CRAI: Convex Risk Appetite Index
A five-dimensional cross-asset composite measuring real-time risk appetite, built from paired ETF ratios converted to 60-day rolling z-scores and mapped to a 0-100 scale.
Last reviewed: · Version 1.0 · Identifier CRAI-METHODOLOGY-v1.0
Abstract
The Convex Risk Appetite Index (CRAI) is a daily 0 to 100 cross-asset composite that summarises the market’s risk-taking posture along five independent dimensions: equity size preference (IWM/SPY), credit quality preference (HYG/LQD), consumer cyclicality (XLY/XLP), global risk preference within equities (EEM/EFA), and regional banking stress (KRE/SPY). Each ratio is standardised against its own 60-day rolling distribution, mapped to a 0 to 20 point scale, and summed. The resulting composite is adaptive to the prevailing volatility regime and is intended as an input feature alongside fundamentals, positioning, and flow metrics, not as a standalone trading signal. This paper documents the construction, sources, sign conventions, interpretation thresholds, and known limitations.
1. Motivation
The VIX is the most widely cited risk sentiment gauge. It measures one thing well: implied volatility priced into one-month S&P 500 options. That is useful, but it is a single dimension of a multi-dimensional construct. A market can have a low VIX and simultaneously exhibit defensive rotation within equities, widening credit spreads, emerging-market outflows, and regional bank stress. The VIX alone will not tell you that.
The CRAI is designed as the minimum cross-asset complement. Each of its five components is a relative price, not an absolute price. This matters: relative prices encode expressed preference between two tradeable alternatives, which is a cleaner signal than an absolute price movement that could be driven by macro factor loadings common to both legs.
Each component is z-scored against its own 60-day trailing distribution rather than against a global or long-sample distribution. This adapts the index to the prevailing volatility regime. A one-standard-deviation ratio move during a calm 2017-like regime is a different signal than a one-standard-deviation move during a March 2020 regime, and the rolling-window approach lets CRAI respect that.
2. Component ratios
CRAI aggregates five price ratios. Each ratio is directional: an increase expresses greater risk appetite along that dimension, a decrease expresses lesser.
Small-cap equities carry higher economic sensitivity, less analyst coverage, and weaker balance sheets. An IWM outperformance regime expresses confidence that domestic growth continues and that marginal credit is flowing to smaller firms. An IWM underperformance regime is classic late-cycle behaviour and historically leads the broad market into recessions.
HYG is the iShares High Yield Corporate Bond ETF and LQD is the iShares Investment Grade Corporate Bond ETF. The ratio compresses when high-yield outperforms investment grade, which occurs when credit spreads tighten and investors reach for yield. It widens when high-yield underperforms, which occurs when spreads blow out and investors move up the quality curve.
XLY is the Consumer Discretionary sector ETF and XLP is the Consumer Staples sector ETF. A rising ratio expresses that consumers are expected to maintain or increase discretionary spending; a falling ratio expresses a defensive rotation toward non-cyclical necessity consumption. The ratio leads retail sales data by roughly 3 to 6 months in post-1990 regimes.
EEM is the MSCI Emerging Markets ETF and EFA is the MSCI EAFE (Europe, Australasia, Far East developed) ETF. An EEM/EFA ratio expansion expresses willingness to hold currency, political, and liquidity risk in exchange for higher expected return. A compression expresses flight to the relative safety of developed non-US equities.
KRE is the SPDR S&P Regional Banking ETF. Regional banks are the marginal supplier of domestic small-business and commercial-real-estate credit, and their equity prices embed the market’s view of yield-curve shape, credit quality, and deposit flight risk. A KRE/SPY expansion expresses confidence in the credit creation channel; a compression expresses banking stress.
3. Rationale for these five choices
The five channels are not arbitrary. They were selected to cover the major axes of risk-taking that are independently priced in US-accessible ETF markets, with minimum mutual correlation so that each channel carries information the others do not.
Size (IWM/SPY) and cyclicality (XLY/XLP) are both equity-internal but capture different dimensions: size is about balance-sheet strength and analyst coverage premium, cyclicality is about consumer demand expectations. Credit quality (HYG/LQD) is a fixed-income signal that responds to default expectations and liquidity conditions, which lead equity-internal signals by days to weeks. Global risk (EEM/EFA) picks up dollar-funding conditions, commodity-exporter pressure, and geopolitical risk that do not appear in US-only channels. Regional banking (KRE/SPY) picks up deposit-flight and commercial-real-estate transmission channels that became first-order signals after the March 2023 episode.
Channels are equally weighted. A weighted-average approach was considered and rejected. Equal weighting imposes the prior that we do not know, ex ante, which channel will carry the most signal in the next regime. Weights optimised on historical data overfit, and any weight above 1/5 on a single channel can be dominated by idiosyncratic moves in its underlying ETFs (for example a single large issuer rebalance in LQD, or a single large component of KRE that is in restructuring).
4. Formulas
ratio_t = numerator_price_t / denominator_price_t mean_t = mean(ratio over last 60 trading days) stdev_t = stdev(ratio over last 60 trading days) z_t = (ratio_t − mean_t) / stdev_t
points_t = clamp((z_t + 2) / 4 × 20, 0, 20)
This maps a 60-day z-score of -2 (or lower) to 0 points, a z-score of 0 to 10 points, and a z-score of +2 (or higher) to 20 points. The affine-then-clamp construction produces a bounded output that never goes negative, never exceeds 20, and degrades gracefully in extreme regimes (very large z-scores simply saturate rather than dominating the composite).
CRAI_t = Σ points_i_t for i in {size, credit, cyclicality, global, banks}Sum of five per-channel scores. Range: 0 (all five channels at z ≤ -2) to 100 (all five at z ≥ +2). When a channel is unavailable (stale data, ETF trading halt, index reconstitution day), its score is re-scaled against available channels so the composite remains on the 0 to 100 scale. An availability flag is published alongside the number.
5. Interpretation thresholds
Thresholds are descriptive regime labels calibrated to the distribution of CRAI values from January 2015 through March 2026. They are not probability-of-outcome calibrations.
As with CNLI, the direction of CRAI over the prior 10 and 30 trading days is at least as important as the level. A rising CRAI inside the Neutral band has different implications than a falling CRAI inside the Elevated band.
6. Known limitations
- Rolling-window regime adaptation has a short memory. A 60-day window means that extended regimes (for example, a year-long risk-off period) will eventually re-centre, and the CRAI can read near 50 even when by longer-horizon standards risk appetite is severely depressed. Users concerned with long-horizon positioning should pair CRAI with longer-window absolute metrics (for example, the level of HY OAS relative to its 10-year history).
- ETF wrappers, not underlying assets. The five ratios use ETF prices, which can diverge from their underlying baskets during stress (creation/redemption friction, authorised-participant balance-sheet constraints). HYG in particular is known to trade at discounts during credit-market dislocations that understate the severity of underlying bond spread widening. CRAI will reflect the ETF price, which is investable, but users should be aware that during stress the CRAI can read less negative than the underlying credit picture.
- Equally weighted channels. Equal weights are the right prior in the absence of strong theory, but there are regimes (for example pure rates-driven sell-offs) where one or two channels move while the others stay anchored. In such regimes CRAI under-reacts relative to what a single-channel enthusiast would observe. This is accepted as a feature rather than a bug: CRAI is designed to signal when multiple dimensions of risk appetite are moving together.
- No fixed-income duration channel. CRAI does not incorporate long-duration Treasury versus cash (for example TLT/BIL) as a sixth channel. This was considered and rejected because that ratio is dominated by rates expectations rather than risk appetite, and adding it would contaminate the composite with a macro-rates signal. Users interested in that dimension should read it alongside CRAI, not inside it.
- US-centric. Four of the five channels are US-listed, US-exposure instruments. EEM/EFA is the one cross-border channel. An international investor whose benchmark is non-USD will find CRAI informative but incomplete as a measure of their risk appetite conditions. A future version (v2) may add currency-hedged variants.
- Not a forecasting model. CRAI does not produce calibrated probabilities, Sharpe-tested signals, or trading rules. It is a state descriptor of cross-asset risk posture. Any backtested strategy built on CRAI should be evaluated on its own merits, not by invoking CRAI as a pre-validated feature.
7. Data sources and update cadence
- IWM, SPY, HYG, LQD, XLY, XLP, EEM, EFA, KRE: FMP end-of-day close prices, US trading days only
- 60-day rolling statistics: computed daily, no smoothing, no seasonal adjustment
- Update cadence: once per US trading day at 21:00 UTC after official close; intraday values not published
- Holiday handling: CRAI uses the last published value; no interpolation across non-trading days
The five channel-level scores are published alongside the composite at /indicators/crai, so that users can see which channels are driving a given move and apply their own reweighting if they prefer.
8. References
- Baker, M. and Wurgler, J. (2006). “Investor Sentiment and the Cross-Section of Stock Returns.” Journal of Finance, 61(4), 1645-1680.
- Adrian, T., Crump, R. and Moench, E. (2013). “Pricing the Term Structure with Linear Regressions.” Journal of Financial Economics, 110(1), 110-138.
- Fama, E. and French, K. (1993). “Common risk factors in the returns on stocks and bonds.” Journal of Financial Economics, 33(1), 3-56.
- Pastor, L. and Stambaugh, R. (2003). “Liquidity Risk and Expected Stock Returns.” Journal of Political Economy, 111(3), 642-685.
- Ben-Rephael, A., Kandel, S. and Wohl, A. (2012). “Measuring Investor Sentiment with Mutual Fund Flows.” Journal of Financial Economics, 104(2), 363-382.
- Asness, C., Frazzini, A. and Pedersen, L. (2019). “Quality minus junk.” Review of Accounting Studies, 24, 34-112.