Generalized Autoregressive Conditional Heteroskedasticity Finance Essay - Free Essay Example

Many companies, both producers and/or users of commodities can be negatively impacted by sudden price changes in their production inputs or outputs. Producers of commodities such as in the mining, oil or farming industries would sure benefit from increasing prices of their respective outputs, but face a risk of very serious losses and even bankruptcy should the opposite happens. On the other hand, within those industries and most others, some commodities are also used as production inputs and therefore would negatively impact companies may prices rise. In all cases, the overall price volatility in commodities is often negatively perceived and, to the extent of a companys level of exposure to commodities in its production process, can be seen as a very serious business risk. (). In order to reduce some of the risk and often with the objective of protecting their profit margins, companies will resort to hedging. The risk management strategy of hedging can be described as a way limit or offset the probability of a loss from the volatility in the price of a commodity, securities and/or currency (Hull, 2012). For the purpose of this thesis, a hedge will be defined as taking a short position in the futures market in order to cover one contract of a long position held in the spot market by the hedger. Other derivatives such as forward contracts or options are also used for hedging purposes, but futures are seen as the most dominant in commodity markets mainly because of their liquidity and transparency advantages (Geman, 2005). The exact amount of the futures contract to be purchased against that one spot position is called the hedge ratio (HR) and the HR chosen to minimize the variance (volatility) of the hedgers portfolio will be referred to as the minimum varia nce hedge ratio (MVHR). Countless research papers have been written about MVHR, its relevance and the different ways of estimating it (see, for example Johnson 1960; Ederington, 1979; Myers 199). With constant advancements in the field of Econometrics, researchers began investigating more and more complex methods to derive the MVRH, for example by incorporating time variation into the estimation of the variance-covariance matrix (see, for example .. ****************). However, no clear consensus has been reached yet on the best ways to construct a MVHR, and many of the empirical studies considering assumptions and estimated variables, concluded to somewhat contradictory results. Furthermore, many of the newer, more complicated models require cumbersome econometric models and, therefore, might not be most suitable for actual use by companies in the commercial world. This thesis aims at capturing the recent advancement made on the MVHR while considering and testing models that could be considered as (to be continued (About 1 more page)talk a bit about the commodities +++ the rest of this thesis willÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¦ÃƒÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¦ ) Framework The Spot and Futures Markets The spot market can be defined as a market where a commodity is bought or sold for immediate (or with a minimum lag) physical delivery. Not that long ago, those markets where actual physical places where buyers and sellers would meet to exchange, for example, their crops. Its important to note that all commodities are traded on spot markets. In the 18th century, some U.S. farmers started selling their own crops at the time of planting to help finance them and across the ocean, in London, metal began trading in the same fashion, leading the way to the first derivative market: the forward market (Geman, 2005). We can consider this market as an informal one where over-the-counter contracts for future delivery of commodities are exchanged by participants. The standardization of such informal markets by ways of controlling quantities, qualities, dates of deliveries and locations, led to the establishment of the Futures exchanges (Bailey, 2005; Hull, 2012). Some of the better known exchanges are, for example, the Chicago Board of Trade (CBOT) founded in 1848 (agricultural and financial futures), the Chicago Mercantile Exchange (CME) founded in 1874 (livestock and financial), the New York Mercantile Exchange (NYMEX) (precious metal and energy) and the London Metal Exchange (LME) (base metal). On these exchanges, standardized contracts are bought and sold by a variety of participants with different objectives. First we have the hedgers, whose opposite positions to their own spot exposure have for goal to reduce risk and protect their profit margins. Second we have the speculators who, taking advantage of the quasi costless characteristic of futures contracts, will use them to speculate on commodity prices. Third comes the arbitrageurs whose presence is essential to make sure the relationship between spot and future prices as well as prices on different exchanges remains true. In principal, the value of a futures contract should approximat e the spot market price plus the cost of carrying the commodity, such as interest, storage and insurance costs. If such difference came to exist, arbitrageur would take position in the markets making a risk free profit and bringing prices back in line in the process. And finally, futures, often due to their unique correlation to financial markets, are now increasingly used by portfolio managers in order to hedge their general portfolio risk (Bailey, 2005; Geman, 2005). Hedging with Futures Contracts As previously discussed, hedging is primarily done with intent of reducing risk. Four basic categories of futures exists where the underlying can be a physical commodity (such as it is the case in this thesis), a foreign currency, an asset earning interest or and index (Hull, 2012). Also, different hedging strategies exists as some hedgers want to protect only part of their exposure sometimes due to a certain risk profile or some industry standards, and others, highly risk averse participant, will choose to eliminate the price risk as much as possible, often preferring to protect their profit margins deriving from their main business activities. Throughout this thesis such an assumption will be made as the HR will be built with the intent of hedging as much as possible the exposure of a risk-averse hedger. This can be referred to as a pure risk-avoidance hedging strategy (Bailey, 2005). In practice, hedgers will use futures contracts in two ways. Companies knowing they will have to buy a certain asset in the future can choose to lock in the price of that asset and buy a long position in a related futures contract (referred to as a long hedge). Alternatively, some companies such as commodity producers will know the approximate quantity of an asset they will have to sell in the future and will want to lock in today the price of that asset (this is referred to as a short hedge). The later way will be used in this thesis to construct the hedged portfolio used in order to assess the hedge effectiveness. As only the variance reduction is considered, using either ways would give the same results. Basis Risk Although hedging aims at reducing risk, doing it right is often not as simple as just buying or selling the opposite quantity of the exposure. This is mainly due to the introduction of basis risk in the equation. Understanding it is essential to understand the reasons being the HR. Basis is defined as: Best example of Basis risk is the German Company and its oil positionÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¦ A Look at the Selected Commodities Optimal Hedge Ratio OHR A Review Static versus dynamic hedging OHR for Commodities OHR The Methods To perform an empirical study of the minimum variance hedging strategy, the HR needs to be estimated with the help of some statistical models. (see (19) page 8) No Hegde NaÃÆ'ƒÂ ¯ve Hedge Constant OLS Rolling window OLS EWMA OLS Simplified GARCH (1,1) Data Analysis As the aim of this thesis is to provide evidence of the best hedge ratio methodology using recent data, only the quantitative approach will be used, providing empirical results onÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¦. Statisitcal MethodologyÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¦ Introduce the reason for the 3 periods (financial crisis.. volatility effect, etc) Statistical Tests Test for Normality Test for Stationary Time Series Test for Autocorrelation Test for Heteroskedasticity Statistical Tests Results Delimitations and Assumptions The main assumption in this thesis, as it also is in most literature relating to OHRs, is that the hedger has perfect knowledge of the amount of commodities needed or produced at a future date. In reality, this is obviously rarely the case, therefore producers or users of commodities will use estimates to construct their hedging strategy (). Delimitations: This thesis do not differentiate between long and short hedgers, exclude foreign exchange risk and possible correlation, Only cover Futures (not Options and FWDs), Focus only on Commodities, No forcast tool intended Only OLS (normal + rolling window) is used, leaving aside GARCH etc Assumptions: Risk aversion, In this thesis, as it the case for most of the literature written on OHRs, only the variance is used as the measure of risk (see for example: balbalbal), therefore making the generally accepted assumption which gives equal weight to both positive and negative returns. Since Markowitz (1952), the variance became the most widely used measure of risk but this traditional approach has been criticized by some (Cotter 2005, etc) who suggested that OHR estimations could be improved if tail specific metrics such VaR, Semi-Variance and LPM were also evaluated. (is this needed because of risk aversion ) Other assumptions: The hedge period is set and sure at the time od hedging No FX is considered Empirical Findings Optimal Hedge Ratio The Results Discussion () Conclusion There is no question to the importance for companies of having a sound and tested risk management strategy. As one of the most traded derivative instruments for commodities, futures certainly play an important role in the hedging process. Appendix