The most common way of measuring risk factors is to evaluate the likelihood that events will occur and what their impact would be. Risk is the volatility of presently unknown future outcomes, for example returns. This uncertainty implies possible good or bad outcomes. One popular way to quantify risk exposure is in terms of Value at Risk (VaR).
4.1 Risk as spread in returns Returns are changes in price that are relative to some initial price. The return series can visualize the price volatility better than the price series. The percent change in value (returns) in the time period from t-1 to t is:
St St 1 rt = 100 (4.1) St 1 where St is the price of an asset at time t. The return series provides the data for a volatility modeling. By modeling the return distribution, probabilistic quantification of losses and gains can be calculated and compared between di erent investments [6]. VaR can be calcu- lated from the probability distribution for asset values or returns.
In favor of normally distributed historical data of some security returns, their probability distribution can be presented by:
1 µ r 2 p r = exp ( ) (4.2) ( ) p2⇡ 2 ( 2 2 ) where µ is the mean and is the standard deviation of the historical returns. Cumulative normal distribution is:
x0 F x = Pr x x µ, = f y µ, dy (4.3) ( 0) ( 0| ) ( | ) π 1 . . VALUE AT RISK 7
The probability that a return events is below some fixed value a is:
1 a µ P x a = 1 + er f (4.4) ( ) 2( ( p2 )) 1 a µ P x a = 1 er f (4.5) ( ) 2( ( p2 )) where the error function and the complementary error function are defined as:
2 x er f x = exp w2 dw (4.6) ( ) p⇡ ( ) π0 2 1 er f x = 1 exp w2 dw (4.7) ( ) p⇡ ( ) πx 4.2 Value at Risk
Value at Risk (VaR) measures the worst loss expected over a given time interval at a given confidence level. VaR is defined by the following statement: "I am c percent certain that I will not loose more than X dollars in the next T days” where the variable X is the VaR of the portfolio and c is the confidence level. VaR is a popular measure because it provides a single number summarizing the total risk and it is easy to understand. Given the historical probability distribution for returns, VaR calculates the probability of su ering certain losses over a fixed time period. Following the assumption that returns are normally distributed, the value at risk for the time period of T days is [6]:
VaR ↵, , , T, V = ↵V , (4.8) ( R T 0) 0 R T where R,T is the standard deviation for T days calculated as follows: