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HYPERLIQUID · PERPETUAL FUTURES

APEX

APEX-USD perpetual · 24/7 trading on Hyperliquid

▸ Advanced metrics · M2M bundle

hyperliquid · perp-apex · fresh · feed 0s old
24h sparkline · 60 pts 12.34%
realized vol (ann.)
150.60%
max drawdown
1.25%
sharpe
113.34
ulcer index
0.35%
RMS drawdown
pain index
0.28%
mean drawdown
mod. VaR 95%
0.00%
Cornish-Fisher
martin ratio
48530.63
ret / ulcer
CDaR 95%
0.73%
cond. drawdown
gain/pain
1.38
Σgain / Σ|loss|
sterling
23528.56
ret / CDaR
omega (θ=0)
1.38
upside/downside
roll spread
2.5 bps
implied (price-only)
bars used
2000
store
spread
24h Δ
12.34%
flow lean
carry
longs_pay
10.95%
signalNEUTRALconfidence 30%
  • 24h change +12.34%
  • funding: longs pay — perp shorts get paid to wait
Same bundle via M2M API: /api/m2m/hl-apex/bundle · venue execution: hyperliquid
LIVEPOLL0SRCFRESH482ms--:--:-- UTC8NEXT8.0sUP0s--:--HIST0/30
▶ STREAMING·HYPERLIQUID·POLYMARKET·0 POLLS·SRC FRESH·UPTIME 0s·NEXT POLL 8.0s·CC0 OPEN DATA·HYPO.MARKETS·▶ STREAMING·HYPERLIQUID·POLYMARKET·0 POLLS·SRC FRESH·UPTIME 0s·NEXT POLL 8.0s·CC0 OPEN DATA·HYPO.MARKETS·
MARK · live
$0.288
24h Δ · live
12.34%
24h vol · live
$0.1M
APEX · live 24h price
n=25 · μ=0.2651 · σ=0.0094 · range [0.2560, 0.2882] · R²=0.818 RISING +12.37%σ NORMAL 3.56%LAST 0.28820.28820.28020.27210.26410.2560μ = 0.2651max 0.2882min 0.2560dataMA(5)OLS R²=0.82μ lineμ ± σ bandmaxminlive endpoint
25 closes · last $0.29
Funding direction · live
Long fee 48.1%Short fee 51.9%SHORT FEE51.9%
Σ = 0.0%
Σ-sides total = 0.00% (100.00pp arb gap)
H(p) entropy = 0.999 / 1.00 bits (100%) · max uncertainty (~50/50)
Long fee
48.1% +0.00pp
Short fee
51.9% +0.00pp
1h funding 0.001250% · longs pay
Hourly contract volume · live
n=25 · Σ=463,802 · μ=18552.1 · σ=7856.3 · CV=0.42RISING +63% h/hcumulative energy ↗ · 50% by h=15010,84121,68232,52243,363μ = 1855243,36350%h1h5h9h13h17h21h25#1 peak#2-3> μactivequietμ linecum energy
peak 43363 contracts
Live numerics · pulse on poll
LIVE NUMERICS9 metrics·POLL 0
snapshot age
482ms
$mark $
$0.2877
$mid $
$0.2877
prev-day close
$0.2561
Δ24h Δ %
+12.343%
$24h vol $
$122.68k
open interest $
$1.35M
%funding (1h)
0.001250%
%funding (yr)
+10.95%/yr

§1 · 24h time-series

Close price · hourly
n=25 · μ=0.2651 · σ=0.0094 · range [0.2560, 0.2882] · R²=0.818 RISING +12.37%σ NORMAL 3.56%LAST 0.28820.28820.28020.27210.26410.2560μ = 0.2651max 0.2882min 0.2560dataMA(5)OLS R²=0.82μ lineμ ± σ bandmaxmin
mark $0.2877 · 24h 12.34% · range $[0.2560, 0.2882]
OHLC candles · hourly
n=25 · up 21 · down 4 (84% up) · range [0.2547, 0.2893] · σ=0.0094 · CV=0.04 · bodyµ=51%STRONG BULLISH +12.95%CLOSE 0.2882 vs OPEN 0.2552 (+12.95%)&#9650; CLOSE 0.28820.28930.28060.27200.26340.2547μ close = 0.2651O0.255 H0.257 L0.255 C0.256 (+0.51%)O0.255 H0.257 L0.255 C0.256 (+0.51%)O0.257 H0.257 L0.256 C0.257 (+0.21%)O0.257 H0.257 L0.256 C0.257 (+0.21%)O0.257 H0.257 L0.256 C0.256 (-0.23%)O0.257 H0.257 L0.256 C0.256 (-0.23%)O0.256 H0.258 L0.256 C0.257 (+0.56%)O0.256 H0.258 L0.256 C0.257 (+0.56%)O0.257 H0.259 L0.257 C0.258 (+0.47%)O0.257 H0.259 L0.257 C0.258 (+0.47%)O0.258 H0.259 L0.256 C0.257 (-0.45%)O0.258 H0.259 L0.256 C0.257 (-0.45%)O0.257 H0.258 L0.256 C0.256 (-0.21%)O0.257 H0.258 L0.256 C0.256 (-0.21%)O0.256 H0.258 L0.256 C0.257 (+0.21%)O0.256 H0.258 L0.256 C0.257 (+0.21%)O0.257 H0.258 L0.257 C0.258 (+0.12%)O0.257 H0.258 L0.257 C0.258 (+0.12%)O0.258 H0.259 L0.258 C0.259 (+0.35%)O0.258 H0.259 L0.258 C0.259 (+0.35%)O0.259 H0.261 L0.258 C0.261 (+0.92%)O0.259 H0.261 L0.258 C0.261 (+0.92%)O0.260 H0.263 L0.260 C0.262 (+0.49%)O0.260 H0.263 L0.260 C0.262 (+0.49%)O0.262 H0.263 L0.262 C0.262 (+0.28%)O0.262 H0.263 L0.262 C0.262 (+0.28%)O0.262 H0.263 L0.262 C0.263 (+0.09%)O0.262 H0.263 L0.262 C0.263 (+0.09%)O0.263 H0.267 L0.262 C0.267 (+1.58%)O0.263 H0.267 L0.262 C0.267 (+1.58%)O0.267 H0.269 L0.266 C0.267 (+0.07%)O0.267 H0.269 L0.266 C0.267 (+0.07%)O0.267 H0.270 L0.266 C0.270 (+1.02%)O0.267 H0.270 L0.266 C0.270 (+1.02%)O0.269 H0.270 L0.265 C0.267 (-1.00%)O0.269 H0.270 L0.265 C0.267 (-1.00%)O0.266 H0.269 L0.266 C0.269 (+0.79%)O0.266 H0.269 L0.266 C0.269 (+0.79%)O0.269 H0.270 L0.268 C0.269 (+0.16%)O0.269 H0.270 L0.268 C0.269 (+0.16%)O0.269 H0.270 L0.268 C0.270 (+0.33%)O0.269 H0.270 L0.268 C0.270 (+0.33%)O0.270 H0.277 L0.269 C0.276 (+2.30%)O0.270 H0.277 L0.269 C0.276 (+2.30%)O0.276 H0.281 L0.274 C0.281 (+1.74%)O0.276 H0.281 L0.274 C0.281 (+1.74%)2.6%O0.280 H0.289 L0.280 C0.287 (+2.60%)O0.280 H0.289 L0.280 C0.287 (+2.60%)O0.288 H0.289 L0.286 C0.288 (+0.13%)O0.288 H0.289 L0.286 C0.288 (+0.13%)#1#5#9#13#17#21#25up bar (C≥O)down bar (C<O)MA(5) closeμ closedoji (~no body)biggest body
25 bars
Hourly volume (base units)
n=25 · Σ=463,802 · μ=18552.1 · σ=7856.3 · CV=0.42RISING +63% h/hcumulative energy &nearr; · 50% by h=15010,84121,68232,52243,363μ = 185527,837 · 18.1% peak7,837 · 18.1% peak18,086 · 41.7% peak18,086 · 41.7% peak17,986 · 41.5% peak17,986 · 41.5% peak23,678 · 54.6% peak23,678 · 54.6% peak10,750 · 24.8% peak10,750 · 24.8% peak30,371 · 70.0% peak30,371 · 70.0% peak12,711 · 29.3% peak12,711 · 29.3% peak14,338 · 33.1% peak14,338 · 33.1% peak9,658 · 22.3% peak9,658 · 22.3% peak10,702 · 24.7% peak10,702 · 24.7% peak8,616 · 19.9% peak8,616 · 19.9% peak11,813 · 27.2% peak11,813 · 27.2% peak20,708 · 47.8% peak20,708 · 47.8% peak27,137 · 62.6% peak27,137 · 62.6% peak18,597 · 42.9% peak18,597 · 42.9% peak21,659 · 49.9% peak21,659 · 49.9% peak18,657 · 43.0% peak18,657 · 43.0% peak16,935 · 39.1% peak16,935 · 39.1% peak22,193 · 51.2% peak22,193 · 51.2% peak16,126 · 37.2% peak16,126 · 37.2% peak15,803 · 36.4% peak15,803 · 36.4% peak24,253 · 55.9% peak24,253 · 55.9% peak17,319 · 39.9% peak17,319 · 39.9% peak24,506 · 56.5% peak24,506 · 56.5% peak43,36343,363 · 100.0% peak43,363 · 100.0% peak50%#1#5#9#13#17#21#25#1 peak#2-3> μactivequietμ linecum energy
Σ vol 463802 · peak 43363 · CV 0.42

§2 · Returns distribution (log-returns)

Histogram of rₜ = ln(pₜ/pₜ₋₁)
n=24 · 12 bins · μ=0.0046 · σ=0.0079 · skew=0.77 (right-skewed) · kurt=0.22 (mesokurtic)108530 1-95.59bpbin -95.59bp · n=1 · 10.0% peakbin -95.59bp · n=1 · 10.0% peak 1-66.70bpbin -66.70bp · n=1 · 10.0% peakbin -66.70bp · n=1 · 10.0% peak 1-37.80bpbin -37.80bp · n=1 · 10.0% peakbin -37.80bp · n=1 · 10.0% peak 2-8.91bpbin -8.91bp · n=2 · 20.0% peakbin -8.91bp · n=2 · 20.0% peak 1019.98bpbin 19.98bp · n=10 · 100.0% peakbin 19.98bp · n=10 · 100.0% peak 248.88bpbin 48.88bp · n=2 · 20.0% peakbin 48.88bp · n=2 · 20.0% peak 277.77bpbin 77.77bp · n=2 · 20.0% peakbin 77.77bp · n=2 · 20.0% peak 1106.66bpbin 106.66bp · n=1 · 10.0% peakbin 106.66bp · n=1 · 10.0% peak135.55bp 2164.45bpbin 164.45bp · n=2 · 20.0% peakbin 164.45bp · n=2 · 20.0% peak193.34bp 2222.23bpbin 222.23bp · n=2 · 20.0% peakbin 222.23bp · n=2 · 20.0% peakμΔ < 0 · loss barsΔ ≈ 0 · flatΔ > 0 · gain barsN(μ,σ²) referenceμ line · ±σ band shaded
n=24 · positive 19 · negative 5
Q-Q plot · standardised rₜ vs N(0,1)
n=24 · skew=0.72 · kurt=0.36 · near 17 / mid 7 / far 0 · OLS slope=0.98 intercept=-0.00APPROXIMATELY NORMALMILDLY HEAVY UPPERLOWER TAIL NORMAL-3σ-3σ-2σ-2σ-1σ-1σ+0σ+0σ+1σ+1σ+2σ+2σ+3σ+3σsample ↓marginal: sample bars + theoretical N(0,1) curve →theoretical Φ⁻¹(p) →↑ sample z-quantile|Δ| < 0.3σ · on the line|Δ| < 1σ · moderate|Δ| ≥ 1σ · outliery = x refOLS fit

§3 · Spot quote

Mark price
$0.2877
Mid price
$0.2877
24h change
+12.34%
Mark–mid spread
1.22 bps
Prev-day close
$0.2561

§4 · Sample moments (prices)

Descriptive statistics · 5-number summary · shape diagnostics
SAMPLE MOMENTS · N=25STRONGLY RIGHT-SKEWED (G₁=1.10)
μ MEAN0.2651$95% CI: [0.2614$, 0.2688$]
σ STD DEV0.0094$σ² = 0.890×10⁻⁴ · CV = 3.56%
med MEDIAN0.2624$Q₁ 0.2575$ · Q₃ 0.2690$
FIVE-NUMBER SUMMARY · BOX PLOT
min 0.2560$Q₁ 0.2575$med 0.2624$Q₃ 0.2690$max 0.2882$μ
SKEWNESS · G₁1.099right-skewed
−3−10+1+3
EXCESS KURTOSIS · G₂0.227mesokurtic · normal-like
−30+2+4+6
μ ↔ medianμ > med · right-tailed|μ−med| / σ = 0.29
σ × 1.349 ↔ IQRconsistent with normalratio = 1.10
range ↔ σconcentrated (range < 4σ)range / σ = 3.41
μ = mean · σ = standard deviation · CV = coefficient of variation. Skew (G₁): >0 right-skewed. Kurt (G₂, excess): >0 leptokurtic. 95% CI = μ ± 1.96·SE.

§5 · Returns analytics (log-returns)

Risk-adjusted performance · log-returns
RETURNS · RISK-ADJUSTEDEXCEPTIONAL EDGE · SR=55.37
μᵣ MEAN / h+0.486121%drift is positive per h · |μ|/σ = 0.592
σᵣ STD / h0.821767%σ²ᵣ = 0.675×10⁻⁴ · CV = 1.69×
σ ANNUALISED76.91%/yrscaled by √8760 (hourly→yearly) · 0.822%/h base
RISK-ADJUSTED PERFORMANCE
SHARPE (annualised)55.37excellent · top-decile
-2-10+1+2+3+4
SORTINO (annualised)78.46strong downside-adjusted
-2-10+1+2+3+4
CALMAR (return / max-DD)100.00exceptional DD control
-20+2+4+6
RETURN-DISTRIBUTION SHAPE
SKEWNESS · G₁0.77right-skewed · heavy positive tail
-3-10+1+3
EXCESS KURTOSIS · G₂0.75mesokurtic · normal-like tails
-30+2+4+6
SORTINO vs SHARPEdownside vol < total vol · favourableSoR / SR = 1.42
CALMAR · DD CONTROLdrawdown control exceptionalCR = 100.00
EXPECTED EDGE+4258.42%/yr driftμ × 8760 = annualised expectation
rₜ = ln(pₜ/pₜ₋₁). σ × √8760 = annualised. Sharpe = μ/σ scaled; Sortino uses downside-only vol; Calmar = annual return / max drawdown.

§6 · Risk metrics

Tail risk + drawdown · downside diagnostics
TAIL & DRAWDOWN RISKELEVATED · 95% VaR 0.51%
VaR₉₅ (h)0.508%5% prob of larger adverse h move
VaR₉₉ (h)0.969%1% prob · extreme-tail threshold
ES₉₅ (CVaR)0.814%expected loss given 5% tail event
MAX DRAWDOWN1.09%1h from peak to trough
TAIL-RISK LADDER (h losses)
0 · no lossVaR₉₅0.508%VaR₉₉0.969%ES₉₅0.814%worst tail ←→ zero loss
MAX DRAWDOWN PROFILE
PEAK26.96$
1.09% drawdown over 1h
26.66$TROUGH
ES / VaR · TAIL THICKNESSmoderate fat tail|ES₉₅| / |VaR₉₅| = 1.60× (normal ≈ 1.25)
VaR₉₉ / VaR₉₅ · CONCENTRATIONextreme-tail dominated · severe outliersratio = 1.91× (normal ≈ 1.41)
DRAWDOWN · CAPITAL DURATIONmoderate drawdownrecovery needed: +1.11% (compounding)
VaR = quantile loss · ES (CVaR) = expected loss conditional on tail · DD = peak-to-trough decline. Under normality ES₉₅/VaR₉₅ ≈ 1.25; ratio > 1.5 ⇒ fat-tail regime.

§7 · Technicals

RSI(14)
89.2 · overbought
Bollinger %B
1.053 · above upper band
Bollinger upper
$0.2862
Bollinger MA
$0.2672
Bollinger lower
$0.2481

§8 · Time-series structure

Regime & autocorrelation diagnostics
TIME-SERIES STRUCTUREREGIME: TRENDING · variance ratio > 1
ρ(1) AUTOCORR+0.153within white-noise band
ρ(2) AUTOCORR+0.314lag-2 not significant
H · HURST EXPONENT0.885strongly persistent
OLS TREND · t-STAT+10.176significant @ α=0.05
HURST EXPONENT [0, 1]
H = 0.885STRONGLY PERSISTENT
0
anti-persistent
0.45
mean-reverting
0.5
random walk
0.55
persistent
1
strongly trending
AUTOCORRELATION FUNCTION · ρ(k) for k=1..5
k=1+0.153k=2+0.314k=3-0.105k=4-0.053k=5-0.0340+1−1+0.410.41+ momentum (ρ > +0.41)− reversal (ρ < −0.41)noise (within band)±2/√n threshold
OLS TREND · t-STAT · [-5, +5]
−5 reject−1.960 retain H₀+1.96+5 reject
REGIME CLASSIFICATIONTRENDING · variance ratio > 1from Hurst + ρ(1) joint diagnosis
PREDICTABILITY · score 0.92very high · strong structure|ρ(1)| + 2·|H − 0.5| heuristic
TREND SIGNIFICANCESIGNIFICANT @ 1% (|t|=10.18)α=0.05 critical |t|=1.96 · α=0.01 |t|=2.58
ρ(k) = lag-k sample autocorrelation · H = R/S Hurst exponent · t = OLS-trend t-statistic. Significance bands at ±2/√n approximate the 95% white-noise envelope. α=0.05 critical |t|=1.96; α=0.01 |t|=2.58.

§9 · Microstructure

24h volume (USD)
$122.68k
Open interest (USD)
$1.35M
Vol / OI (turnover)
0.09x
1h funding
0.001250%
Funding (annualised)
+10.95%/yr

§10 · Position sizing

Continuous Kelly (μ/σ²)
10.000× leverage · optimal log-utility leverage
Half-Kelly
5.000× · industry-standard conservative
Quarter-Kelly
2.500×

§11 · Hourly return heatmap

24-hour signed Δln-r grid · green = up · red = down
HOURLY RETURN HEATMAP · n=24 bars · best 2.37% · worst -1.10% · typical |Δ| 0.67%BULLISH SESSION +11.67%BEST+2.37%10hWORST-1.10%04hTYPICAL |Δ|0.67%mean absoluteCUMULATIVE+11.67%Σ signed ΔSTREAK↗ 7up-runASIA · 00-08 UTCμ +0.35% · Σ +2.79%EUROPE · 08-16 UTCμ +0.91% · Σ +7.31%US · 16-24 UTCμ +0.19% · Σ +1.56%CUMULATIVE Δ PATH · final +11.67%+11.67%-0.18%0.22% · 12h0.22% · 12h0.22%12h-0.39% · 13h-0.39% · 13h-0.39%13h0.56% · 14h0.56% · 14h0.56%14h0.33% · 15h0.33% · 15h0.33%15h-0.53% · 16h-0.53% · 16h-0.53%16h-0.19% · 17h-0.19% · 17h-0.19%17h0.21% · 18h0.21% · 18h0.21%18h0.20% · 19h0.20% · 19h0.20%19h0.41% · 20h0.41% · 20h0.41%20h0.89% · 21h0.89% · 21h0.89%21h0.29% · 22h0.29% · 22h0.29%22h0.27% · 23h0.27% · 23h0.27%23h0.10% · 00h0.10% · 00h0.10%00h1.59% · 01h1.59% · 01h1.59%01h-0.04% · 02h-0.04% · 02h-0.04%02h1.06% · 03h1.06% · 03h1.06%03h-1.10% · 04h-1.10% · 04h-1.10%04h▼ WORST0.74% · 05h0.74% · 05h0.74%05h0.16% · 06h0.16% · 06h0.16%06h0.29% · 07h0.29% · 07h0.29%07h2.23% · 08h2.23% · 08h2.23%08h1.69% · 09h1.69% · 09h1.69%09h2.37% · 10h2.37% · 10h2.37%10h★ BEST0.32% · 11h0.32% · 11h0.32%11hTIME PATTERNEurope-led (+7.31%)RUNSup max 8 · down max 2BREADTH79% up · 21% down
19 up bars · 5 down · best 2.37% · worst -1.10% · typical |Δ| 0.674%

§12 · Equity curve & underwater drawdown

Cumulative compounded return + running peak-to-trough
EQUITY & DRAWDOWN ANALYSIS · n=25 barsSTRONG PROFIT +12.26% · SHALLOW DDFINAL+12.26%MAX DD-1.10%RECOVERYFULLY RECOVEREDMAX RUN-UP+12.26%UNDERWATER9/25 (36%)STREAK↗ 7EQUITY CURVE · end 1.1226 · peak 1.1226 · range [0.9982, 1.1226]1.12260.9982break-even = 1★ PEAK 1.1226UNDERWATER DRAWDOWN · max -1.10% · moderate0%-1.10%▼ TROUGH -1.10%TOP DRAWDOWN PERIODS · 4 total#1 -1.10%bar 18-20 · 3 bars · recovered#2 -0.71%bar 6-9 · 4 bars · recovered#3 -0.39%bar 3-3 · 1 bars · recoveredDD SEVERITYmoderate (max -1.10%)RECOVERYfully recoveredTIME UNDER WATER36% of session · 9/25 bars
final equity 1.1226 (12.26%) · max DD -1.10% · time-under-water 9/25 bars

§13 · Rolling-window statistics (w = 6 bars)

Rolling annualised Sharpe ratio · green positive · red negative
n=19 · +17 / −2 (89% positive) · μ=59.20 · σ=42.23PROFITABLE STRATEGYLAST 106.57 (+1.12σ vs μ)135.0767.540.00-67.54-135.07μ = 59.20-0.28-0.28-0.56-0.5623.0923.0918.6118.6131.7031.7080.3680.36135.07135.07120.38120.3899.2899.2878.5978.5979.7579.7531.3931.3938.4738.4739.5539.5522.9822.9847.8147.8152.7352.73119.27119.27106.57106.57v > 0 · positivev < 0 · negativeμ mean lineμ ± σ bandlatest bar (outlined)
latest 106.568 · range [-0.56, 135.07] · μ 59.197 · positive Sharpe = excess-return-per-risk earned by buying-and-holding through this window
Rolling annualised volatility (%)
n=19 · μ=62.4750 · σ=28.4638 · range [24.5842, 110.8403] · R²=0.764 RISING +139.21%σ EXTREME 45.56%LAST 96.6859110.840389.276267.712246.148224.5842μ = 62.4750max 110.8403min 24.5842dataMA(3)OLS R²=0.76μ lineμ ± σ bandmaxmin
latest 96.69% · range [24.58%, 110.84%] · μ 62.47% · σ̂ scaled to annualised (×√8760)
Rolling lag-1 autocorrelation ρ(1)
n=19 · +9 / −10 (47% positive) · μ=-0.162 · σ=0.335CLOSE TO MARTINGALELAST 0.020 (+0.54σ vs μ)0.7370.3680.000-0.368-0.737μ = -0.162-0.211-0.211-0.161-0.1610.1560.1560.0420.0420.3460.3460.1600.1600.0110.0110.0220.022-0.248-0.248-0.518-0.518-0.586-0.586-0.468-0.468-0.594-0.594-0.535-0.535-0.737-0.737-0.252-0.2520.1490.1490.3330.3330.0200.020v > 0 · positivev < 0 · negativeμ mean lineμ ± σ bandlatest bar (outlined)
latest 0.020 · |ρ| > 0.3 ⇒ regime with persistence (ρ > 0) or reversal (ρ < 0) · |ρ| ≤ 0.1 = consistent with random walk

§14 · Hypothesis tests (α = 0.05)

Formal inference at 5% significance
1 of 6 REJECT · mixed evidence1 reject·5 pass·α = 0.05
𝒩

Jarque-Bera

FAIL TO REJECTns

H₀: Δln-r ~ Normal(μ, σ²)

STATISTIC
2.9050
p-VALUE (log scale)
0.2340
α
10⁻⁴10⁻³10⁻²10⁻¹1
p ≥ α · null retainednormality not rejected
ρ

Ljung-Box(h=5)

FAIL TO REJECTns

H₀: No serial autocorrelation up to lag 5

STATISTIC
3.8889
p-VALUE (log scale)
0.5676
α
10⁻⁴10⁻³10⁻²10⁻¹1
p ≥ α · null retainedconsistent with white noise
Ψ

Dickey-Fuller (τ_μ)

FAIL TO REJECTns

H₀: p has a unit root (non-stationary)

STATISTIC
2.1678
p-VALUE (log scale)
0.9990
α
10⁻⁴10⁻³10⁻²10⁻¹1
p ≥ α · null retainedrandom-walk behaviour (crit ≈ -2.86)
±

Wald-Wolfowitz runs

FAIL TO REJECTns

H₀: Sign sequence of Δ is random

STATISTIC
0.0540
p-VALUE (log scale)
0.9569
α
10⁻⁴10⁻³10⁻²10⁻¹1
p ≥ α · null retainedsigns appear random (9 runs)
χ

KPSS (μ stationarity)

REJECT H₀**

H₀: p IS level-stationary

STATISTIC
0.8250
p-VALUE (log scale)
0.0062
α
10⁻⁴10⁻³10⁻²10⁻¹1
p < α · rejection zonenon-stationary (crit 0.463)
χ

Variance ratio q=3

FAIL TO REJECTns

H₀: Δln-r is a random walk · VR = 1

STATISTIC
1.4644
p-VALUE (log scale)
0.1431
α
10⁻⁴10⁻³10⁻²10⁻¹1
p ≥ α · null retainedVR 1.446 ≈ 1 (RW behaviour)
Each row states an explicit null H₀, the test statistic, an approximated p-value, and the decision. REJECT means evidence against H₀. KPSS complements ADF (rejecting both ⇒ ambiguous; rejecting one ⇒ clean verdict).

§15 · Spectral analysis (DFT periodogram)

Power spectrum of Δln-r · ‖X̂(k)‖²/n
n=12 bins · noise floor μ=6.54e-5 · top T=12.00h (23.4%) · top-3 cover 52.6%2 SIGNIFICANT CYCLEScumulative energy ↗ (2 bins above 2× noise)1.8e-41.4e-49.2e-54.6e-50.0e+0μ noise floor2× noise (significance)period 24.0 · power 8.96e-5 · 11.4% energyperiod 24.0 · power 8.96e-5 · 11.4% energyperiod 12.0 · power 1.84e-4 · 23.4% energyperiod 12.0 · power 1.84e-4 · 23.4% energyperiod 8.0 · power 8.64e-5 · 11.0% energyperiod 8.0 · power 8.64e-5 · 11.0% energyperiod 6.0 · power 8.72e-5 · 11.1% energyperiod 6.0 · power 8.72e-5 · 11.1% energyperiod 4.8 · power 2.53e-5 · 3.2% energyperiod 4.8 · power 2.53e-5 · 3.2% energyperiod 4.0 · power 3.48e-5 · 4.4% energyperiod 4.0 · power 3.48e-5 · 4.4% energyperiod 3.4 · power 1.05e-5 · 1.3% energyperiod 3.4 · power 1.05e-5 · 1.3% energyperiod 3.0 · power 1.32e-5 · 1.7% energyperiod 3.0 · power 1.32e-5 · 1.7% energyperiod 2.7 · power 9.01e-6 · 1.1% energyperiod 2.7 · power 9.01e-6 · 1.1% energyperiod 2.4 · power 9.20e-5 · 11.7% energyperiod 2.4 · power 9.20e-5 · 11.7% energyperiod 2.2 · power 1.37e-4 · 17.5% energyperiod 2.2 · power 1.37e-4 · 17.5% energyperiod 2.0 · power 1.58e-5 · 2.0% energyperiod 2.0 · power 1.58e-5 · 2.0% energy50% by T=6.0h#1 dominantT=12.00h#2T=2.18h#3T=2.40hT=2hT=3hT=4hT=6hT=8hT=12hT=16hT=24h← shorter cycle (high freq · Nyquist=½) · period T (bars per cycle) · longer cycle (low freq · 1/n) →#1 dominant#2 peak#3 peak> 2× noisenoiseμ floor2μ sig.cum energy
dominant period ≈ 12.00h (freq 0.083) · concentrates 23.4% of total energy · Σ|X̂|²/n = 7.845e-4

▸ Depth section using sovereign-store price series (5000 bars · effective 5257847 bars/year) — annualisation reflects native polling cadence, not upstream timeframes.

§16 · NOSTRADAMUS continuous quant — perp leverage & bootstrap MC

Continuous-price extension of the prediction-market quant module. Kelly growth on observed returns (Merton μ/σ² parametric vs argmax empirical), Monte-Carlo equity fan bootstrapped from the historical return distribution at quarter-Kelly leverage, and an annualized return decomposition. Sweep parameters in the simulator.

§17 · Continuous Kelly

Continuous-Kelly growth · g(f) = E[ln(1 + f·r)]
f★ empirical 8.00× · g(f★) 0.011%/barparametric μ/σ² 65.11× · μ 0.002% · σ 0.05%
μ per barmean
0.002%
σ per barvol
0.05%
Empirical f★argmax g(f)
8.00×
from observed distribution
Parametric f★μ/σ²
65.11×
Merton continuous-time
Half-Kelly½ f★
4.00×
~⅔ of full growth, half the variance
Quarter-Kelly¼ f★
2.00×
industry default — survives model error
0.00%0.00%0.01%0.01%0.01%0.0×1.6×3.2×4.8×6.4×8.0×leverage fraction fexpected log-growth per bar
g(f) empiricalf★ argmaxparametric f★
Maximum expected log-growth from leveraging the historical return distribution. Empirical f★ argmaxes the sample expectation; parametric f★ = μ/σ² is Merton's continuous-time optimum.

§18 · MC equity fan

Bootstrapped equity fan at 3.00× leverage
Median CAGR/bar 0.004% · annualized Sharpe 67.55400 paths × 720 bars · leverage 3.00× · bootstrap from 4999 observed returns
Sharpe / barμ/σ
0.029
annualized 67.55
μ per barafter L
0.004%
σ per barafter L
0.14%
VaR 95%5%
0.13%
per-bar worst-case
CVaR 95%ES
0.30%
mean tail loss
Max DD (median)MDD
-0.1%
0.92×0.97×1.02×1.06×1.11×1.16×0120240360480600720startbar #equity multiple
median25/75 band5/95 band
Median path with 25/75 and 5/95 percentile bands across 400 simulated careers. Bars resample with replacement from the observed return distribution — preserves fat tails the parametric model misses.

§19 · Annualized breakdown

Annualized return components
APR 1000% · APY 1000% · Sharpe 71.88σ ann 110% · Sortino 45.55 · n 4999 · ⚠ capped (n=4999 too small to support 8760-bar projection)
0%1725%3450%5175%6901%8626%1000.0%APR (simple)1000.0%APY (compound)110.4%Ann. vol σ7188.2%Sharpe (ann)4554.7%Sortino (ann)
Simple APR vs compounded APY · annualized volatility · risk-adjusted Sharpe and Sortino. All scaled by √(periods/yr).

§20 · GARCH(1,1) volatility band

GARCH(1,1) · conditional vol envelope (±2σ)
GARCH persistence α+β = 0.980· σ̂ₜ = 1.001% · long-run σ = 2.236%
0.2550.2640.2730.2820.2920.301t-4999t-4166t-3333t-2500t-1666t-833t-0

Persistence near 1 ⇒ vol clusters strongly (slow mean reversion). Long-run σ is the unconditional target the conditional vol orbits. The ±2σ band reflects time-varying scale, unlike a flat-vol band.

Time-varying volatility band fitted to the price series. Persistence α+β > 0.98 means vol shocks decay slowly — recent moves stay relevant.

§∞ · Provenance & attestation

Snapshot fetched
2026-06-14 11:25:15 UTC
Snapshot age
482ms
History points
25 hourly closes
Page rendered
2026-06-14 11:25:15 UTC
Storage policy
no persistence — fetched on every request
SHA-256 attestation
f37e498bb981a96f92e46329b459db0e93b655f8b28a31baa0faf70dc085593c · deterministic hash of the source snapshot — proves this page was rendered from this exact data
Open data licence
CC0 / public domain · free to mirror, syndicate, analyse

§∞-2 · Related markets · explore more

Also see: /arb opportunities · RSS feed

Market depth

live order book · Hyperliquid perp
Depth within 1bp
$0
bid $0 · ask $0
Depth within 5bp
$900
bid $627 · ask $273
Depth within 10bp
$2.74K
bid $2.08K · ask $653
Depth within 50bp
$19.42K
bid $9.94K · ask $9.48K
Mid price
0.287665
(best bid + best ask) / 2
Spread
8.0bp
(bestAsk − bestBid) / mid
Imbalance (whole book)
+0.152
bid-heavy
Imbalance (top-5)
-0.037
ask-heavy top-of-book

Slippage scenarios

live book walk · Hyperliquid perp

Simulating a market order at three notionals against the live book. Slippage = avg execution price vs. mid, in basis points. Worst fill = price of the deepest level touched. Live JSON: /api/asset/hl-apex/slippage?size=10000&side=buy

SideNotionalAvg fillSlippageWorst fillLevelsStatus
BUY$1.00K0.2879098.47bp0.2881004FILLED
BUY$10.00K0.28854930.71bp0.28938017FILLED
BUY$100.00K0.28869235.69bp0.28996020PARTIAL
SELL$1.00K0.2874886.15bp0.2873803FILLED
SELL$10.00K0.28691426.12bp0.28599016FILLED
SELL$100.00K0.28647741.31bp0.28562020PARTIAL

Funding carry

LONGS PAY · shorts receive
Hourly funding
+1.250e-5
0.00125% / hr
Annualised APR
10.958%
hourly · 24 · 365.25
Long: days to 1% carry
33.3d
longs pay
Short: days to 1% carry
33.3d
shorts receive
SideDirectionAnnualised carryDays → 1%Days → 10%
LONGPAY-10.958%33.3d333.3d
SHORTRECEIVE10.958%33.3d333.3d

/api/asset/hl-apex/carry · same metrics, JSON

Volume profile

real volume · Hyperliquid candlesstep $ 1 · 25 records
Price binBarsVolumeDistribution
$0.000000–$1.000025$463.80K

★ POC = Point of Control (highest-volume bin). Live JSON: /api/asset/hl-apex/volprofile?priceStep=1

Order flow

BID-LEAN · +0.563 · Hyperliquid candles
Bars (buy / sell)
19 / 5
1 unclassified
Buy weight
$356.30K
real volume
Sell weight
$99.66K
real volume
Net delta
$256.64K
buyers net
Imbalance
56.29%
(buy − sell) / (buy + sell)
Toxicity (VPIN)
56.3%
one-sided / toxic
Impact (|Δp|/vol)
needs real volume

Sparkline = cumulative delta over the 25-record window./api/asset/hl-apex/flow?rollingWindow=30

Cascade clusters

DOWN · 2 found · deepest 1.09% · Hyperliquid candles

Price-only proxy for forced-unwind clusters. No exchange liquidation feed is wired — read each row as a candidate event, not a confirmed liquidation.

#WindowDurationPeak → TroughDrawdownBars
#12026-06-14 04:00:00Z0ms0.2695700.2666201.094%1
#22026-06-13 16:00:00Z2.0h0.2583100.2564700.712%3

/api/asset/hl-apex/cascades?windowMs=10800000&minDrawdownPct=0.005 · full list + parameters in JSON

Risk metrics

sovereign store · 5,000 barsperiods/year ≈ 5.26M
Realized vol (annualised)
110.41%
σ per bar = 0.000482
Mean return (annualised)
7936.36%
μ per bar = 0.000015
Sharpe (rf=0)
71.88
annualised; risk-free assumed zero
Max drawdown
1.94%
peak 0.27 → trough 0.27 over 750 bars

/api/asset/hl-apex/risk · same metrics, JSON