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| Type | Bachelor's Thesis |
| Scope | Discipline-based scholarship |
| Title | Affine models of the commodity term structure |
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| Institution | University of Zurich |
| Faculty | Faculty of Economics, Business Administration and Information Technology |
| Date | 2011 |
| Zusammenfassung | Introduction As commodity markets have witnessed a significant growth over the recent years a growing body of publications has evolved, proposing a variety of commodity term structure models. The most prominent ones by E.S. Schwartz (1997) and the well known “Theory of storage” by Kaldor (1939) serve as theoretical basis for this thesis. Theses models will be estimated and analysed by measuring their performance in a mean reversion long-short strategy based on the difference between the calculated model future price and the observed market price of eleven commodities spread over all five commodity categories. The four implemented models are: Mean reverting spot price, mean reverting convenience yield, long term price reversion (fix) and long term price reversion with a dynamic term structure. Method Bloomberg data of future contract maturities of up to 5 years is fed into the Matlab framework and compared with the calculated model prices from the four available models out of historical data. The calculated difference of this observed data and model data, triggers a short term investment decision based on under- or over-valuation of a specific contract, going long the most undervalued contract and shorting the most overvalued one till the next evaluation period. So to speak the strategy has no market risk exposure, as it is flat in the underlying it realizes only model and term structure risk. Performance and risk measures are then derived from the resulting profit and loss time series (value at risk, standard deviation, maximum draw-down etc.). In addition to that a detailed analysis on the characteristics of the trading decisions is made (which maturities, long/short, difference between maturities, development of the convenience yield etc.) to understand precisely what the strategy does and to identify possible systematic behaviour. A comparison to selected benchmarks (risk-free 3Mt LIBOR, S&P 500 and Goldman Sachs Commodity Index) completes the view on the models performances. Conclusion Data shows that, notwithstanding the fact that commodity prices appear to move randomly, significant profits can be realized with term structure based trading strategies, which don't include direct exposure to market risks of the underlying commodity. Plotted in a risk-return graph, most models perform reasonably, but the long term price reversion models are two real out-performers, that beat benchmarks and the other models in a significant way. A statement in current literature, that information from the different ends of the curve leads to “prices with no economical sense” (Lautier, 2003a, p.17) in calculations could not be reproduced, as shown in the maturity selection histogram of the long term price models, that use 5y contract information for the calculation of the whole reference term structure and prices. Some extraordinary high performances of agricultural commodities, were possible within the models as they showed some very illiquid contracts with unchanged prices over long time spans, which led to artificial under/over valuation and therefore unrealisable returns. Though a certain minimum trading activity on the whole curve is needed, as it is the case with most energy commodities, so that the models work properly. The models work fine for energy commodities and industrial metals but a successful application to agricultural commodities and precious metals could not be confirmed with the available price data. |
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