TY - UNPB

T1 - The role of cointegration for optimal hedging with heteroscedastic error term

AU - Gatarek, Lukasz

AU - Johansen, Søren

PY - 2017

Y1 - 2017

N2 - The role of cointegration is analysed for optimal hedging of an h-period portfolio. Prices are assumed to be generated by a cointegrated vector autoregressive model allowing for stationary martingale errors, satisfying a mixing condition and hence some heteroscedasticity. The risk of a portfolio is measured by the conditional variance of the h-period return given information at time t. If the price of an asset is nonstationary, the risk of keeping the asset for h periods diverges for large h. The h-period minimum variance hedging portfolio is derived, and it is shown that it approaches a cointegrating vector for large h, thereby giving a bounded risk. Taking the expected return into account, the portfolio that maximizes the Sharpe ratio is found, and it is shown that it also approaches a cointegration portfolio. For constant conditional volatility, the conditional variance can be estimated, using regression methods or the reduced rank regression method of cointegration. In case of conditional heteroscedasticity, however, only the expected conditional variance can be estimated without modelling the heteroscedasticity. The findings are illustrated with a data set of prices of two year forward contracts for electricity, which are hedged by forward contracts for fuel prices. The main conclusion of the paper is that for optimal hedging, one should exploit the cointegrating properties for long horizons, but for short horizons more weight should be put on the remaining dynamics.

AB - The role of cointegration is analysed for optimal hedging of an h-period portfolio. Prices are assumed to be generated by a cointegrated vector autoregressive model allowing for stationary martingale errors, satisfying a mixing condition and hence some heteroscedasticity. The risk of a portfolio is measured by the conditional variance of the h-period return given information at time t. If the price of an asset is nonstationary, the risk of keeping the asset for h periods diverges for large h. The h-period minimum variance hedging portfolio is derived, and it is shown that it approaches a cointegrating vector for large h, thereby giving a bounded risk. Taking the expected return into account, the portfolio that maximizes the Sharpe ratio is found, and it is shown that it also approaches a cointegration portfolio. For constant conditional volatility, the conditional variance can be estimated, using regression methods or the reduced rank regression method of cointegration. In case of conditional heteroscedasticity, however, only the expected conditional variance can be estimated without modelling the heteroscedasticity. The findings are illustrated with a data set of prices of two year forward contracts for electricity, which are hedged by forward contracts for fuel prices. The main conclusion of the paper is that for optimal hedging, one should exploit the cointegrating properties for long horizons, but for short horizons more weight should be put on the remaining dynamics.

KW - Faculty of Social Sciences

KW - hedging

KW - cointegration

KW - minimum variance portfolio

KW - maximum Sharpe ratio portfolio

KW - C22

KW - C58

KW - G11

KW - hedging

KW - cointegration

KW - minimum variance portfolio

KW - maximum Sharpe ratio portfolio

M3 - Working paper

T3 - University of Copenhagen. Institute of Economics. Discussion Papers (Online)

BT - The role of cointegration for optimal hedging with heteroscedastic error term

ER -