Most investable assets and techniques typically fall into two broad groups: productive and scarce.
This is a very important concept for portfolio construction and asset allocation on the asset owner level because productive assets and scarce assets are likely to have concave and convex profiles, respectively, with respect to key risk aspects.
Practitioners who’re aware of the concave and convex nature of productive and scarce assets and techniques can higher hedge their risks in deflationary and – especially – inflationary crises. We suggest that portfolios that include each productive and scarce assets can achieve similar performance to the S&P 500 with less risk than portfolios that contain only productive assets.
The nature of productive and scarce assets
The purpose of productive assets is to finance, support, and supply the means for productive activities within the economy in exchange for promised future money flows. For example, stocks promise future dividends and loans promise future coupons.
The issuance of equity and debt securities is subject to external constraints, primarily as a result of the sustainability of capital markets. Shocks hit these assets with downward asymmetry, suggesting supply curves. The returns from these assets arise from the economic growth they’re intended to finance.
Scarce assets and techniques, then again, exist for reasons apart from financing productive activities. They are limited in scope or capability and will or may not promise regular money payments.
Examples of scarce assets include gold, another goods and natural resources, high-value art, and other collectibles. “Safe” government bonds with low or negative yields, reserve currencies and a few global macro strategies are also scarce assets. The returns of those assets arise from their scarcity, which is usually linked to produce curves.
How to quantify productivity and scarcity
Because directly modeling – and even conceptualizing – “supply curves” will be difficult or not possible in lots of cases, we as a substitute measure the asymmetric risk statistics of observed asset returns. The results are detailed in our article: “The concave and convex profiles of productive and scarce assets.”
We use coskewness to measure the convexity of asset returns with respect to a lot of key risk aspects: inflation, rates of interest, credit and equity. We also use standard skewness to measure the “convexity of an asset with respect to itself” or “autoconvexity”.
These coskewness and convexity measures provide insight into an asset’s tendency to understand or depreciate when risk aspects develop into volatile. In our work, we quantify the place of investable assets and techniques on the spectrum from productive to scarce, based on their skewness and parallelism with respect to key risk aspects. Such an overall spectrum is shown for prime asset classes in Figure 1.
Empirically, stocks, duration-hedged corporate bonds – and more generally “higher beta” and “positive carry” strategies – are likely to be concave with respect to the important risk aspects and are auto-concave (negatively skewed) to the productive group.
In contrast, “safe” Treasuries, gold, the U.S. dollar versus a broad basket, and fast-moving momentum strategies are likely to be empirically convex with respect to key risk aspects and are autoconvex (positively skewed). the scarce group. We observe that as a way to be convex, an asset or strategy should have some intuitive economic scarcity.
Exhibition 1.
Productivity, scarcity, convexity, concavity
Convex or scarce assets and techniques are likely to have low beta relative to stocks. However, a low beta value doesn’t guarantee convexity, as we empirically display in our work.
The parallelism with inflation risk serves to enhance and enrich traditional risk metrics corresponding to equity beta and bond duration. Although many assets can have a low correlation with inflation, their parallelism will be more significant and chronic, with large potential losses (or gains within the case of scarce assets) during times of macroeconomic instability. Inflation itself is a highly distorted, abnormal process with serious extreme events.
Figure 2 shows the monthly excess returns of high yield bonds and the Barclay CTA Index in comparison with the surplus returns of the S&P 500. High yield bonds respond concavely to S&P 500 returns, while the Barclay CTA Index responds convexly relative to the S&P 500.
Exhibition 2. High yield bonds are concave to the S&P 500, CTAs are convex
Notes: Left panel: High Yield vs. S&P500, right panel: Barclay CTA Index vs. S&P500. Period 1990-2022. Horizon=1M. The quadratic model fit is shown for every asset.
Figure 3 shows the monthly returns of 4 productive and 4 scarce assets plotted against the inflation risk factor. The top panel shows the broad U.S. stock market (S&P 500), returns on investment grade bonds (maturity hedged), high yield bonds, and the Bloomberg Commodity Index, each in comparison with the patron price index month-over-month.
With the exception of the Bloomberg Commodity Index, assets generally have a weak correlation to inflation, but all have significant negative convexity. In contrast, the 4 assets at the underside, namely US Treasuries, gold, the US Dollar Index (DXY), and a straightforward four-asset momentum strategy (with a one-month look-back), show a convex response to inflation innovation.
We imagine that the convex reactions are as a result of an underlying value of the asset or strategy. In practice, convexity metrics can tell us which assets are more likely to perform above their linear or beta risk in times of high risk and uncertainty – that’s, in a crisis.
Appendix 3. Productive assets are concave to CPI, scarce assets are convex
Notes: Top panel for 4 productive assets, bottom panel for 4 scarce assets. Period 1973-2022. Horizon=1M. The quadratic model fit is shown for every asset.
Convex and concave responses to cost movements are well-known from textbook options payouts: most assets are empirically concave or convex with respect to key risk aspects. Remembering the pioneering work of Arrow And Debreuin addition to Black and ScholesAnd MertonThese convexities are central to asset return profiles in a world of multidimensional risks and unsure outcomes.
Appendix 4. Concave and convex Black-Scholes option prices and payoffs
In practice
From an investor’s perspective, productive assets generally provide an impact on nominal GDP growth, while scarce assets are critical for resilience in recessionary and inflationary environments.
For example, in a standard 60/40 portfolio, stocks are productive and bonds are short on duration. Bond maturity is a very good diversifier in a deflationary recession, but other scarce assets also can mitigate rising inflation and deflationary recessions.
These scarce assets can and must be used to construct diversified portfolios.
Our article proposes a technique for combining concave and convex assets into an overall investor-specific portfolio: “4×4 target parity.” In this text, which we summarized in a previous blog post, we show, using simulations spanning greater than 50 years, that goal-oriented portfolios can produce competitive returns with the S&P 500 at about half the chance.
