The traditional approach to invest in different asset classes in order to achieve portfolio diversification proved to be of limited utility during the 2008 financial crisis. Many asset classes provided little diversification as their correlations increased, indicating they respond to similar fundamental drivers.

The shift from asset classes to factor models found a renewed interest. Factor models try to explain common sources of risk and return amongst individual securities. A good starting point to build a parsimonious factor model that explains most of the cross-sectional risk of multi-asset portfolios could be a simple set of macro drivers, such as: equity, interest rates, credit and commodities:

- Equities measure long term global growth and overall profitability of companies
- Rates measure the time value of money, specifically how future rates and inflation modify asset values
- Commodities measure prices for hard assets, capturing supply-demand
- Credit measures corporate defaults and risk aversion to illiquidity

From the above, only equity and rates can be directly mapped to risk factors and considered “pure”: equities is a “risk on” factor that measures growth and profitability, whereas nominal rates is a “risk off” that measures uncertainty in future cash flows. Corporate credit and commodities are less straightforward as they measure overlapping risk factors.

Corporate credit, for example, measures both “risk on” and “risk off” components within the same security. We wrote about that in a related article.

Thus, in order to build a factor model that captures economic growth, inflation, illiquidity and risk aversion using the 4 macro factors above, we need to do something about credit and commodities. To see why this is the case, let's build a simple correlation with 4 liquid ETFs proxying for the 4 macro factors above, namely: SPY, AGG, HYG and GSG:

This correlation is obtained with daily returns for the 4 ETFs using 15 years of data. It can be seen that AGG captures a unique driver of risk but the lower 3x3 sub-matrix comprised of HYG, SPY and GSG is highly correlated. High yield has a 70% positive correlation with equities.

Before these macro factors can be used to capture fundamental drivers of risk and return across asset classes we need to orthogonalize them. The literature prescribes a statistical method called PCA (principal component analysis) to do that. We prefer something more intuitive and simpler:

Assuming that equities and rates are building blocks, we proceed to orthogonalize our corporate credit proxy by finding its residual after “removing” the effect of the building blocks:

$$ \small X_{creditPure} = X_{credit} -\left[\beta_{equity} X_{equity} + \beta_{rates} X_{rates}\right] $$

The above residuals are computed with a rolling window of 90 days and exponential decay. Technically speaking they incorporate both the constant intercept plus the residual. If we plot %% \small X_{creditPure} %% as an index rebased to 100, the last 3 years of total return look like this:

The light green plot above is for HYG: it's total return for the last 3 years would be close to 15%, indicating the benefits of global growth and profitability. The dark plot indicates the total return of the "pure HYG", when influences from rates and equity have been removed. It's total return is close to -12%, indicating that risk aversion to illiquidity, which is what remains after equity and nominal rates are removed, would have been detrimental given the exuberance experienced in the last 3 years.

Next we proceed to orthogonalize the commodities proxy against the 3 pure factors using the same procedure.

$$ \small X_{commodityPure} = X_{commodity} -\left[\beta_{equity} X_{equity} + \beta_{rates} X_{rates} + \beta_{creditPure} X_{creditPure} \right] $$

The resulting factors have minimal overlap and capture unique fundamental drivers:

Notice we still preserved the negative correlation between rates and equity (desirable) and all other off-diagonal terms are close to zero. Thus, building a portfolio that responds to all 4 “pure” factors above would be truly diversified.

We use this “pure” factor model for US (and other regional ones) throughout Everysk. Because they are not investable (other than the 2 building blocks- equity and nominal rates), we also developed optimization models that synthesize them using a basket of equities and/or ETFs, which we will describe in a companion article.