The key ingredient in models of ‘growth-at-risk’ is an index of financial conditions. If you want to understand how financial conditions affect growth risk, you need a good measure of said financial conditions.
The usual approach is to use the Chicago Fed’s National Financial Conditions Index (NFCI), which we have used before. The NFCI is constructed by averaging the z-scores of more than one hundred measures of financial stress. This is problematic at three levels. First, most variables contain more noise than signal so that averaging over lots and lots of them lowers the signal-to-noise ratio. Second, some of these variables are almost certainly causally downstream from others — which means that conditioning on them simultaneously is not kosher, as I explained in the previous dispatch in a slightly different context. Third, empirically, the NFCI responds very weakly to market developments. For instance, it barely budged last March when financial conditions were extremely tight (see graph below). So the NFCI is quite problematic as a measure of global financial conditions.
Adrian and coworkers have therefore resorted to construct their own measure of financial stress. The strategy is to carry out a partial least squares regression of the NFCI on seven macrofinancial variables including risk spreads, the VIX and property returns. Again, this is problematic at two levels. First, property returns (on the house price index and commercial real-estate index) are causally downstream from risk spreads and the VIX — they do not belong in the same regression. Second, anchoring to the NFCI sort of defeats the purpose of the exercise. We want to do better than the NFCI, not track it! So this solution not entirely satisfactory.
OK, so we should throw out the property returns and keep the risk spreads. But what should the left-hand side variable be? It can’t be GDP growth (as in the “macro risk premium” of Adrian et al. 2010) because the point of constructing the FCI is to predict growth risk — that’d be like assuming the answer.
I think I have hit upon the solution. Let’s say we want to combine the information in a number of risk spreads. The next graph displays the term spread (T10Y2Y), credit spread (BAA10Y), High Yield spread (BofA OAS), mortgage spread (30-year prime rate less the yield on the 30-year bond), the VIX, and the SP500. All of these variables contain information on financial conditions in real time. When the various credit spreads widen, when the VIX rises, when the SP500 falls, financial conditions tighten. The interpretation of the term spread is not so obvious because of a confounding structure: wider term spreads increase forward-looking estimates of bank net worth, who respond by increasing lending. So, unlike credit spreads, it is not clear at all that wider term spreads mean tighter financial conditions — this is one reason why summing the z-scores of lots of variables doesn’t work.
In fact, if you look at the correlation between these variables (all of whom are observable in real time at arbitrary frequencies), you see the astonishing fact that the term spread is positively correlated with returns on the SP500 and negatively correlated with the credit spreads.
The next graph shows the hierarchical clustering of the same (using Ward’s method and Pearson’s correlation metric). The term spread clusters with the SP500, the credit spreads cluster tightly together, the mortgage spread and the VIX cluster weakly together. The last four are at a great patristic distance — distance measured along the tree — from the first two because higher values of the former indicate tighter financial conditions while higher values of the latter (SP500, T10Y2Y) indicate looser financial conditions.
Looking at the correlation structure of these variables, the solution immediately suggests itself. What should replace the NFCI on the left-hand side of the partial least squares (PLS) regression is market returns. The logic is obvious: variables that are contemporaneously correlated with market returns are polarized in one direction (higher values imply looser financial conditions), variables that are anti-correlated with market returns are polarized in the other direction (higher values imply tighter financial conditions). The former should therefore enter with a positive sign; the latter with a negative sign. In fact, PLS does this automatically. The loadings that we obtain from the PLS regression estimator are the signed weights we ought to use to obtain our FCI from the risk spreads. The key idea here is to replace the NFCI on the left-hand side with market returns.
But the estimation problem must be approached with care. We must first-difference the spreads to avoid spurious correlations. Handling the VIX requires even greater care. Because it is fat-tailed we log transform it. But because it is already a derivative quantity, we do not first-difference it. For the SP500, we use log returns. Finally, we robustly standardize all variables to have zero mean and unit variance. We work at the weekly frequency. The heat map and hierarchical clustering tree shown above display information from the correlation matrix of these transformed variables. The next graph shows the loadings of the response — the PLS algorithm guarantees that the linear combination of the variables with these signed weights has the highest correlation with market returns.
We construct the FCI as a linear combination of the z-scores of the original variables (spreads and log VIX levels) using the loadings as the coefficients. We center the FCI at 100, so that values higher than 100 denote looser than average financial conditions and conversely. The next graph displays the FCI thus obtained. Market observers will recognize the high fidelity of the information on financial conditions captured by our measure.
Our FCI can be aggregated or constructed at lower frequencies (say quarterly) or higher frequencies (say daily or by tick time). The next step is to test whether our measure of financial conditions contains more predictive information about growth risk than the NFCI and other measures that track it, such as Adrian et al.’s PLS-FCI. The other direction I would like to investigate is whether our measure of financial conditions contains significant predictive information about future returns. That is, does it make a good return-forecasting variable for dynamic asset pricing? And further down the line, can we use it to design systematic trading strategies that yield superior risk-adjusted returns without using any leverage at all — such as the one we explored in ‘Strategic Asset Allocation’? This is exciting stuff.
Question: they claim to have 100+ indices for NFCI, is it possible to do a mass hierarchical categorization of a larger set of base indices to see if the S&P and VIX/Spreads being tied up to other factors (e.g. employment, material cost change, global trade, stocks v income) since there might be a Turchin-esque double helix going on.