VaR, Smoothing, Liquidity Risk, and Risk Aggregation

A mid-tier fund-of-funds reported 4.8% five-year volatility on a book with material equity long/short exposure. A diligent allocator ran the return series through a first-order autocorrelation test and found 0.38, extraordinarily high for something that should be near zero. After unsmoothing with the Fisher (2005) approach, the "true" standard deviation rose to about 7.2%, and the Sharpe collapsed from 1.4 to roughly 0.9.

Three specialized terms for futures account levels. Futures contracts have no single clear measure of value, so the CTA industry uses three account-level terms. Trading level is the base amount or denominator used to calculate returns and fees, and the amount of capital traded in the active risk account. Funding level is the total cash or collateral the investor posts to support the trading level, with a rock-bottom minimum equal to the margin collateral the exchanges require.

$$\text{Trading Level}=\text{Funding Level}+\text{Notional Level}$$

For example, a CTA requires a $600,000 minimum. The investor funds $400,000 but has it traded as if funded with $600,000.

Common mistakes

• Confusing trading level, funding level, and notional funding. Trading level is the denominator for returns and fees; funding level is cash posted; notional level is the lever in between. Trap: candidates equate funding level with trading level and miss that a 10% trading-level gain is a 15% funding-level gain when an account is 67% funded.
• Dropping the mean from parametric VaR or using the wrong critical value. The curriculum form is $(\alpha \cdot \sigma )+\mu$. At 95% the critical value is −1.6448, not −2.33. Trap: a 95% answer computed with −2.33 overstates VaR.
• Misstating the variance relationship. True variance equals ${\sigma }_{reported}^2(1+\rho )/(1-\rho )$. At $\rho =0.5$ that is a 3× variance multiplier, not 7× or 9×. Trap: inflated multipliers that ignore the closed form.

Bottom line

• Trading Level = Funding Level + Notional Level; Capital-at-Risk (CaR) sums the loss assuming every stop-loss fires at once.
• Parametric VaR = $(\alpha \cdot \sigma )+\mu$; at 95% use $\alpha =-1.6448$ (not −2.33), and μ is often ignored. Variance can be equal- or exponentially-weighted (λ).
• The omega ratio = upper partial moment / lower partial moment; diversified CTAs run near four, equity indices near two.
• Unsmoothing recovers true returns via $R_{true}=(R_{reported}-\rho R_{-1})/(1-\rho )$, executed in three steps.

Exam shortcut

When a vignette gives you reported vol on illiquid funds, the question is almost certainly testing smoothing. Estimate the first-order autocorrelation $\rho$; if it is materially positive, unsmooth with $\text{True Vol}=\text{Smoothed Vol}\times \sqrt{(1+\rho )/(1-\rho )}$ before any Sharpe, VaR, beta, or optimization step. If a choice uses reported vol directly, it is usually the trap. DECISION: Normal, liquid linear book with a short horizon, use equal-weight parametric VaR and ignore μ.

The full lesson (about 5,192 words, 35 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.

Learning objectives

• alpha systematic risk
• portfolio options
• delta hedging
• delta hedging observations
• mean reversion diversification
• hierarchy alpha
• types alpha
• risk premia betas
• manufactured alpha evidence
• benchmarking attribution overview
• single factor benchmarking
• multifactor benchmarking
• alt asset benchmarking
• benchmarking commodities
• benchmarking managed futures
• benchmarking pe
• peer group benchmarks
• benchmarking re
• margin collateral
• var managed futures
• other liquidity methods
• smoothed returns
• modeling smoothing
• unsmoothing hypothetical
• unsmoothing re data
• risk measurement overview
• risk aggregation
• info categories
• data freq daily weekly monthly
• data freq quarterly annual
• cybersecurity
• risk mgmt structure process

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