Volatility Trends and Optimal Portfolios: the Case of Agricultural Commodities
While the financial world is experiencing a crisis, the prices of most agricultural commodities have remained high, although exhibiting extreme volatilidy. Motivated by evidence showing that volatility trends are present in agricultural commodity prices, we analyze stochastic processes whose unconditional variance changes with time. This analysis suggests a semi-parametric model for capturing the trending behavior of second moments, in which these moments are polynomial-like functions of time. Based on this model, we formulate the portfolio problem faced by an investor when the variances and the covariances of the returns of the available assets are trending. Then, we obtain an approximate solution of the problem, which is based on the consistent estimation of the order of variance-covariance growth and apply it for the construction of an optimal portfolio of agricultural commodities. It is shown that the performance of this portfolio is superior to those of alternative portfolios which are formed by employing methods not accounting for the presence of volatility trends in commodity returns.
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