Methodology

1. Where the data comes from and how it is checked

Every input is loaded and checked by one shared daily data step before any beta is calculated. The same step feeds the other two Gyre Research analytics, so all three read the same prices on the same day.

1.1 Universe

The universe is the current S&P 500 membership from the newest month-end index-weight snapshot, plus SPY for the validation check in Section 3. Weights, not just names, come from that snapshot: they drive the cap-weighted benchmark.

1.2 Prices, and what stops a run

Prices are split- and dividend-adjusted daily closes from a commercial market-data provider. After loading, a shared clean-up drops rows with no or a non-positive close, a very large one-day move that reverses the next day (a bad print), and a price far from its local median (a run of bad prints); a large move that does not reverse is kept, because it may be real. A gap of at most two trading days is filled with the previous close. Every dropped or filled point is logged with its value. Then a gate decides whether anything may be calculated:

1.3 Sector and market capitalization

Sector and industry come from each company’s profile at the same market-data provider; they drive the “My Sector” benchmark and the sector ranks. Market capitalization is the profile’s own figure; when the profile has none, it is shares outstanding × the latest adjusted close. A company without a market capitalization is left out of the cap-tier benchmarks and takes part in everything else.

2. Calculation Methodology

2.1 Daily Return Computation

For each security and benchmark, daily simple returns are computed from adjusted closing prices:

Adjusted close prices incorporate splits and dividends, ensuring returns reflect actual investor experience.

2.2 Benchmark Construction

Five benchmark types are constructed for each security:

All composite benchmarks require a minimum of 5 constituents on any given date. Dates with fewer constituents are excluded from the benchmark series.

The other composites are built from today’s members. The equal-weighted, sector and cap-tier composites follow the companies in the index now, with today’s weights and sectors, not the index as it stood in the past. That is right for measuring a current member’s beta against its peers, and it is why the backtest (Section 4) does not use them: it builds the index as it stood on each past day instead. The cap-weighted composite is rebuilt point in time (since October 8, 2026); the default benchmark is SPX as measured by SPY, a fund that has held the index of each day (the cap-weighted composite was the default until October 8, 2026).

2.3 Market Cap Tiers

2.4 Lookback Windows

Betas are calculated over six lookback windows to capture both short-term dynamics and longer-term structural relationships:

2.5 How is the asymmetric beta computed?

For each security × benchmark × lookback window combination, the return series are aligned on common trading dates. Days are then split by benchmark return direction:

A beta is published wherever it is mathematically defined: at least two aligned observations on that side, with non-zero benchmark variance. There is no editorial minimum above that floor. Arbitrary thresholds (formerly 15 observations per side) were removed on June 14, 2026 because they suppressed valid estimates without telling anyone. Where a value cannot be computed the result is null with an explicit reason, never a silent omission, and the up-day and down-day counts behind every estimate are stored and reported. Precision is communicated by the confidence interval rather than by withholding the number: a beta from few observations is published with a wide interval, which is more informative than its absence.

For each subset, beta is computed as:

Producing five output values per calculation:

1. Up-Beta (β⁺) — sensitivity to rising markets
2. Down-Beta (β⁻) — sensitivity to falling markets
3. Asymmetry Score — β⁺ − β⁻: positive when the stock has moved more with the market on up days than on down days over the window. It describes the window; the backtest (Section 4) tests how much of it carries into the next year
4. Standard Beta — full-window OLS beta (all days)
5. Adjusted Beta — 2/3 × standard beta + 1/3 (Blume adjustment, mean-reverting toward 1.0)

2.6 How precise is each beta? (Confidence intervals)

Every up, down and tail beta is published with a 95% confidence interval. Beta is the ordinary least-squares slope, so its standard error is:

SE(β) = √( SSE / ((n − 2) × S_xx) )

where SSE is the residual sum of squares and S_xx the centred sum of squares of the benchmark returns. The interval is β ± t_{(n−2, 0.975)} × SE(β), and the dashboard shows it as a half-width: 1.242 ±0.221 means the interval runs 1.021 to 1.463.

This is what makes the low observation floor safe. Without an interval, a beta estimated from a handful of days and one estimated from five hundred are two numbers that look equally authoritative. With one, the difference is visible and nothing has to be withheld. Two degrees of freedom are consumed by the fit, so an interval requires at least three observations; at exactly two the line passes through both points, the beta is real and the interval is undefined rather than zero-width, and the estimate is shown without one.

The interval describes sampling precision only. It assumes the usual regression conditions and says nothing about regime change — a narrow interval is not a promise that the relationship will persist.

2.7 What happens when the market falls hard? (Tail beta)

Down beta answers “how does this security move when the market falls”. It blends every down day, from a routine quarter-percent drift to a genuine sell-off. Tail beta answers the narrower question a risk officer actually asks: how does it move when the market falls hard.

The threshold is one standard deviation of the benchmark's own returns over the same window, so it means the same thing across a mega-cap composite and a sector peer group rather than imposing a single percentage everywhere:

Tail days: dates where R_benchmark < −1σ

Beta on that subset is computed exactly as in Section 2.5. A tail beta is published only where at least 20 tail days fall inside the window. On SPX (as measured by SPY) as of November 10, 2026, the newest 504 trading days contain 54 days beyond −1σ and only 10 beyond −2σ (the newest 252: 29 and 5) — a beta from a handful of observations is noise, which is why the threshold is one standard deviation and not two. On that date the windows holding at least 20 such days are the 2y and 1y lookbacks; shorter windows show no tail beta.

A blank tail beta means the sample cannot support an estimate, not that the security has no tail behaviour. The number of tail days behind each estimate is shown alongside it.

The measure is worth reading precisely where it disagrees with down beta. A security can track the market through ordinary declines and then gap in a real sell-off; up beta and down beta will look almost symmetric while the tail estimate is materially higher. Tail beta is a conditional historical estimate — not a stress scenario, a factor model or a forecast.

2.8 Where does this method come from?

Splitting beta by the sign of the market return is not a Gyre invention. It sits in a literature on downside risk that starts from Markowitz’s observation that investors do not treat upside and downside deviation alike, and the sources below are the ones this implementation actually rests on.

• Blume, M. E. (1971). “On the Assessment of Risk.” The Journal of Finance 26(1). doi:10.1111/j.1540-6261.1971.tb00584.x — and Blume, M. E. (1975), “Betas and Their Regression Tendencies,” The Journal of Finance 30(3), doi:10.1111/j.1540-6261.1975.tb01850.x. These establish that estimated betas regress toward 1.0 over time, which is the basis for the adjusted beta in Section 2.5 (2/3 × β + 1/3).
• Bawa, V. S. & Lindenberg, E. B. (1977). “Capital market equilibrium in a mean-lower partial moment framework.” Journal of Financial Economics 5(2). doi:10.1016/0304-405X(77)90017-4 — the formal treatment of a beta conditioned on the downside of the market.
• Harlow, W. V. & Rao, R. K. S. (1989). “Asset Pricing in a Generalized Mean-Lower Partial Moment Framework.” The Journal of Financial and Quantitative Analysis 24(3). doi:10.2307/2330813 — generalises that framework to an arbitrary reference return rather than the mean.
• Ang, A., Chen, J. & Xing, Y. (2006). “Downside Risk.” The Review of Financial Studies 19(4). doi:10.1093/rfs/hhj035 — the empirical result, in U.S. stocks 1963–2001, that downside beta carried a risk premium distinct from ordinary beta. Our survivorship-free backtest of the S&P 500 from 1992 to 2026 did not find a reliable one (Section 4; the dashboard’s Backtest section shows the full result).

Where this dashboard departs from those papers: they mostly condition on the market return relative to its mean, while the up/down split here conditions on the sign of the return (Section 2.5) and the tail estimate conditions on one standard deviation below zero (Section 2.7). The sign split is the simpler and more legible convention for a published reference table; it is not the same estimator as a lower partial moment beta, and results here should not be read as replicating those papers.

3. How do we know the pipeline is right? (Post-calculation sanity check)

After all beta calculations complete, a built-in sanity check validates the entire pipeline end-to-end:

How the checks run: the SPY-beta check is part of the pipeline’s live test (asymmetric_beta.py --test-live), which calculates from the live data into a scratch store; the figures above are from the production run. Every day, the data step checks that each S&P 500 composite’s daily returns have a correlation above 0.95 with SPY’s, and reports a composite that fails to the operators; a composite with fewer than 5 members on a date has no return that date.

4. How the backtest works

The dashboard’s Backtest section tests, against history, six claims about asymmetric beta (B1–B6 below). It runs beside the study (Section 5), which tested the two hypotheses on which a trading use would rest and rejected both. The backtest’s rules were written down and published before the first run, and every result is shown whether or not it supports the claim. It is re-run every day after the calculation.

1. Who is in the test. On the last trading day of every month since March 1992, the companies in the S&P 500 on that day, including those later removed, acquired or bankrupt, that have a price on that day. Prices are a survivorship-free history (a licensed historical data set to July 2026, continued with the returns of the daily price feed), and a company that leaves the index keeps being priced for a year.
2. The signal. Up-beta, down-beta, tail beta, total beta and asymmetry, by exactly the calculation this page uses, on the 252 trading days ending that day, against the S&P 500 as it stood each day (a cap-weighted index of the members of the day). A company needs at least 200 of those 252 days.
3. What happens next. Positions are taken at the close of the next trading day. Returns are measured over the following 1, 3, 6 and 12 months; next-year betas are measured with the same calculation on the following 252 trading days. A company that stops trading earns its return to its last price and then 0%.
4. The claims tested. B1 (the main test): does a company’s asymmetry now rank its asymmetry next year? B2: does a portfolio of the most asymmetric companies behave asymmetrically next year? B3: do the most asymmetric companies earn more? B4: do companies with the highest down-beta earn more? B5: does down-beta forecast next year’s down-beta better than ordinary beta does? B6: do down-beta and tail beta persist?
5. Statistics. Each measure is calculated across companies on each month end and then averaged over time. The t-statistic allows for overlapping holding periods (Newey-West). Portfolio results are shown against 1,000 random portfolios of the same size and net of trading costs of 10 and 25 basis points.
6. The verdict. Supported needs the stated sign, a t-statistic of at least 2 over the whole history, and the same sign from 2021 onward (a period held back from the design). Contradicted is at least 2 standard errors the other way. Everything else is Not supported.

Limits. Each company carries one sector for its whole history. The last-day move of a company that is bought out or goes bankrupt is often missing from price data. A membership change takes effect on its published effective date where the list of index changes gives one, otherwise at the snapshot date (quarter-end before 2005, month-end after). Coverage before 2000 is below 100%. Trading costs are fixed estimates. The complete pre-registered design is the analytics backtest methodology, method version 4.

5. The study’s tests

The study tested two hypotheses about asymmetric beta in S&P 500 stocks: that a stock’s asymmetry lasts long enough to exploit in a long/short equity portfolio, and that short-term asymmetry reverts in a way that can be traded. Both were rejected. The tests ran in seven groups, A to G. This section says what each group did and gives the figures the study reports; the study page gives the conclusion.

Rules common to every group. The members of the S&P 500 on each day, including companies later removed, acquired or bankrupt (survivorship-free), from 1992; the beta calculation of Section 2; the index as it stood each day as the market, and SPY wherever returns are compared, so a trade is measured against beta × SPY. Each test’s rule was written down before it ran. Results are averaged across stocks and then over time, with t-statistics that allow for overlapping periods, a correction for running many tests at once, and 2021 onward reported separately as a period held back. Groups F and G were designed after group E’s results were seen, and their pass rules were made strict for that reason.

The study’s conclusion, and what we continue to publish, are on the study page.

For questions about our methodology or data sources, contact team@gyreresearch.com.