ARBITRAGE AND THE FORWARD GOLD PREMIUM: REPLY.

This section responds to a comment on an article which observed a positive relationship between the dollar forward premium on gold and the ratio of gold to dollar assets in international reserve portfolios. In addition to the specific application to the study, the author's comment suggests a general problem for empirical portfolio studies that he does not explicitly identify. Multicollinearity plagues all empirical portfolio studies, almost by definition. An analysis of demand for an asset must include rate of return on assets that are close substitutes. But if assets are close substitutes so that they appear together in portfolios, the behavior of utility-maximizing portfolio managers means that the return on assets will be highly correlated, just as the author observes is the case for dollars and gold. But this problem only has operational significance if the correlation among explanatory variables is so high as to result in overly enlarged standard errors on the estimated coefficients attached to explanatory variables. The only gain to correcting for multicollinearity might be reduction of some of the standard errors. In general, the multicollinearity problem can be reduced if it is possible to show that n explanatory variables can be reduced to n-1 by means of a nearly exact linear relationship between any two explanatory variables.