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Multi-Period VaR-Constrained Portfolio Optimization with Applications to the Electric Power Sector

Paul R. Kleindorfer and Lide Li

Year: 2005
Volume: Volume 26
Number: Number 1
DOI: 10.5547/ISSN0195-6574-EJ-Vol26-No1-1
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Abstract:
This paper considers the optimization of portfolios of real and contractual assets, including derivative instruments, subject to a Value-at-Risk (VaR) constraint, with special emphasis on applications in electric power. The focus is on translating VaR definitions for a longer period of time, say a year, to decisions on shorter periods of time, say a week or a month. Thus, if a VaR constraint is imposed on annual cash flows from a portfolio, translating this annual VaR constraint into appropriate risk management/VaR constraints for daily, weekly or monthly trades within the year must be accomplished. The paper first characterizes the multi-period VaR-constrained portfolio problem in the form Max {E � kV} subject to a set of separable constraints over the decision variables (the level of assets of different instruments contained in the portfolio), where E and V are, respectively, the expected value and variance of multi-period cashflows from operations covered by the portfolio. Then, assuming the distribution of multi-period cashflows satisfies a certain regularity condition (which is a generalization of the standard Gaussian assumption underlying VaR), we derive computationally efficient methods for solving this problem that take the form of the standard quadratic programming formulations well-known in financial portfolio analysis.



Modeling Term Structure Dynamics in the Nordic Electricity Swap Market

Dennis Frestad, Fred Espen Benth, and Steen Koekebakker

Year: 2010
Volume: Volume 31
Number: Number 2
DOI: 10.5547/ISSN0195-6574-EJ-Vol31-No2-3
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Abstract:
We analyze the daily returns of Nordic electricity swaps and identify significant risk premia in the short end of the market. On average, long positions in this part of the swap market yield negative returns. The daily returns are distinctively non-normal in terms of tail-fatness, but we find little evidence of asymmetry. We investigate if the flexible four-parameter class of normal inverse Gaussian (NIG) distributions can capture the observed stylized facts and find that this class of distributions offers a remarkably improved fit relative to the normal distribution. We also compare the fit with that of the four-parameter class of stable distributions; the NIG law outperforms the stable law in the vast majority of cases. Thus, the NIG family of distributions, which allows for stochastic dynamics in terms of L�vy processes that are suitable for pricing derivatives and Value-at-Risk measurements, is a serious candidate for modeling term structure dynamics in the Nordic electricity market.



Comparing the Risk Spillover from Oil and Gas to Investment Grade and High-yield Bonds through Optimal Copulas

Md Lutfur Rahman, Syed Jawad Hussain Shahzad, Gazi Salah Uddin, and Anupam Dutta

Year: 2022
Volume: Volume 43
Number: Number 1
DOI: 10.5547/01956574.43.1.mrah
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Abstract:
This paper compares the tail dependence and risk spillovers from the oil and gas to high-yield (HY) and investment grade (IG) bond markets. We use time-varying optimal copula framework to examine the dependence and further quantify upside and downside risk spillovers. We also explore how energy futures can be used to hedge risk of HY and IG bond portfolios. Our results show that the bond returns are more sensitive to risk shocks in the oil market compared to gas market. We find both negative and positive tail dependence between the bond and energy pairs and the relationship is stronger during the oil-crunch period. The dependence however is asymmetric across the tails. Finally, compared to oil futures, gas futures are found to be better hedge for the bond investment. These results can help in managing portfolio risk and designing optimal asset allocation strategies. These might also assist in formulating policies and regulations to manage the effects of cross-market risk transmissions.





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