Systematic Alpha in Digital Asset Markets: A Risk-Adjusted Survey

1. Introduction

Digital asset markets have produced a short list of systematic return sources that recur across venues and cycles. This paper surveys five of them: carry and basis, time-series momentum, cross-sectional momentum, mean reversion (short-term reversal and liquidity provision), and the volatility risk premium. For each, we set out who pays and why, what the published evidence finds, when the payment tends to stop, and what can go wrong. We then compare the five on one framework and describe a general approach to sizing them by market regime.

The title uses "alpha" in its broad sense: return sources that a systematic process can access. "Risk-adjusted" means the sources are compared by their risks, not by risk-adjusted returns. This paper does not measure the return of any of them. It reports no strategy returns, backtests or risk-adjusted performance, from Hedgehog or from anyone else. Crypto backtests are short and sensitive to sample, costs and venue. Published predictability also tends to decay (McLean and Pontiff, 2016), and deviations of crypto perpetual prices from their no-arbitrage values have narrowed over time, consistent with growing arbitrage capital (He, Manela, Ross and von Wachter, 2026). A ranking of past results would mostly describe the past.

Instead, we describe the academic evidence in words and measure the market quantities each source depends on, from funding rates and futures basis to implied volatility, serial correlation, correlation across coins and order-book depth. All come from public data through 25 October 2026, unless a snapshot date is given. A funding rate is not the return of a carry position. An implied minus realised volatility gap is a market statistic, not the profit or loss of any option position. We keep that distinction throughout.

Three themes run through the paper. First, the level of crypto carry is partly an artefact of contract design, and funding and basis levels fell to around cash rates in 2026. Second, the five sources share one leverage cycle, so a book that holds several of them is less diversified in a deleveraging than in calm markets. Third, four of the five are, in shape, short a tail. Their risk is set by the regime more than by the average size of the premium. This motivates the general sizing framework in Section 11.

2. Background and evidence: where the payments come from

A systematic return source is a payment that one group of participants makes, on average, to another, and that a rule can collect. The traditional literature has four relevant families. Carry is the part of expected return visible in advance; carry strategies across asset classes have tended to suffer together in global recessions (Koijen, Moskowitz, Pedersen and Vrugt, 2018). Time-series momentum is the tendency of an asset's own past return to predict its next one; across 58 futures and forward contracts the effect lasts about a year and then partly reverses (Moskowitz, Ooi and Pedersen, 2012). Short-term reversal is a payment to those who supply liquidity, and it rises when constrained intermediaries withdraw (Nagel, 2012). The variance risk premium is the gap between the price of variance in options and the variance that follows (Carr and Wu, 2009).

What differs in crypto is the plumbing. Perpetual futures are by far the most popular crypto derivative, with daily volume of more than USD 100 billion (He, Manela, Ross and von Wachter, 2026). A perpetual has no expiry. Longs and shorts instead exchange a funding payment tied to the gap between the perpetual and spot prices (Ackerer, Hugonnier and Jermann, 2026). Leverage is high and liquidation is automatic. BitMEX offered up to 100x leverage, and one study collected over 425,000 liquidation events from it (Soska et al., 2021). Exchanges act as venue, custodian and clearing house at once. On 19 May 2021, when liquidations peaked, major exchanges reported outages, citing network congestion (IMF, 2021).

Arbitrage capital is scarce and segmented. Price gaps between exchanges have been large and recurrent, wider across countries than within them, and they widen when bitcoin rises sharply (Makarov and Schoar, 2020). Schmeling, Schrimpf and Todorov (2023) find that crypto carry is driven mainly by a volatile convenience yield. In booms, smaller investors chase trends and demand leveraged long exposure. Scarce arbitrage capital meets that demand, and margin spikes and liquidations limit it in sell-offs. That is the common thread of this survey. The payments are large because the capital that would compete them away is constrained, and the constraint binds hardest in stress.

3. Data and method

All statistics in this paper come from public data, fetched through exchange and central-bank interfaces and computed with scripts kept with the unaltered raw responses. Table 1 lists the datasets. Data definitions follow the venues' documentation (Binance; Bybit; Deribit) and FRED (DTB3; SP500).

Conventions. Returns are daily log returns, UTC close to close. Single-day and single-week moves quoted in per cent, such as the worst day, moves above 10% and falls of more than 5%, are simple price changes. All other statistics use log returns. Volatility is annualised with the square root of 365, because crypto trades every day. Daily funding is the sum of the day's settlements multiplied by 365, and days with incomplete settlements are dropped. The quarterly basis is (F/S - 1) x 365 / days to expiry. The 3-month Treasury bill rate is converted from FRED's 360-day discount basis to a 365-day bond-equivalent yield. Forward realised volatility on day t uses the daily returns from t+1 to t+30, without demeaning. Coinbase and Binance daily returns correlate at 0.991 for BTC and 0.994 for ETH.

Regime labels. The trend state on day t is up when BTC's close on day t-1 sits above its 200-day simple average, and down otherwise. The volatility state is the tercile of BTC's trailing 30-day realised volatility on day t-1, with cut-offs of 45.7% and 66.9% set over 2016 to 2026. Both use the previous day's information, although the cut-offs are set with the whole period in view. They describe the market. They are not trading signals, and they are not Hedgehog's regime estimate.

Inference. Serial correlation tests use a t-statistic that is robust to volatility clustering. Variance ratios follow Lo and MacKinlay (1988), with two-sided p-values from a wild bootstrap of 10,000 draws with a fixed seed (Kim, 2006), which keeps volatility clustering but removes serial dependence.

What the statistics are not. Every figure here is a market statistic, not the return of a strategy. Funding is a gross payment between longs and shorts, and the annualised basis is a gross rate before fees, margin, collateral and venue costs. A hedged carry position also bears spot-perpetual divergence, fees, collateral costs, margin calls and venue risk. An option seller's result depends on strikes, path, hedging and margin, and DVOL is an index, not a traded price.

4. Findings: how crypto prices behave

Two properties of crypto prices shape every return source: fat tails and strong volatility clustering. Table 2 summarises BTC and ETH.

Volatility has fallen since the 2021 cycle but remains high. BTC's annualised volatility was 81.1% in 2021, 43.6% in 2023 and 44.9% in 2026 to date. ETH's was 108.7%, 46.6% and 60.6%. BTC had 11 days with moves above 10% in 2021, none in 2025 and two in 2026, including a fall of 14.0% on 5 February 2026.

Volatility clusters strongly. The autocorrelation of absolute daily BTC returns is 0.21 at one day, 0.07 at 30 days and 0.02 at 90 days. For ETH it is 0.23 at one day. In 2023 to 2026 the one-day BTC figure is 0.17. Recent volatility therefore carries information about the weeks ahead, which underlies the case for sizing by forecast risk discussed in Section 11.

BTC spent 61.7% of days from February 2016 in the uptrend state. Trend spells are short at the median and long in the tail. The 36 uptrend spells had a median length of 5.5 days and a longest of 732 days. The 35 downtrend spells had a median of 3 days and a longest of 384. The short medians reflect frequent crossings near the average. Volatility states are steadier: high-volatility spells had a median of 16 days and low-volatility spells 12. A regime label used for sizing therefore needs smoothing or hysteresis, or it will trade every crossing. A forthcoming paper, Regime Detection in Digital Asset Markets, will cover this in detail.

5. Findings: carry and basis

Who pays and why. Holders of leveraged long exposure pay. Perpetual longs pay funding to shorts, and dated futures trade above spot, because many traders prefer leveraged, unfunded upside to buying coins. The demand is extrapolative: past returns predict futures-spot deviations (He et al., 2026). The receiver holds spot and sells the derivative. That party is paid for supplying balance sheet, posting collateral at an exchange, and bearing the risk of a forced early exit.

What the literature finds. Schmeling, Schrimpf and Todorov measure crypto carry as the annualised gap between futures and spot prices. Their 2023 working paper finds that it averages above 10% a year and can reach 60% a year, and that interest-rate differentials explain little of it. High carry predicts future crashes and coincides with a rising price of crash insurance (Schmeling, Schrimpf and Todorov, 2023). A 2025 version of the paper reports carry that sometimes exceeds 40% a year and varies strongly over time (Schmeling, Schrimpf and Todorov, 2025). He et al. (2026) find that deviations of perpetual prices from no-arbitrage values are larger than in traditional currency markets, that they co-move across coins, and that they decline by about 22 percentage points a year on average.

Part of carry is contract design. On Binance's BTCUSDT perpetual, which settles every 8 hours, the funding formula has an interest component of 0.01% and a clamp of 0.05% (He et al., 2026, citing Binance's own documentation). Funding equals the interest component whenever the average premium sits within 0.05% either side of it. That pins funding at 10.95% a year in quiet markets. Of 7,808 Binance BTCUSDT settlements since 10 September 2019, 34.8% were exactly 0.0100%. On Bybit's BTCUSDT perpetual, since March 2020, the share was 40.3%. Deribit's inverse perpetuals have no interest component. Under Deribit's current specification, funding is zero while the premium sits within a damper of plus or minus 0.025%, and accrues continuously (Deribit, 2026). Median daily BTC funding was 2.1% a year on Deribit from May 2019, against 8.2% on Binance from September 2019. Theory agrees: the strength of the funding anchor shapes the perpetual price, and linear and inverse contracts price differently (Ackerer, Hugonnier and Jermann, 2026).

The anchor binds far less often. The share of Binance BTCUSDT settlements at exactly 0.01% fell from 66.9% in late 2019 and 42.1% in 2024 to 17.2% in 2025 and 6.7% in 2026 to date (Table 3). In 2026, 25.5% of settlements were negative, and the 95th percentile of daily funding was 9.2% a year, below the 10.95% anchor. That points to weaker demand for leveraged long exposure than in earlier cycles.

Carry is a trend-and-leverage variable. Mean Binance BTCUSDT funding was 17.5% a year on uptrend days and 3.4% on downtrend days, and the share of negative days was 4.4% and 23.7% (Table 4). When an uptrend coincided with high volatility, mean funding was 33.3%. In a downtrend with high volatility it was 1.1%, and on Deribit's inverse perpetual it was -6.0%, with 61.3% of days negative. Thirty-day average funding correlates at 0.30 with BTC's trailing 30-day return. This matches Schmeling, Schrimpf and Todorov's account: carry rises with trend-chasing demand for leverage and falls when that demand reverses.

Persistent levels, short spells. Daily Binance BTCUSDT funding is persistent: its autocorrelation is 0.83 at one day, 0.54 at seven days and 0.35 at 30 days. Yet its 147 negative spells had a median length of 2 days, and the longest lasted 11. Venues move together but not in lockstep: since March 2020, daily BTC funding has correlated at 0.78 between Binance and Bybit and 0.67 between Binance and Deribit.

Dated futures tell the same story. The annualised basis on Binance's USDT-margined BTC quarterly future averaged 8.27% a year from February 2021, with a median of 5.65% and a peak of 67.39% on 17 February 2021 (Table 5). It correlates at 0.87 with 30-day average perpetual funding. It averaged 18.52% in 2021, 2.46% in 2022 and 3.27% in 2026, when it ranged from 0.01% to 5.56%. ETH's USDT-margined basis was negative on 37.9% of days in 2022.

Regulated access. On 10 January 2024 the SEC approved the listing and trading of spot bitcoin exchange-traded products (SEC, 2024). Regulated capital can now hold the spot leg in an ETF and sell CME futures. In industry research for CF Benchmarks, a benchmark administrator, Pilipczuk reports that the CME front-month annualised basis approached 25% in February 2024 and fell below 10% in April 2025. The same report shows CME bitcoin futures open interest rising from about 30,000 contracts in early January 2024 to a record near 45,000 in late November 2024 (Pilipczuk, 2025).

Carry against cash. Table 6 sets funding and the quarterly basis against the 3-month US Treasury bill, converted to a bond-equivalent yield. In 2021 average funding exceeded the bill by 30.56 percentage points and the basis by 18.48. In 2026 to 25 October, funding averaged 3.02% a year against a bill average of 3.79%, and was below the bill rate on 50.3% of days. The basis averaged 3.27%, against 3.78% for the bill on the same days, and was below the bill rate on 54.3% of days. These are comparisons of gross rate levels, not returns: a hedged position bears costs and risks that a bill does not. Funding and basis levels have fallen to around cash rates, in line with He et al.'s (2026) finding that deviations have narrowed, which they link to more arbitrage capital and easier margining.

Main risks.

• Venue failure. Exchanges can fail, halt withdrawals or go offline at peak liquidation. FTX paused customer withdrawals on 8 November 2022 and filed for bankruptcy on 11 November 2022 (SEC complaint, 2022).
• Margin on the hedge leg. A sharp rally can liquidate the short leg when collateral sits elsewhere.
• Auto-deleveraging. On 10 October 2025, auto-deleveraging forcibly closed profitable positions on the other side of liquidated trades (FTI Consulting, 2025), which can remove a carry book's hedge leg.
• No convergence date. A perpetual need never converge to spot.
• Collateral. Stablecoin or token margin carries issuer and peg risk, which a forthcoming paper, The Perpetual Futures Basis: Microstructure and Capture, will cover.
• Crowding. As arbitrage capital arrives, the premium has tended to shrink.

6. Findings: momentum, time-series and cross-sectional

Who pays for trends. Moskowitz, Ooi and Pedersen (2012) find time-series momentum consistent with initial under-reaction and delayed over-reaction, and find that speculators gain from it at the expense of hedgers. Anchoring, herding and trading by participants who do not seek profit, such as central banks and corporate hedging programmes, also help explain trends (Hurst, Ooi and Pedersen, 2017). In crypto, investor attention predicts returns, demand for leverage is extrapolative, and liquidation cascades can extend moves. The counterparties are traders who fade moves at the wrong moment, and forced sellers.

What the literature finds. Crypto returns have little exposure to stock-market and macroeconomic factors, while a strong time-series momentum effect and proxies for investor attention predict them (Liu and Tsyvinski, 2021). Using trading volume to locate bitcoin's trading session, Shen, Urquhart and Wang find that the first half-hour return predicts the last half-hour, most strongly in sessions with the highest volume or volatility. They attribute this to liquidity provision rather than late-informed trading (Shen, Urquhart and Wang, 2022).

The trend property in prices is weak and unstable. Time-series momentum relies on positive serial correlation at the trading horizon (Table 7). In the full BTC sample, variance ratios rise to 1.384 at 90 days and 1.839 at 365 days, with wild-bootstrap p-values of 0.06 and 0.05. That pattern comes from the boom-bust cycles before 2023. In 2023 to 2026 no BTC or ETH variance ratio is significant at any horizon, and ETH's 365-day ratio is 0.742, below 1. Long-horizon ratios rest on few independent observations, so power is low. The trend property depends on the regime and has been weak since 2023.

When trend rules struggle. Trend rules depend on sustained directional moves and suffer in ranges and at sharp turning points. Our trend-state spells show the range problem: the median spell either side of the 200-day average lasted 3 to 5.5 days. In equities, momentum crashes are partly predictable. They occur in panic states, after market declines and with high volatility, when markets rebound sharply (Daniel and Moskowitz, 2016). Momentum's risk varies over time and is predictable, and scaling exposure by recent volatility nearly eliminated the crashes (Barroso and Santa-Clara, 2015).

Cross-sectional momentum. Momentum across coins is one of three factors, with the crypto market and size, that explain the cross-section of crypto returns (Liu, Tsyvinski and Wu, 2022). The evidence varies with the sample: one study of 143 coins from 2014 to 2018 found no significant momentum (Grobys and Sapkota, 2019). Begušić and Kostanjčar (2019) find momentum strongest among the most liquid coins and link it to herding. Fičura finds weekly momentum in large, liquid coins and weekly reversal only in small, illiquid ones (Fičura, 2023). Using almost 2,000 coins from 2014 to 2020, Dobrynskaya finds momentum at horizons under a month, strongest at about two weeks, and reversal from about four to six weeks, far sooner than in equities. Weekly rebalancing carries significant transaction costs (Dobrynskaya, 2022, in the author's summary for HSE University). Factor premia also show momentum, which originates in coin-level momentum (Fieberg, Liedtke, Metko and Zaremba, 2023).

Diversification across coins shrinks in downtrends. Cross-sectional momentum needs dispersion between coins and suffers when one factor dominates, as in downtrends (Table 8). Across 20 large coins since 2021, average pairwise correlation was 0.72 on downtrend days against 0.54 on uptrend days, and the first principal component explained 73.4% of variance against 57.1%. On the 87 days when BTC fell more than 5%, the median beta of the coins to BTC was 1.40, against 1.10 on other days. A long-short coin book that looks market-neutral in calm periods can carry hidden beta in a sell-off. Correlation on large-move days is biased by conditioning on BTC's own move, so the rise in beta is the more robust reading.

Crowding. When the abnormal return correlation among the stocks a momentum strategy trades is high, those stocks subsequently revert, as crowded trading pushes prices past fundamentals (Lou and Polk, 2022). In crypto, rising co-movement of funding across venues and rising open interest are possible analogues. This paper does not test them.

Main risks.

• Whipsaw in sideways markets.
• Gap risk through stops in a market that trades every hour.
• Crash risk at turning points after declines.
• Hidden beta and short-side constraints in cross-sectional books.
• Survivorship and delisting in coin universes.
• Turnover costs. In equities, trading costs remove most high-turnover anomalies (Novy-Marx and Velikov, 2016).

7. Findings: mean reversion and liquidity provision

Who pays and why. Mean reversion in crypto takes two forms: short-term reversal of a coin's own price, and convergence of related prices across venues or instruments. Both are payments for supplying liquidity or balance sheet. Traders who need immediacy, such as forced sellers and liquidated positions, pay those who absorb their orders and hold the inventory. In equities this compensation rises sharply when the VIX is high, because constrained intermediaries withdraw (Nagel, 2012).

What the literature finds. The payment concentrates where risk is highest. Across more than 3,600 coins, daily returns reverse in the cross-section: coins that fell the previous day tend to rise relative to those that rose. The effect is driven by illiquidity, and the largest coins show daily momentum instead (Zaremba, Bilgin, Long, Mercik and Szczygielski, 2021). Returns to liquidity provision concentrate in smaller, more volatile and less liquid pairs, where adverse selection is likely greater (Bianchi, Babiak and Dickerson, 2022). Cross-venue price gaps widen when bitcoin rises sharply (Makarov and Schoar, 2020). Within each 8-hour funding cycle, trading activity and bid-ask spreads follow a U-shape (Ruan and Streltsov, 2025).

Reversal at the index level is weak. The full-sample lag-one autocorrelation of daily BTC returns is -0.048, with a robust t-statistic of -1.84 (Table 7). Reversal was strongest in 2020 to 2022, at -0.093 for BTC and -0.097 for ETH, with two-day variance ratios of 0.909 and 0.905 and wild-bootstrap p-values of 0.05. Since 2023 it has been -0.037 and -0.022. Among the hourly lags tested (1, 2, 3, 6, 12 and 24 hours), only the 24-hour lag is significant for both coins; ETH's two-hour lag is also significant at the 5% level. Across 68,439 hours from 2019 to 2026, the autocorrelation at exactly 24 hours is -0.032 for BTC (robust t -5.26) and -0.037 for ETH (robust t -6.31). The pattern is consistent with a time-of-day effect, possibly linked to funding settlement times or regional trading sessions, rather than general reversal.

Costs decide. Reversal and liquidity provision are high-turnover activities. In equities, trading costs remove most high-turnover anomalies, and a buy/hold band is the most effective simple way to cut them (Novy-Marx and Velikov, 2016). Crypto trading costs vary by venue and over time, so estimates need to come from the venues traded. The Corwin-Schultz and Abdi-Ranaldo estimators track changes in crypto liquidity well, while the Kyle-Obizhaeva estimator and the Amihud ratio better capture levels and differences across venues (Brauneis, Mestel, Riordan and Theissen, 2021).

Main risks.

• Inventory risk in cascades, when prices keep moving.
• Adverse selection from informed flow.
• Venue outages when liquidity is most needed.
• Small scale. The effect is strongest in illiquid coins, where the most a strategy can take is small.
• Relationship breaks. Cross-venue spreads can widen when withdrawals halt.

8. Findings: the volatility risk premium

Who pays and why. Option buyers pay: hedgers buying puts, traders buying calls in rallies, and leveraged holders buying protection. Option sellers are paid for bearing jump and crash risk under capital constraints. Deribit tick data support limits to arbitrage in market makers' option supply (Alexander, Deng, Feng and Wan, 2023).

What the literature finds. Almeida, Grith, Miftachov and Wang estimate the bitcoin variance risk premium from Deribit options between July 2017 and December 2022 (Almeida et al., 2025). In annualised variance units they report risk-neutral and physical variances of 0.72 and 0.58, a premium of 0.14, against about 0.02 that they cite for the S&P 500. The premium is higher in a low-volatility cluster (0.17) than in a high-volatility cluster (0.12), and in calmer markets investors appear more concerned about variance and upside risk. Realised variance significantly exceeded implied between 15 March and 8 April 2020.

Implied usually exceeds realised. We compare Deribit's DVOL index, which uses the implied volatility smile of the relevant expiries to gauge 30-day annualised implied volatility (Deribit, 2021), with the volatility that followed over 30 days (Table 9). DVOL readings come from Deribit's public interface (Deribit API). Between 24 March 2021 and 25 September 2026, BTC DVOL exceeded subsequent realised volatility by a median of 9.9 volatility points (ETH 7.3). The gap has a long left tail. BTC's 5th percentile was -19.8 points and its minimum -46.3; ETH's minimum was -108.4.

The gap is narrowest in calm markets. In the lowest third of BTC DVOL readings, the median ratio of implied to subsequent realised volatility was 1.122, against 1.297 in the highest third (Table 10). By realised-volatility state, the median ratio was 1.137 in the low state and 1.385 in the high state.

Reconciling with the literature. This looks like the opposite of Almeida et al.'s result, but the studies measure different things. They use variance units over 27 days from July 2017 to December 2022, with regimes from clustering option-implied densities. We use volatility ratios over 30 days from March 2021 to September 2026, with states from realised volatility or DVOL, and our sample includes the calm years of 2023 to 2026. Both show that the size of the premium varies by regime, and neither supports assuming a single regime pattern. A forthcoming paper, Volatility Risk Premia in Crypto Options, will examine this further.

2026 has been unusual. BTC's mean gap was -0.4 points for readings from 1 January to 25 September 2026, the only year in the BTC sample with a negative mean. The months with the most negative daily gaps in the BTC series were January 2026 (-46.3 points, the sample minimum), April 2021 (-41.5), May 2021 (-40.9) and February 2026 (-36.6). On 25 October 2026, BTC DVOL stood at 38.8 against trailing 30-day realised volatility of 24.9.

Not always crash insurance. The correlation between daily changes in BTC DVOL and BTC returns was -0.33 over the full sample and -0.57 in 2026, but +0.33 in 2023, when implied volatility rose with prices. In some years buyers pay for upside convexity, which matches Almeida et al.'s finding on upside risk in calm markets.

Main risks.

• Jump and gap risk. A short option book is short gamma through liquidation cascades.
• Calm-to-shock transitions, when the gap between implied and realised volatility is narrowest.
• Venue concentration. Deribit held about USD 31.6 billion of BTC options open interest on 26 October 2026. This paper does not measure its share of the market.
• Collateral in coin-margined accounts falls with the underlying.
• Strike liquidity and hedging model risk away from the money.

9. A common framework for comparison

Table 11 compares the five sources on the same dimensions. All entries are qualitative and rest on the evidence above.

Four of the five are short a tail. Carry, cross-sectional momentum, liquidity provision and option selling are each a payment for bearing losses that arrive in stress. Time-series momentum differs in shape. Its losses come mainly from whipsaw in ranges and reversals at turning points, rather than from one large tail event. For the four, the regime is the main determinant of risk, not the average size of the premium.

The sources are linked through leverage. Funding, basis, trend strength and implied volatility move with the same leverage cycle. Funding rises with BTC's trailing return, the basis correlates at 0.87 with funding, the implied-realised gap is widest when volatility is already high, and the common factor across coins strengthens in downtrends. A book that combines several sources is therefore less diversified in a deleveraging than in calm markets. A forthcoming paper, Multi-Strategy Portfolio Construction Under EVAR Constraints, will cover how to combine them.

Arbitrage capital and publication compress premia. The 2026 readings for funding and basis, and the weakness of price persistence since 2023, fit that pattern. Averages that include 2020 and 2021 overstate current funding and basis levels.

10. Stress: when the sources move together

Stress events differ in cause. Table 12 shows Binance BTCUSDT funding around the 12 largest one-day BTC falls since funding data begin, at least eight days apart.

Five of the 12 falls, all in 2020 and 2021, came after a week in which funding sat between the 79th and 96th percentile of its history, when demand for leveraged long exposure was high. The four falls of 2022 and the fall of 5 February 2026 came after funding between the 24th and 44th percentile. Three of the 2022 falls coincided with credit and counterparty failures. TerraUSD collapsed in May 2022. Three Arrows Capital and crypto lenders including Celsius were in distress in June 2022 (FSOC, 2022). FTX collapsed in November 2022 (SEC complaint, 2022). We do not attribute a cause to the February 2026 fall. A funding-based warning sees leverage, not counterparty failure. Twelve events are a small sample, the percentiles use the full history including later data, and the table does not test a signal.

The crash of 10 October 2025 is absent: BTC's close-to-close move that day was -7.2%, smaller than any in the table, although the damage within the day and in leveraged positions was severe. FTI Consulting reports that perpetual funding had climbed from around 10% annualised to nearly 30% by 6 October 2025, which it links to the Ethereum rally, without naming venues or contracts. The contracts in our data rose less. Binance BTCUSDT funding did not exceed its 10.95% anchor at any point in 2025. Between 15 September and 10 October, the highest daily reading on our six BTC and ETH perpetuals was 26.9%, on Deribit's BTC perpetual on 5 October. FTI also reports that bid-ask spreads widened from single-digit basis points to double-digit percentages at the extremes on 10 October (FTI Consulting, 2025).

The link to equities changes by regime. The weekly correlation between BTC and the S&P 500 was 0.20 from November 2016 to October 2026. It ranged from -0.09 in 2019 to 0.43 in 2022, and was 0.27 in 2026 to date. In the 20 worst S&P 500 weeks of the sample, BTC fell in 15, with a median weekly move of -2.7% against -5.1% for the index. Annual figures rest on about 52 weeks each, so they are imprecise. IMF staff reported a similar shift: a correlation of 0.01 in 2017 to 2019 and 0.36 in 2020 to 2021, without stating the return frequency (Adrian, Iyer and Qureshi, 2022). Daily returns on matching trading days in our data give 0.02 and 0.37 for the same periods, close to those figures. On our weekly measure they give 0.05 and 0.25.

Depth is thin relative to open interest. The most a strategy can take is set by stressed depth, not average volume. At 14:52 UTC on 26 October 2026, a day after our cut-off, Binance spot, Coinbase and Kraken each held between USD 6.7 million and USD 21.0 million of BTC per side within 1% of mid (Table 13). Binance USD-M BTCUSDT perpetual open interest was USD 7.51 billion at 00:00 UTC that day, and Deribit BTC options open interest was 392,464 BTC, about USD 31.6 billion notional at the underlying price. Depth collapses in stress. FTI Consulting estimates that on 10 October 2025 BTC top-of-book depth fell by more than 90% on key venues, which it does not name (FTI Consulting, 2025). Top-of-book depth is a narrower measure than the depth within 0.1% and 1% of mid in Table 13.

Open interest is itself volatile. Bybit BTCUSDT perpetual open interest averaged USD 0.53 billion in 2021 and USD 5.83 billion in 2025, and its largest seven-day fall in coin terms was 74.4%, in the week to 27 May 2021. Deleveraging is fast, and it removes liquidity at the same time.

11. Regime-conditioned sizing: a general framework

This section sets out a general framework for sizing systematic crypto return sources by regime, drawn from the literature and the statistics above. It describes considerations, not recommendations. It is not a description of Hedgehog's models, signals, parameters or strategy library (Section 12).

1. Forecast risk. Volatility clusters (Section 4), so sizing on forecast volatility rather than constant notional changes the risk profile. Moreira and Muir (2017) report that reducing exposure when volatility is high improved risk-adjusted outcomes for equity factors and currency carry, because volatility moves more than expected returns. Later work finds the improvement unreliable in real time: across 103 equity strategies, volatility-managed portfolios were not systematically better than their unmanaged versions out of sample (Cederburg, O'Doherty, Wang and Yan, 2020). Across more than 60 assets, volatility targeting reduced the likelihood of extreme returns (Harvey et al., 2018).
2. Momentum and crash states. In equities, momentum crashes cluster after large declines with high volatility (Daniel and Moskowitz, 2016), and scaling by momentum's own recent risk nearly eliminated them (Barroso and Santa-Clara, 2015).
3. Carry and leverage. High carry predicts future crashes (Schmeling, Schrimpf and Todorov, 2023), so a high funding level also carries information about crash risk. Open interest, co-movement of funding across venues and coins, venue concentration and the cash rate add information.
4. Option selling and starting volatility. In our sample, implied volatility exceeded subsequent realised volatility by the smallest margin when implied volatility was low (Section 8). The starting level of implied volatility is therefore part of the risk of selling options.
5. Stressed depth. Order-book depth can be measured directly (Table 13), and it can vanish in stress. FTI Consulting estimates that BTC top-of-book depth fell by more than 90% on key venues on 10 October 2025 (FTI Consulting, 2025).
6. One leverage exposure in stress. Correlations across coins and sources rose in downtrends, so limits at book level matter as much as limits on each source.
7. What a regime estimate knew on the day. Regimes bring abrupt, persistent changes in means, volatilities, autocorrelations and correlations, and shifts can materially change optimal portfolios (Ang and Timmermann, 2012). A label computed with hindsight, or without hysteresis, flatters any rule that uses it.

12. How this relates to Hedgehog

Hedgehog Capital is an AI-first global macro research-and-risk service for professional and high-net-worth investors only. It is not available to retail investors or to US citizens or residents. Its central AI does the research and the risk. Each client's own Hedgehog AI runs it on the client's exchange accounts, through its execution engine and a trade-only key. Client capital stays on the client's own exchange accounts at Kraken, Coinbase, Deribit, Binance or Hyperliquid. It is never pooled and never held by Hedgehog, and Hedgehog is not a fund. Clients set which strategies run and at what size.

Hedgehog's published risk approach also conditions risk on the market regime. Risk is monitored in real time, and research and the regime are refreshed every day. The regime estimate is refreshed across cross-asset signals, realised volatility and spread behaviour. EVAR conditions the loss distribution on the regime the market is actually in, and updates it in real time. When EVAR rises for a strategy, that strategy's position limit tightens. When it falls, the limits widen again. The framework in Section 11 is drawn from the literature and the statistics in this paper. It is not a description of Hedgehog's models, signals, parameters or strategy library, and this paper reports nothing about how Hedgehog's strategies have performed.

13. Implications for allocators

The evidence raises several points for professional investors assessing systematic crypto programmes. They are general observations for education. They are not advice, and not a recommendation of any strategy or service.

• Design and premium. Funding of 10.95% a year on Binance's BTCUSDT perpetual is the contract's interest component, not evidence of a market premium. Venues without an interest term, and the cash rate, give a cleaner comparison.
• Recent levels and cycle averages. Binance BTCUSDT funding averaged 30.6% a year in 2021 and 3.0% in 2026 to date, so averages that span cycles say little about current levels.
• Behaviour by regime. A description of a return source tells more when it covers uptrends and downtrends, and high and low volatility, not only the average.
• Linked sources. Diversification measured in calm markets overstates diversification in a deleveraging.
• Stressed depth. FTI Consulting estimates that BTC top-of-book depth fell by more than 90% on key venues on 10 October 2025, and depth in calm conditions is already small relative to open interest (Section 10).
• Venue risk. Exchange failure, withdrawal halts, auto-deleveraging and collateral depegs affect every source here. Capital held on an investor's own exchange accounts is not pooled with other investors' capital, but it still carries the risk of the exchange itself.
• Hindsight in regime labels. A label computed with information from after the date flatters any rule that uses it.
• Decay. Widely traded premia have tended to shrink as capital arrives.

14. Risks and limitations

• Market statistics, not returns. None of the figures measures what any strategy would have achieved after costs, margin and venue risk.
• Short samples. DVOL starts in March 2021, the USDT-margined basis in February 2021 and Binance funding in September 2019. Overlapping 30-day windows make daily volatility observations highly dependent: the 2,012 daily DVOL comparisons contain only about 67 non-overlapping 30-day windows. Long-horizon variance ratios rest on few independent observations, annual correlations on about 52 weeks, and the sell-off table on 12 events.
• Venue selection. Funding and basis come from Binance, Bybit and Deribit; the CME basis differs in level and investor base.
• Venue survivorship. Every venue in our data still operates in 2026. Venues that failed, such as FTX, a large perpetual venue until November 2022, are absent, so the statistics exclude the venues where losses were realised.
• Survivorship. The 20-coin set includes only coins still listed in 2026 and is chosen by their size in 2026.
• Snapshots. Depth and Deribit open interest are single readings from 26 October 2026, a day after the cut-off.
• Simple regime labels. The volatility and DVOL tercile cut-offs are set over the whole sample, so they use hindsight.
• Measurement. Close-to-close realised volatility understates intraday variability.
• Changing rules and data. Exchanges can change funding parameters and intervals, and public histories can be revised. Deribit's funding specification is cited as updated on 21 October 2026 and is applied here to history from 2019.
• Secondary sources. Some evidence comes from industry research (CF Benchmarks, FTI Consulting) or from summaries of working papers published by the authors' universities (Ruan and Streltsov; Dobrynskaya) rather than the underlying papers.

15. Conclusion

Crypto offers a short list of systematic return sources with clear economic roots. Leveraged demand pays carry. Attention and liquidation cascades feed trends. The need for immediacy pays reversal. Demand for protection and for upside pays the volatility premium. The evidence for each is real but sample-dependent, and in several cases it has weakened over time.

The market statistics point to three conclusions. First, part of what looks like carry is contract design, and funding and basis levels fell to around cash rates in 2026. Second, the sources share one leverage cycle, so their diversification falls when it is most needed. Third, most of them are short a tail, so the regime sets their risk more than the average premium does. These findings motivate regime-conditioned sizing: scaling to forecast risk and stressed depth, conditioning each source on the states in which it has failed, and judging every regime estimate on what was known at the time. Such sizing does not remove the tail. Its aim is to change how much of the tail a book holds when the regime turns.

About the data

Market statistics in this paper were computed by Hedgehog Capital Research from public data. Daily BTC and ETH prices come from Coinbase Exchange (from July 2015 and May 2016); daily prices for 20 large coins and hourly BTC and ETH prices from Binance spot; perpetual funding from Binance USD-M (from September 2019), Bybit (from March 2020) and Deribit (from May 2019); quarterly futures and index prices from Binance (from July 2020); implied volatility from Deribit's DVOL index (from March 2021); open interest from Bybit, Binance and Deribit; and the 3-month US Treasury bill rate and S&P 500 index from FRED. Every venue in the data still operates in 2026. Data run through the UTC daily close of 25 October 2026, except order-book depth and Deribit open interest, which are snapshots taken at 14:52 UTC on 26 October 2026, and Binance open interest, read at 00:00 UTC that day. Returns are daily log returns; single-day and single-week moves quoted in per cent are simple price changes. Volatility is annualised with the square root of 365. Daily funding is annualised by multiplying by 365, and the quarterly basis by multiplying by 365 and dividing by days to expiry. The bill rate is converted from FRED's discount basis to a bond-equivalent yield. Trend and volatility labels use BTC's 200-day average and trailing 30-day realised volatility on the previous day. Variance ratios use two-sided wild-bootstrap p-values from 10,000 draws with a fixed seed. All figures are descriptive market statistics, not the returns of any strategy. The fetch and analysis scripts and the unaltered raw responses are retained. Re-running the analysis on the retained data reproduces every figure. A fresh fetch would not reproduce the 26 October snapshots, and exchanges can revise their histories.