P(A∩B) = P(A)P(B|A) E[X] = Σx·P(x) Var(X) = E[X²] - (E[X])² Z = (X - μ) / σ χ² = Σ(O-E)²/E F = s₁²/s₂² t = (x̄ - μ)/(s/√n) r = Cov(X,Y)/(σₓσᵧ)
RSI = 100 - 100/(1+RS) MACD = EMA₁₂ - EMA₂₆ %K = (C-L₁₄)/(H₁₄-L₁₄)×100 ATR = (1/n)Σ|H-L| CCI = (TP - SMA)/(.015×MD) Williams %R = (H₁₄-C)/(H₁₄-L₁₄) ROC = (P₁ - Pₙ)/Pₙ × 100 OBV = ΣV × sign(ΔP)
ROE = NI / SE ROA = NI / TA D/E = TD / TE P/E = Price / EPS EV/EBITDA = EV / EBITDA FCF = OCF - CapEx ROIC = NOPAT / IC EPS = (NI - PD) / WAS
σₚ² = w'Σw SR = (Rₚ - Rf) / σₚ β = Cov(Rᵢ,Rₘ) / Var(Rₘ) IR = αₚ / σ(εₚ) VaR = μ - zα × σ ES = E[R | R ≤ VaR] MDD = max(DD) Calmar = CAGR / MDD
PV = FV / (1+r)ⁿ FV = PV × (1+r)ⁿ PMT = PV × [r(1+r)ⁿ]/[(1+r)ⁿ-1] NPV = Σ[CFₜ/(1+r)ᵗ] - I₀ IRR: 0 = Σ[CFₜ/(1+IRR)ᵗ] MIRR = ⁿ√(FVₚ/PVₙ) - 1 PI = PV(CI) / PV(CO) DPP = I₀ / CF̄
C = S₀N(d₁) - Ke⁻ʳᵀN(d₂) P = Ke⁻ʳᵀN(-d₂) - S₀N(-d₁) Δ = ∂V/∂S Γ = ∂²V/∂S² θ = ∂V/∂t ν = ∂V/∂σ ρ = ∂V/∂r λ = ∂V/∂q
Y = α + βX + ε R² = 1 - SSR/TSS β̂ = (X'X)⁻¹X'Y DW = Σ(eₜ-eₜ₋₁)²/Σeₜ² AIC = 2k - 2ln(L) BIC = k·ln(n) - 2ln(L) JB = (n/6)[S² + (K-3)²/4] LM = n·R²
ARIMA(p,d,q) φ(L)Δᵈyₜ = θ(L)εₜ ACF(k) = γₖ/γ₀ PACF = φₖₖ GARCH: σₜ² = ω + αε²ₜ₋₁ + βσ²ₜ₋₁ EGARCH: ln(σₜ²) = ω + α|εₜ₋₁| VAR: Yₜ = Φ₁Yₜ₋₁ + εₜ VECM: ΔYₜ = αβ'Yₜ₋₁ + εₜ
MSE = (1/n)Σ(yᵢ - ŷᵢ)² RMSE = √MSE MAE = (1/n)Σ|yᵢ - ŷᵢ| R² = 1 - SS_res/SS_tot Precision = TP/(TP + FP) Recall = TP/(TP + FN) F1 = 2·(P·R)/(P + R) AUC-ROC = ∫TPR dFPR
RWA = Σ(Aᵢ × RWᵢ) Tier 1 = CET1 + AT1 LCR = HQLA / NCOS NSFR = ASF / RSF PD = P(default) LGD = 1 - RR EAD = CCF × UL + DB EC = EAD × PD × LGD
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Market Closed

🛡️ Advanced Risk Analyzer

Comprehensive portfolio risk assessment with VaR, CVaR, CDaR and Monte Carlo simulations

Portfolio Weights

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Error:

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Value at Risk (95%)
$0
Daily VaR
Conditional VaR
$0
Expected Shortfall
CDaR (95%)
$0
Conditional Drawdown at Risk
Ulcer Index
0.0
UCI
Portfolio Volatility
0%
Annualized
Sharpe Ratio
0.00
Risk-adjusted return
CDaR (95%)
0%
Conditional Drawdown at Risk
Sterling Ratio
0.00
Return/Avg Drawdown
Martin Ratio
0.00
Excess Return/UCI
Tail Risk Ratio
0.00
P95/P5 ratio

Monte Carlo Simulations - Distribution Comparison

Normal Distribution
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VaR 95%
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CVaR 95%
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Kurtosis
t-Student Distribution
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VaR 95%
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CVaR 95%
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Degrees of Freedom
Bootstrap Distribution
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VaR 95%
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CVaR 95%
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Kurtosis (Bootstrap)

VaR vs CVaR Comparison

📈 Historical Portfolio Performance & Drawdown Analysis

Rolling Beta Analysis - Different Time Windows

📊 Risk Contribution Analysis

Risk Contribution by Asset (%)

Asset Correlation Matrix

Strong Positive (+0.7 to +1.0)
Assets move together
Moderate (+0.3 to +0.7)
Some relationship
Neutral (-0.3 to +0.3)
Little correlation
Negative (-0.3 to -1.0)
Diversification benefit

Component VaR - Individual Asset Contributions

Component VaR data will appear here after analysis

Risk Analysis by Time Horizon

Risk horizon metrics will appear here after analysis

Stress Testing - Market Scenarios

Stress test results will appear here after analysis