ARB-USD Risk Analysis

Risk for ARB-USD is decomposed into five families: dispersion (volatility, beta, idiosyncratic variance), tail risk (Value at Risk, Conditional VaR, fitted t-distribution degrees of freedom), drawdown (historical max, simulated 95th-percentile, recovery time), correlation (to broad market, sector, factor portfolios), and regime sensitivity (how ARB-USD's risk profile changes across low, medium, and high volatility regimes). Each family produces multiple metrics; ARIA reports them all rather than hiding nuance behind a single risk score.

Value at Risk (VaR) for ARB-USD is computed two ways. First, historical simulation: sort the trailing 1,000 daily returns, read the 5th and 1st percentiles, scale by holding period. Second, Monte Carlo: simulate 10,000 paths using t-distributed shocks (degrees of freedom fit per asset, typically 4-8 for equities) with GARCH(1,1) volatility clustering. ARIA reports the more conservative of the two methods, because the cost of underestimating VaR is much higher than the cost of overestimating it. We cover the mechanics in our blog post on Value at Risk.

Conditional VaR (also called Expected Shortfall) tells you the average loss in the worst 5% of paths for ARB-USD, not just where the bad tail starts. CVaR is a strictly better metric than VaR for fat-tailed distributions because it captures severity, not just frequency. A ARB-USD position with a 95% VaR of -8% but a CVaR of -25% is a fundamentally different risk profile than one with a 95% VaR of -10% and a CVaR of -13%. Both look reasonable on the surface; only one will survive a tail event.

Maximum drawdown for ARB-USD is reported in three flavors. Historical: the worst peak-to-trough decline over the trailing 1-year, 3-year, and 5-year windows. Simulated: the 95th-percentile drawdown across 10,000 Monte Carlo paths over the chosen horizon. Recovery: the time required to climb back to the previous peak after the worst observed drawdown. The simulated number is the one that matters for position sizing because the single worst historical path is unstable; the 95th percentile is robust.

Beta for ARB-USD is computed not just against SPY but against the Fama-French factor model (market, size, value, momentum, quality). This decomposition is informative because a high market beta with high quality-factor loading is a different bet than a high market beta with high small-cap loading. The factor decomposition tells you what kind of exposure ARB-USD actually provides. We also report idiosyncratic volatility — the residual variance after factor exposures are removed — which is the variance that diversification can reduce.

Position sizing for ARB-USD follows the Kelly criterion with two safeguards. First, we use calibrated probabilities from the ML ensemble (post-isotonic-regression), not raw scores, so the input to Kelly is honest. Second, we clamp the Kelly fraction at 5% of total capital regardless of how confident the model claims to be. Full Kelly is too aggressive for any real portfolio; fractional Kelly is the conservative choice that practitioners actually use. The Sharpe and Sortino ratios for ARB-USD are reported alongside, with the Sortino specifically penalizing only downside volatility — closer to how most investors actually experience risk.