Historical return volatility provides an important market-based input for DLOM analysis.
Volatility measures the variability of investment returns over time; it does not measure whether returns are expected to rise or fall. All else equal, a holder who cannot sell an interest immediately may face greater economic exposure when the underlying value is more volatile.
AbbottModelDLOM uses observed public-market evidence to provide quarter-specific volatility information for the selected reference cohort.
Daily Logarithmic Returns
AbbottModelDLOM calculates volatility using daily continuously compounded logarithmic returns. For successive available daily price observations, the return is:
rₜ = ln(Pₜ / Pₜ₋₁)
where:
- rₜ is the logarithmic return for day t;
- Pₜ is the current price; and
- Pₜ₋₁ is the preceding available price.
An adjusted closing price is used when available. If an adjusted closing price is unavailable, the calculation uses a positive unadjusted closing price.
This return convention is consistent with the lognormal price-process assumptions underlying the exchange-option models. Under this framework, prices are modeled as lognormally distributed, while continuously compounded returns are modeled as normally distributed.
One-Year Look-Back Period
Daily volatility is estimated from logarithmic returns observed during the trailing 365 calendar days, corresponding to the conventional 252-trading-day year used in the model.
The actual number of available return observations may be lower because of exchange holidays, missing observations, listing history, or intermittent trading. The 365-calendar-day period defines the historical look-back window; 252 trading days provides the standardized basis for annualizing daily volatility:
σannual = σdaily × √252
Using a trailing one-year window allows the volatility estimate to reflect relatively recent market conditions while providing a broader evidence base than a short-term return window.
The volatility look-back period is distinct from the DLOM model horizon. The look-back period identifies the historical observations used to estimate volatility. The model horizon represents the prospective period during which the holder is exposed to restricted or delayed liquidity.
Volatility Calculation
Daily volatility is calculated as the population standard deviation of the available daily logarithmic returns in the trailing 365-calendar-day window:
σdaily = √[(1/N) × Σ(rₜ − r̄)²]
where:
- σdaily is daily volatility;
- N is the number of available daily logarithmic returns;
- rₜ is the logarithmic return for day t; and
- r̄ is the mean daily logarithmic return over the measurement window.
The corresponding annualized volatility is:
σannual = σdaily × √252
Annualized volatility provides a familiar reporting convention. For model calculations, daily volatility is paired with a horizon expressed in trading days. This is mathematically consistent with pairing annualized volatility with a horizon expressed in trading years.
Reference-Cohort Evidence
A closely held subject company does not have directly observable market-price returns. The platform therefore uses the selected public-company reference cohort to provide market-based evidence concerning the volatility associated with companies of comparable size and industry classification.
The platform presents the lower-quartile, median, and upper-quartile volatility of the selected cohort. These measures support sensitivity analysis and allow the analyst to evaluate a range of volatility assumptions rather than relying on one unexplained point estimate.
The same selected cohort is used consistently across the platform’s performance, liquidity, DLOM, and Mandelbaum analyses. This preserves the connection between the displayed reference companies and the volatility evidence used in the analysis.
Quarter-Specific Measurement
Market volatility can change materially over time in response to economic conditions, company events, industry developments, investor expectations, and broader market uncertainty.
AbbottModelDLOM associates the volatility evidence with the selected valuation quarter. Each company’s volatility estimate uses historical price information available through the applicable quarter-end measurement date.
This quarter-specific approach reduces reliance on current market conditions when the valuation date falls in an earlier period and provides a market-based measure associated with the economic environment applicable to the selected quarter.
Role in DLOM Analysis
Volatility and the applicable model horizon are separate but related DLOM inputs. Volatility measures the variability of returns, while the horizon measures the period during which the holder is exposed to restricted or delayed liquidity.
The applicable exchange-option model uses these inputs to estimate the economic effect of the holder’s inability to achieve immediate liquidity. All else equal, greater volatility or a longer supported horizon will generally increase the estimated economic cost of delayed liquidity, although the result depends on the structure and assumptions of the selected model.
Volatility should not be converted into a separate premium and then added to the model result. Once volatility has been incorporated into the applicable DLOM model, an additional adjustment based on the same volatility evidence could count the same economic effect twice.
Interpretation and Professional Judgment
Historical volatility is an empirical measure, not a forecast or guarantee of future price behavior. It may be affected by unusual company events, thin or intermittent trading, corporate actions, market disruptions, missing observations, structural changes, and the selected measurement period.
The analyst remains responsible for evaluating whether the reference-cohort evidence is relevant to the subject interest and whether company-specific facts support an alternative volatility assumption.
AbbottModelDLOM provides a transparent, market-based analytical foundation, but it does not replace professional judgment.