# Factor model for Gold has low adjusted R2

I am trying to build up a factor model for gold. To be able to identify the correct factors, I did a correlation analysis between a few factors vs gold and I integrated this analysis with what I saw in literature. I ended up with a set of factors as: VIX Index, EURUSD currency, H15X10YR Index (which is the US 10YR real rate). However, after running my ridge regression (I choose ridge due to the fact that I had already an idea of the factors and they are only 3, otherwise in case of many factor and no idea I would opt for lasso), my adjusted R2 is "only" 36%..am I missing something? after checking the time history I see that the gold has quite a similar trend with my factors, especially with the H15X10YR Index, but my level of "explicability" is only 36%. Can anybody highlight me on the reason of this please? Luigi

• Are you using past values of those factors to predict gold returns? Or using contemporaneous returns to just explain gold returns? – kurtosis Aug 13 '20 at 23:09
• You should be careful in interpreting the $R^2$ as a measure of explicability. It is very sensitive to a variety of things and the regularization implies it is no longer the square of the Pearson Product Moment Correlation Coefficient. Since $R^2$ is poor measure of goodness of fit and is not a measure of model quality, you should be careful in interpreting it or granting it too much importance. – Dave Harris Aug 14 '20 at 3:29
• @DaveHarris, thanks for highlight these aspects on R2. if not R2, what would you suggest to use to measure the explicability of a factor model? any other metrics? in terms of model quality I use purged with embargo cross validation for estimating the regularization parameter. thanks – Luigi87 Aug 14 '20 at 7:15

I will assume you are using factors and gold returns that are contemporaneous. With that setup, you are essentially trying to explain or decompose gold returns.

For an explanatory regression of a commodity (which is internationally traded), an $$R^2$$ of 36% is pretty good. Lots of factors can affect gold returns: Indian wedding season (a major effect on gold markets which you should not overlook), volatility in developing market currencies, and hyperinflation in large economies. You are omitting all of those effects. To still explain 36% of the variance is something to be proud of.

You may have expected more, but working with returns reveals how explaining changes in an asset isn't as simple as just showing a few similar-looking plots and exclaiming voila! I would not be upset at getting a 36% $$R^2$$ for my first model and one using only three factors.

• the returns I am using go from 2003 up to june 2020. Thanks for your answer. I am not indeed prone to look at how much the time histories are similar, cause I know the visual check can be misleading but this time was pretty evident they were similar. Anyway as you pointed out there may be many other factors which I kept out. – Luigi87 Aug 14 '20 at 7:08