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Bachelorarbeit, 2010
82 Seiten, Note: 2,2
Abbreviations
List of Figures
List of Tables
1 Introduction
1.1 Problem definition
1.2 Objectives
1.3 Scope of work
2 Trading Motivation and Theoretical Foundation
2.1 Risk management
2.1.1 Risk definition
2.1.2 Portfolio Management
2.1.3 Portfolio Analysis
2.2 Trading Strategies
2.2.1 Hedge Trading
2.2.1.1 Direction: Buying- and Selling hedging
2.2.1.2 Motive: Asset-, Anticipative- and Strategic hedging .
2.2.1.3 Coverage: Normal-, Perfect-, Texas and Reversed hedging
2.2.1.4 Application: Pure- and Cross hedging
2.2.1.5 Scope: Micro-, Macro- and Portfolio hedging
2.2.1.6 Adaptation: Static- and Dynamic hedging
2.2.2 Arbitrage Trading
2.2.3 Speculation
3 Commodity Nature and Risk of Oil
3.1 Physical characteristics and refining
3.2 Market Participants
3.2.1 Physical seperation
3.2.2 Trading separation
3.3 Structure of the Oil Market
3.4 Oil pricing arrangements
4 Derivative Instruments to mitigate Commodity Risks
4.1 Nature of Derivative Instruments .
4.2 Common Derivative Instruments in Commodity Trading
4.2.1 Symmetric transactions . .
4.2.1.1 Forwards
4.2.1.2 Futures
4.2.1.3 Swaps
4.2.2 Asymmetric transactions .
4.2.2.1 Options
4.2.2.2 Swaptions
5 Risk Mitigation in Practice
5.1 Forwards & Futures
5.2 Swaps
5.3 Options
5.4 Swaptions
6 Conclusion
Appendix
Bibliography
illustration not visible in this excerpt
6.1 Risk-Return graph with different correlation coefficients
6.2 Usage of derivative instrument according to market situation
6.3 US Gallon output of refined products for one input unit of crude oil (=1 barrel)
6.4 Correlation between WTI Crude / Brent Crude in 2001 and 2008
6.5 Regression slope on relationship between spot and future prices . .
6.6 Convenience yield on BRENT and WTI from 1991 to 1996 in US$ per Barrel
2.1 Hedging strategies overview
3.1 Output of the top 5 refining companies worldwide in 2008
4.1 NYMEX WTI and ICE WTI Crude Oil Definition
4.2 Differences between Futures and Forwards
4.3 Amount held by top 3 companies in NYMEX products
4.4 Effect to option type prices on changing attributes
4.5 The Greeks - Option risk measuring with roman signs
5.1 Example calculation: Hedge ratio calculation for futures
5.2 Example calculation: Determination of fair futures hedging prices .
5.3 Example calculation: Hedging effectiveness calculation for swaps .
5.4 Example calculation: Hedging effectiveness calculation for static option hedging (without delta adjustment) - Scenario at time t0
5.5 Example calculation: Hedging effectiveness calculation for static option hedging (without delta adjustment) - Scenario at time t1
5.6 Example calculation: Hedging effectiveness calculation for dynamic option hedging (with delta adjustment) - Scenario at time t0
5.7 Example calculation: Hedging effectiveness calculation for static option hedging (without delta adjustment) - Scenario at time t1
About the only economic break most Americans have gotten in the last six months has been the drastic drop in the price of oil, which has fallen even more precipitously than it rose. (...) Approximately 60 to 70 percent of the oil contracts in the futures markets are now held by speculative entities. Not by companies that need oil, not by the airlines, not by the oil companies. (...) Last year, 27 barrels of crude were being traded every day on the New York Mercantile Exchange for every one barrel of oil that was actually being consumed in the United States.^{1}
The trading environment of the oil market is inherently unstable, with geology, geopolitics, economics, finance, technology, and environmental concerns having a strong impact at anytime on the market structure. Some risk factors of the oil industry are very hard to pinpoint and market price do not always move in predictable corridors. Purely looking at the introducing web article reveals the allegation that a fundamental interest of market participants, producers and consumers - to determine fair price levels for a particular commodity - is endangered by speculative intentions. As seen in the financial crisis those particular markets have gone through peaks and troughs within a very short period of time. Crude oil prices for instance rocketed from US$50 in early 2007 to almost US$140 in summer 2008 before they plummeted to US$35 again at the end of 2008^{2}.
Even if all price determination factors are taken into account, the likelihood of enormous price volatility remains present for the world commodity number one, hence, various depending industries are keen to mitigate those risks adequately. In the context of high oil prices, economists around the world have started to focus on the possibilities of protecting businesses from the dramatic fluctuation of oil prices. Just within the financial crisis it became obvious, that especially trading houses and financial institutions had been able to adjust their portfolios to the new circumstances very quickly and shift their trading positions to the most lucrative areas. Hence, it was no surprise that banks, for example the Bank of America, announced huge profit leaps, even at times when markets reached ultimate volatility^{3}. However, financial institutions are characterized by dedicated trading knowledge and non- asset structures. Contrary, industries such as aviation or refineries may embody the complete opposite, whilst having one thing in common with the banks: their risk exposure to oil^{4}.
The bachelor thesis opt to answer the question how companies can measure their individual risks and react to take adequate counteraction. The following question should be taken as guideline throughout the bachelor thesis:
1. Risk identification: What are the risks the oil market typically imply?
2. Risk measurement: How can companies measure their individual risks they expose into oil?
3. Risk mitigation options: Which instruments do those companies have to limit the various risks, participate in market trends or even leverage strong asset positions to the energy market? 4. Risk mitigation tactics: Which strategy can be applied in different market scenarios using the various instruments?
In summary, the objective upon writing the thesis is to study and analyse the various derivative instruments available on the global financial market and to present practical examples for hedging oil price risks in accordance with widely known hedging strategies.
The accomplishment of the objective shall be done by studying the current strategies on crude oil hedging, by understanding the nature and characteristics for derivative instruments and the oil market. Based on the objective, this bachelor thesis is separated into four chapters.
The first chapter of discovery will cover trading motivations and raw principles of risk and return. After the theoretical foundation is build to understand the need for risk mitigation activities, the next chapter will purely analyse the nature of commodities and oil in particular. This chapter will encircle the price determinations and key drivers for risk associated with oil for various market participants. Markets and oil in particular bear a lot of risks. For the due course of this study, only commodity risks will be within scope, whilst other risks, such as foreign exchange risks, will only be mentioned alongside.
Chapter 4 will then closely examine commonly used derivative instruments to understand how they work and analyse how those instruments can be applied to eliminate risks that have been identified previously.
Before the conclusion is drawn in the last chapter, chapter 5 will bring all parts together and give practical examples for hedging strategies with the usage of various derivative instruments in the oil sector. Although certain theories are pure mathematical and require complex formulas, I will be concentrating on the mathematical basics and determine the high level business benefits that can be derived from them.
Risk is the eventuality of an upcoming adversity in a negative scenario or a benefit in a positive scenario.^{5}
Klaus Spremann illustrates one particular fact about risk: Risk represents uncer- tainty. Moreover, there is a true relationship between risk and the fundamentals of doing business: companies aim for a maximum return^{6}. It seems obvious that companies operating a risky basis increase the likelihood of both the negative and the positive outcome in an extreme amplitude. However, a stable operation policy may contradict the maximum return approach. Therefore, Risk Management is the process of identifying risks and opt to achieving a desired balance of risk and return through a particular strategy. The risk-return framework incorporates the entire business process of selecting, communicating, valuing and achieving this balance within the firm’s portfolio of assets^{7}. Companies with exposures in oil are particularly faced with various types of risk, whereby the most common categories include^{8}:
- Market Risk (Price, Liquidity, Volatility, Correlation)
- Commodity Risk (Storage, Capacity, Delivery, Transmission)
In addition, literature also mentions human risk, such as trader- and management errors or mismodelling, operational risk, such as fire catastrophes and a lack in sufficient and functional operating systems^{9}. For the course of this thesis, market risk - covered in this chapter - and commodity risk - covered in chapter 3- will dominate the attention. For the case of market risk, the portfolio theory provides a good framework to examine facts about volatility and correlation, whilst it will also provide useful steering methods to optimize a portfolio subject to a desired risk-return ratio.
A portfolio is more than a long list of stocks and bonds. It is a balanced whole, providing the investor with protections and opportunities with respect to a wide range of contingencies”^{10}
A portfolio is a collection of assets and financial positions on these assets^{11}. Due to the complexity and the impact a portfolio, companies are reluctant to not optimize and evaluate assets. Hence, one major theory evolved and developed within the last century is the portfolio theory. Harry Markowitz, the founder of the portfolio selection theory, described the relationship between risk and return. His theory became popular very quickly and still builds the solid ground for portfolio managers around the world. In 1990, Markowitz won the Nobel Prize with two other scientist, Merton Miller and William Sharpe, who further described how risk and return interrelate in markets.
In essence, the portfolio theory starts with the following theorem^{12}: an investor will always choose between different portfolios on the basis of their expected return, one the one hand, and risk, on the other. In this context, the standard deviation of a portfolio can be regarded as a measure of the portfolio’s risk. Markowitz deviates with this “efficient portfolio” approach and view of risk to other scientist, who described risk the probability of loss, known as “Shortfall”^{13}. Since Markowitz is seen as the founder of the first portfolio management model which has been extended by other scientist, the proximate chapter will be focusing on this concept solely. According to Markowitz and considering ceterus paribus, an investor wants a portfolio whose return has a high expected value and a low standard deviation. That implies the selection of a portfolio with a maximal return on a given deviation. A portfolio that meets this conditions is efficient, and a rational investor will always choose an efficient portfolio^{14}. The theorem assumes that investors within this model are always seeking for the best risk-return ratio, which means, that a portfolio with a more lucrative expectation, but higher risk, are not within the scope of the investor^{15}. Although, the findings evolved in the early 1950s and new models are regarded as more practical and accurate, portfolio theory helps to understand risk and trading motives. Throughout the bachelor thesis, the terms correlation (how do two values interrelate on price movements), volatility (how do values annually deviate in return over time) and return will be used, though, portfolio theory will even provide the theoretical foundation for them.
In his theoretical model, Markowitz calculates with the following assumptions^{16}:
1. Market participants do not need to take care about transaction cost, nor taxes.
2. All assets within a portfolio can be selected in all possible combinations.
3. The time period is a two-point model in which values are assigned to a portfolio on time t0 and exit the portfolio in time t1.
The following sub-chapters will outline the calculation and methods for the portfolio theory. An example for a fictive company A with two business operations (revenue streams) will utilise the theory.
Portfolio return μ
As shortly outlined beforehand, the return on assets and the portfolio is, together with risk, the key element of the theory. The portfolio return is dependent on return of single assets, which are unknown and can only be measured adequately for the past. As this expected return bears uncertainty and may be influences by certain variables, it can mathematically also be described as the expected value of a random variable:[Abbildung in dieser Leseprobe nicht enthalten]^{17}. Consequently, the expected return, described with the Greek letter µ, arise from the expected return[Abbildung in dieser Leseprobe nicht enthalten] for a single asset [Abbildung in dieser Leseprobe nicht enthalten]^{18}. On the portfolio view, Harry Markowitz calculates the expected return as the sum of the weighted returns of single assets with the following formula^{19}:
Abbildung in dieser Leseprobe nicht enthalten
For an example, asset i is expected to yield 5% p.a. (60% stake in total business operation), while asset j is expected to return 8% p.a. (40% stake in total business operation). According to the formula the expected portfolio return calculates to 6% per annum.
When calculating the expected return of the single assets, often historical data and future price curves are taken into consideration^{20}. Future curves and price developments models will be in focus at a later stage. However, as it can be seen, the return variable builds on expectations, which are highly subjective per se. This, in turn, bears a high risk of failure and mismodelling and may not coincide with the development in equity^{21}. In order to better understand returns and eventually derive the risk variable for the next part of the portfolio management, Markowitz uses the dispersion of returns over time as further described in chapter 2.1.2. This distribution of returns is often better known as the volatility, which is found by calculating the annualized standard deviation of daily change in price.^{22}.
Portfolio Risk σ
Contrary to the return variable, risk is more complex to compute, simply because the calculation requires two parameters: standard deviation and correlation^{23}. As an example, an ice-cream business may generate profits in sommer time, but will ultimately generate losses during winter times. In turn, a local winter sport business may generate cash-flows in the complete opposite manner, which means that both business models on their own bear a specific risk which is negatively related, hence, a combination of both business streams would essentially reduce the risk - for one or the other - of loss generation.
Variance is dependent on the way in which individual securities interact with each other. This interaction is then described as covariance which essentially is the correlation of security returns. Although, covariance measures by themselves do not provide an indication of the degree of correlation between two securities. Due to that, covariance is standardized by dividing covariance by the product of the standard deviation of the two individual securities in question. This standardized measure is then called the correlation coefficient^{24}. Risk therefore comprises of the following two variables^{25}:
- Standard Deviation of return for the single asset n
- Correlation coefficients of returns for the single asset n and n+1
This means for the be-named example, that the standard deviation is about the question how much the average return for the ice-cream business (and the winter sport business) deviates from one season to another and correlation is about the question how much the return of the ice-cream business moves with the return of the winter sport business.
Standard Deviation Assets yield certain profits and losses which can be regarded as returns, whereby the return often means changes in prices or values^{26}. As those return fluctuate over time, it is very important to know the likelihood of price changes, or returns, over time. Hereby, different asset classes evidence distinct behaviours and characteristics, which essentially can be mapped to a probability graph. This graph shows then the unique distribution of return. The standard deviation is thus a statistical tool and is often referred to as “Distribution Analysis” too, providing crucial information about the input data^{27}. In other words, a price distribution defines probabilities of prices taking on various values to show the path of prices. This curve can be described in various ways, whereby the most important figure is the standard deviation, which suggests the width of the distribution and roughly equals the width of the distribution in which a price will fall into 66% of the time (normal distribution without any skew or kurtosis)^{28}.
The other characteristics are as follows^{29}:
- Mean = Represents the value around which the distribution is centered
- Skew = Reflects whether the prices distribute symmetrically around the mean or are skewed to the left or right of the mean.
- Kurtosis = Describes the “fatness” of the tails of the distribution and provide useful information about the likelihood of extreme events.
As such, the standard deviation can be described as follows^{30}:
Abbildung in dieser Leseprobe nicht enthalten
Very often the standard deviation is being mentioned with the terms variance and volatility. Especially the term volatility is of high interest in the trading area and will be used throughout the thesis. Where variance is simply the standard deviations squared, volatility is the price returns’ standard deviation normalized by time, with time expressed in annual terms. For example, if a volatility for a price is 0.1 and if the current price US$20, then over the next year - very roughly - the price is expected to remain within the range of US$18 to US$22 at 66% of the time^{31}.
Covariance and Correlation As a second, the covariance between two particular assets must be incorporated in the calculation. Again, the covariance expresses the relationship between two values and is of high interest throughout the thesis.
Covariances can be computed by the use of the following formula and input vari- ables^{32}:
Abbildung in dieser Leseprobe nicht enthalten
A more practical approach to the covariance is the correlation approach, which is more standardized and results in values between -1 and 1^{33}. In this circumstance -1 means that two values do perfectly correlate in a negative sense, meaning that an increase of 1% for asset i results in a decrease of asset j of about 1% even. Respectively, a correlation of +1 means a perfect correlation between 2 assets and 0 (as the third extreme) does mean two assets do not move in any tandem function^{34}. The formula for the correlation coefficient is thereby as follows^{35}:
Abbildung in dieser Leseprobe nicht enthalten
Having a look to the formula reveals that both covariance and correlation have a
practical problem with huge portfolios. For instance, a portfolio with only 6 values requires 15 covariances / correlations computations already^{36}.
Combination of Standard Deviation and Correlation In order to determine the ultimate formula for risk, the two variables for standard deviation and correlation must be conjoined using the portfolio variance formula^{37}:
Abbildung in dieser Leseprobe nicht enthalten
Alternatively, the variance can be replaced by the standard deviation, which is simply the square root of the variance^{38}:
Abbildung in dieser Leseprobe nicht enthalten
As for the example outlined above, many books show a two-asset formula which is not only more practical to use, but also of high interest for the case of securing an original position with the second counter position: hedging. The formula for the two-asset model is as follows^{39}:
Abbildung in dieser Leseprobe nicht enthalten
For the example, the two assets i (σ = 10%, x = 60%) and j (σ = 20%, x = 40%) have a correlation coefficient cij of -0.60. In total, the portfolio risk σ p therewith calculates to 6.50%. According to the theory and as it can also be obtained from figure 6.1, the optimal combination of assets i and j results in the minimum variance for a the highest possible return. For the example it means, that the investor can optimize the portfolio by changing the weights of assets i and j to 70% (i) and 30% (j).
The Efficient Frontier is a curve that is formed by those combinations and it can be obtained when having a look at the risk-return graph, where all possible combina- tions of the asset weighting are plotted. Starting from the outlined example, the graph comprises four different correlation coefficients, each builds an respective Efficient Frontier^{40}. Figure 6.1 in the appendix shows this frontier with different correlations. Based on this finding, Harry Markowitz assumes that investors derive their investment decisions according to the μ - σ rule, which means that investors will always seek for the maximum return and lowest risk combination.
According to the rule, there is no other portfolio that offers
1. for the same μ (return) a smaller σ (risk) and
2. for the same σ (risk) and higher μ (return) and
3. a higher μ (return) with a lower σ (risk) simultaneously^{41}.
According to Markowitz, all efficient portfolios must be placed upon the efficient frontier which is given by the original risky assets within the portfolio^{42}. In summary, portfolio theory can be shortened to the following investor guideline: spreading risk is an essential part, however, when all asset returns move in the same manner, up- or downwards, the portfolio is not balanced out and will ultimately fluctuate up-and downwards also. Consequently, the extent to which a new asset contributes to portfolio risk mostly depends on the correlation of its return with the returns to the other assets in the portfolio^{43}. One of the key insights the portfolio theory is that the risk of any individual asset is not the standard deviation of the return to that asset, but the extent to which that asset contributes to overall portfolio risk^{44}. Measuring an asset on its own might result in a very high risk figure, although, in correlation with all other acquired portfolio values, the overall portfolio risk might not have surged.
Market risk
Nevertheless, the theory lacks and runs into estimation problems as the determina- tion of the expected market return is highly subjective. Additionally, the input and computation problem for the covariance / correlation should not be underestimated for portfolios with more than 2 positions^{45}. A more prevailing issue with the whole concept of portfolio management, though, is the fact that a certain risk always remains: the market risk. This systematic risk - contrary to the unsystematic risk - is equated with the risk of the market portfolio which represent the market with all assets and their weighting. Unsystematic risks can be managed through portfolio diversification, hereby, diversification reduces unsystematic risks because the prices of individual securities do not move exactly together. Systematic risks, also known as market risk, exist because there are systemic risks within the economy that affect all businesses.
Therefore other scientist further developed the idea from Markowitz and extended the portfolio theory model to better explain risk and return. Both systematic risk and unsystematic risk are mentioned within one important model: CAPM. Due to the introduction of a risk free security, such as sovereign state bonds or bank deposits, the model changes the efficient frontier from a curved line to a straight line called the Capital Market Line (CML)^{46}. This CML represents the allocation of capital between risk free securities and risky securities for all investors combined. The optimal portfolio for an investor is the point where the new CML tangents the efficient frontier. This optimal portfolio is normally known as the market portfolio. The introduction of a risk free asset changes the risk of a portfolio because risk-free securities have zero covariance and zero correlation with risky assets)^{47}. Investors who are unwilling to accept systematic risks have two options. First, they can opt for a risk-free investment, but they will receive a lower level of return. Higher returns are available to investors who are willing to assume systematic risk. However, they must ensure that they are being adequately compensated for this risk. The other alternative is to hedge against systematic risk by transferring the risk to another market party.
Often, the correlation between the systematic risk (market portfolio) and a portfolio
or a single asset is better known as the beta-factor and be calculated using the following equation^{48}:
Abbildung in dieser Leseprobe nicht enthalten
where
β = beta-factor for an expected return of asset i with the return ri and a market portfolio r_{M}
COV (r i, r _{M}) = covariance between the expected returns r i and a expected market portfolio return r_{M}
VAR (r_{M}) = variance for the expected return of the market portfolio rM
For instance, a portfolio with a β = 0.7 means, that the portfolio is less volatile than the market it was compared to. By definition, the market has a beta of 1. Essentially, there are three categories that the beta-factor can take on^{49}:
- β > 1 = The expected return of the single value ri deviates stronger than the expected return for the market portfolio rM
- β = 1 = The expected return of the single value ri equals the expected return for the market portfolio rM
- β < 1 = The expected return of the single value ri deviates less than the expected return for the market portfolio rM
The beta-factor enables a company to better judge the position in respect of the market and can help to value the likelihood of up- and downswing effects in an easy manner. Yet, companies with risk exposure into commodities, still have problems in securing their positions in the long-run. First, the portfolio of the company may consist several positions and business unit: how can a company measure the risk and returns? What is the expected loss if a core exposed commodity surges by 30% in the next year? Second, evaluating the beta-factors and market portfolios bears a data computation problem: how can a company derive better estimate expected return values? What are the key drivers for the future price development of the economy and single commodities?
[...]
^{1} See CBSnews.com (2009)
^{2} Cf. OPEC (2008)
^{3} See WiWo.de (2009)
^{4} Cf. Kellett (2004, p. 8)
^{5} Cf. Spremann (2003, p. 168)
^{6} Cf. Pilipovic (2007, p. 157)
^{7} Cf. Pilipovic (2007, p. 159)
^{8} Cf. Pilipovic (2007, p. 160)
^{9} Cf. Pilipovic (2007, p. 161)
^{10} See Markowitz (1991, p. 3)
^{11} Cf. Pilipovic (2007, p. 162)
^{12} Cf. Dowd (2005, p. 15)
^{13} Cf. Spremann (2003, p. 170)
^{14} Cf. Dowd (2005, p. 6)
^{15} Cf. Dowd (2005, p. 7)
^{16} See Manfred Steiner (2002, p. 8-9)
^{17} Cf. Spremann (2003, p. 133)
^{18} See Spremann (2003, p. 134)
^{19} See Eller (1999, p. 310)
^{20} Cf. Eller (1999, p. 312)
^{21} Cf. Spremann (2003, p. 312)
^{22} Cf. Spremann (2003, p. 154)
^{23} Cf. Spremann (2003, p. 185)
^{24} Cf. Christoph Bruns (2003, p. 626)
^{25} Cf. Spremann (2003, p. 185)
^{26} Cf. Pilipovic (2007, p. 74)
^{27} Cf. Pilipovic (2007, p. 75)
^{28} Cf. Pilipovic (2007, p. 75)
^{29} Cf. Pilipovic (2007, p. 76)
^{30} Cf. Pilipovic (2007, pp. 77, 78)
^{31} See Pilipovic (2007, p. 217)
^{32} See Manfred Steiner (2002, pp. 10f)
^{33} Compare Christoph Bruns (2003, p. 626)
^{34} Cf. Christoph Bruns (2003, p. 626)
^{35} See Christoph Bruns (2003, p. 627)
^{36} But Cf. Povilas Ani unas (2009, p. 21)
^{37} See Pilipovic (2007, p. 33)
^{38} See Spremann (2003, p. 189)
^{39} See Spremann (2003, p. 189)
^{40} Cf. Spremann (2003, p. 190)
^{41} See Manfred Steiner (2002, p. 8)
^{42} Cf. Spremann (2003, p. 193)
^{43} Cf. Dowd (2005, p. 7)
^{44} See also Spremann (2003, p. 191)
^{45} But cf. Povilas Ani unas (2009, p. 21)
^{46} Cf. Spremann (2003, p. 211)
^{47} Cf. Spremann (2003, p. 212)
^{48} See Spremann (2003, p. 256)
^{49} See Spremann (2003, p. 257)
Masterarbeit, 82 Seiten
Masterarbeit, 70 Seiten
Magisterarbeit, 53 Seiten
Masterarbeit, 82 Seiten
Masterarbeit, 70 Seiten
Magisterarbeit, 53 Seiten
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