Выбор модели для расчета динамического коэффициента хеджирования
This paper studies the problem of calculation the dynamic hedge ratio for the portfolio consisted of two assets. Commonly it’s solved assuming that the investor’s risk aversion is infinite. Then the optimal hedge coefficient is equal to ratio of covariance of the hedged and hedging assets to the variance of the latter. It’s natural to assume that the optimal hedge ratio also dependы on the investor’s attitude to risk. In this paper this fact is implemented via maximization of the investor’s expected utility, which depend on the portfolio return and variance. Consequently if, for example, prices move upwards, the optimal hedge ratio is less than under the assumption of absolute risk aversion and vice versa. In the paper eight portfolios, consisted of Russian blue-chip stocks and futures, are estimated. Multivariate volatility models GO-GARCH and cop-GARCH are applied to estimate the conditional covariances and variances of hedged portfolio returns. There are additional parameters in the error term distribution, including skewness parameter, due to the existence of asymmetry effects in the financial assets returns’ distribution [Kroner, Ng, 1998]. The hedge effectiveness is estimated on the out-of-sample period using the maximum attainable risk reduction, unconditional variance of hedged portfolio returns and financial result. It’s shown that in six cases cop-GARCH surpasses GO-GARCH in hedge. Including the degree of risk aversion in the investor’s utility function together with above-mentioned volatility models allows to increase hedge effectiveness up to 65% for some assets
The article is devoted to the estimation of multivariate volatility of a portfolio consisted from twenty American stocks. The six specifications of multivariate volatility models are formulated and estimated. It’s demonstrated that spatial specifications of multivariate volatility models allow not only reduce the dimension of the problem, but in some cases outdo original specifications at in-sample and out-of-sample comparison.
The paper studies the problem of dynamic hedge ratio calculation for the portfolio consisted of two assets – futures and the underlying stock. We apply the utility based approach to account for the degree of risk aversion in the hedging strategy. Seventeen portfolios, consisted of Russian blue-chip stocks and futures, are estimated in the paper. In order to estimate the conditional covariances of hedged portfolio returns, such multivariate volatility models as GO-GARCH, copula-GARCH, asymmetric DCC and parsimonious stochastic volatility model are applied. The hedging efficiency is estimated on the out-of-sample period using the maximum attainable risk reduction, the financial result and the investor’s utility. It’s shown that for 60% of portfolios ADCC surpasses the other models in hedging. Including the degree of risk aversion in the investor’s utility function together with above-mentioned volatility models allows to reach hedging efficiency of 88%.