TradingCalcReturn Unsmoothing Calculator
RISK/STATS · RETURN UNSMOOTHING · ADVANCED
Getmansky-Lo-Makarov MA(2) smoothing index and Blundell-Ward AR(1) volatility inflation: how much is smoothing understating the true volatility of an infrequently-marked return series?
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For infrequently-marked, appraisal-based, or stale-priced series (illiquid tokens, NAV- based funds, real-world-asset positions) whose reported volatility understates the true risk. Fits two complementary models: Getmansky-Lo-Makarov (MA(2)) and Blundell-Ward (AR(1)).
Why "unsmoothing"?
Infrequently-marked or appraisal-based assets (illiquid tokens, NAV-based funds, real-world asset positions) tend to report smoother returns than the truth: a stale price, a lagged valuation, or infrequent marking blends this period's real move with echoes of past ones. That understates volatility, inflates Sharpe ratios, and hides real drawdown risk. This calculator fits two established models that recover an estimate of the true, de-smoothed volatility.
Getmansky-Lo-Makarov (2004)
Models the observed return as a weighted average of the current and two prior true returns:
- Rtobs = θ0Rt + θ1Rt-1 + θ2Rt-2, θ0+θ1+θ2=1
- ξ (smoothing index) = θ02 + θ12 + θ22
- True volatility multiplier = 1 / √ξ
ξ=1 means no smoothing (all weight on θ₀); ξ=1/3 is the maximum possible smoothing for this model (equal weight on all three periods).
Blundell-Ward (1987)
A simpler single-parameter model, originally from real-estate appraisal smoothing:
- Rtobs = αRt-1obs + (1−α)Rt
- α = the observed series' own lag-1 autocorrelation
- True volatility multiplier = √[(1+α)/(1−α)]
Worked example
Blundell-Ward, α=0.6 (a fairly heavily-smoothed series): true volatility multiplier = √[(1+0.6)/(1−0.6)] = √4 = 2.0×. A reported 1% monthly standard deviation is really closer to 2% - the smoothing is hiding half the true risk.
Getmansky-Lo-Makarov, θ=[0.6, 0.25, 0.15] (weight spread across the current and two prior periods): ξ = 0.6² + 0.25² + 0.15² = 0.445, multiplier = 1/√0.445 ≈ 1.50×. Similar order of magnitude to the single-lag Blundell-Ward case above, since most of the weight (0.6) is still on the current period but a meaningful quarter is one period stale.
Where to go next
Once you have a true-volatility estimate, feed it into a corrected Sharpe ratio with the Sharpe ratio calculator, or compare it against a forward-looking volatility forecast with the GARCH volatility calculator.
Use via API or MCP
This calculation is available as a deterministic API call for bots and AI agents.
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What assumptions and edge cases does this calculator use?
Returns are decimals per period (0.02 is 2%), not prices. It needs at least 20 returns. A flat series is refused, as is a fit that does not converge, and the volatility inflation is undefined when the lag-1 autocorrelation is 1 or more. It models smoothing of up to two lags. Not covered: longer smoothing, fee and tax effects, and proof that the smoothing comes from stale prices rather than from the strategy itself.
What does "unsmoothing" a return series mean?
Recovering an estimate of the true, unobserved volatility that an infrequently-marked or appraisal-based series is hiding. Stale prices or lagged valuations make reported returns look smoother (less volatile) than the real underlying asset, which this calculator corrects for.
Why two different models?
Getmansky-Lo-Makarov (MA(2)) is more flexible, fitting how much weight recent true returns get spread across up to 2 prior periods. Blundell-Ward (AR(1)) is a simpler single-parameter model, originally developed for real-estate appraisal smoothing. Comparing both gives a sense of how sensitive the true-volatility estimate is to the specific model used.
What is the smoothing index (xi)?
A concentration measure (1 = no smoothing at all, down to 1/3 for the MA(2) model's maximum possible smoothing) summarizing how spread out the estimated weights are across the current and prior periods. Lower xi means more smoothing, and a larger gap between reported and true volatility.
Is this specific to real estate or hedge funds?
No. The math applies to any infrequently-marked, appraisal-based, or stale-priced return series, including illiquid crypto tokens, NAV-based fund shares, or real-world-asset positions where the reported price update lags the true market move.
How much data do I need?
At least 20 return values, though more data gives a more reliable smoothing estimate, especially for the MA(2) model, which fits 2 coefficients rather than Blundell-Ward's 1.