TCBV Framework

A framework for time-consistent, benchmark-driven valuation of private assets.

TCBV is built for the practical gap between sparse external NAV observations. It defines how true-ups, cash flows, market movement, idiosyncratic events, calibration, and governance can work together in one coherent valuation framework.

Time Consistency Carry value between sparse observations without breaking economic timing.
Benchmark Discipline Use explicit proxies and calibrated beta rather than ad hoc interpolation.
Operational Traceability Preserve calibration evidence, checkpoint state, and continuation history.
Animation showing quarterly NAV observations transforming into a frequent valuation path under TCBV
Quarterly NAV gives you points. TCBV reconstructs the path.

Core Model

NAV Evolution Under TCBV

At the framework level, TCBV treats private-asset valuation as a governed state that moves through four additive legs: true-up, cash flow, market, and idiosyncratic adjustment. The formula below is the compact backbone for the operating rules that follow.

Core Formula

NAVt = NAVt-1 + True Up Adjustments + Cash Flow Adjustments + Market Adjustments + Idiosyncratic Adjustments

Notation Snapshot

Core State

NAVt

The governed fair value state at time t.

Market Base

Et

The exposure base after economically effective cash flows are incorporated and before market adjustment is applied.

Benchmark

Bt

The selected market proxy level used to carry the state across time in a frequency-consistent way.

Sensitivity

β

The calibrated market sensitivity that links the asset to the chosen benchmark path.

True-Up Adjustments

A true-up aligns the state to a newly arrived external observation such as a PCAP or valuation report. It is not a new economic event. The measurement-date difference is propagated through the intervening market path and recognized on the known date.

Cash Flow Adjustments

Cash flow adjustments reflect contributions and distributions at their economic effective time. They update the exposure base that participates in subsequent market movement, subject to the timing rule such as EOD or BOD.

Market Adjustments

Market adjustment is the systematic roll-forward term driven by benchmark movement and market sensitivity. In compact notation, the default form is MAt = Et · (exp(β · Δ ln Bt) - 1), which preserves frequency consistency.

Idiosyncratic Adjustments

Idiosyncratic adjustment captures asset-specific discrete effects that are not explained by the systematic market leg. They are recorded as governed absolute contributions once the information is supportable and approved under policy or committee review.

Operating Example

Single-Asset Walkthrough

This example shows how TCBV behaves in practice for one asset. It runs from 2025-03-15 to 2025-09-28, crosses two external NAV observations, includes contributions and a distribution, and then extends into monthly, weekly, and daily roll-forwards. The event table is ordered by Known Date.

Fund 1 Event Rows

Data Type Effective Date Timing Known Date Investment Type Asset Name Market Proxy Value (USD)
Contribution2025-03-15EOD2025-03-15Fund InterestFund 1Benchmark 1+10,000,000
Idiosyncratic2025-03-31EOD2025-03-31Fund InterestFund 1Benchmark 1-246,951
Contribution2025-05-09EOD2025-05-09Fund InterestFund 1Benchmark 1+650,000
NAV2025-03-31EOD2025-05-15Fund InterestFund 1Benchmark 110,300,000
Contribution2025-07-18EOD2025-07-18Fund InterestFund 1Benchmark 1+400,000
NAV2025-06-30EOD2025-08-14Fund InterestFund 1Benchmark 110,620,000
Distribution2025-08-20BOD2025-08-20Fund InterestFund 1Benchmark 1-900,000

Fund 1 Evolution Checkpoints

Not every date is shown. The checkpoints below are selected to illustrate how externally observed NAVs, known dates, cash flow timing, and market-linked roll-forward logic fit into one continuous valuation path.

Benchmark Assumptions For Fund 1

Market Proxy Date Level Market Sensitivity
Benchmark 12025-03-151,0000.5
Benchmark 12025-03-311,0500.5
Benchmark 12025-05-091,0690.5
Benchmark 12025-05-151,1000.5
Benchmark 12025-06-301,1400.5
Benchmark 12025-07-181,1600.5
Benchmark 12025-08-141,1850.5
Benchmark 12025-08-191,1720.5
Benchmark 12025-08-201,1700.5
Benchmark 12025-09-201,2150.5
Benchmark 12025-09-271,2080.5
Benchmark 12025-09-281,2120.5

2025-03-15

Initial Contribution Recorded

NAV03/15/25 = Previous NAV03/14/25 + Cash Flow Adjustment

= 0.00 + 10,000,000.00 = 10,000,000.00

This is the starting point of the example. There is no prior NAV history, so Previous NAV is set to 0, and the initial contribution establishes the first economic position. Because the contribution is assumed to arrive by EOD, it does not receive any same-day market adjustment on 2025-03-15.

2025-03-31

NAV Without External Information

By 2025-03-31, no external NAV report has been received yet, so the state is advanced from 2025-03-15 to quarter-end only through Market Adjustment. However, the fund manager's policy is to hold a new investment at cost through the end of the first month, so an Idiosyncratic Adjustment offsets that month-one market move.

NAV03/31/25 = NAV03/15/25 + Market Adjustment + Idiosyncratic Adjustment

= NAV03/15/25 + NAV03/15/25 × (exp(ln(Benchmark 103/31/25 / Benchmark 103/15/25) × Market Sensitivity) - 1) - NAV03/15/25 × (exp(ln(Benchmark 103/31/25 / Benchmark 103/15/25) × Market Sensitivity) - 1)

= 10,000,000.00 + 246,950.77 - 246,950.77 = 10,000,000.00

State: NAV = 10,000,000.00

2025-05-09

Contribution Received by EOD

The existing NAV is first rolled forward from the latest path checkpoint through market adjustment, and the EOD contribution is then added as a separate additive term without any same-day market adjustment on the contributed amount itself.

NAV05/09/25 = NAV03/31/25 + Market Adjustment + Cash Flow Adjustment

= NAV03/31/25 + NAV03/31/25 × (exp(ln(Benchmark 105/09/25 / Benchmark 103/31/25) × Market Sensitivity) - 1) + Contribution05/09/25 EOD

= 10,000,000.00 + 10,000,000.00 × (exp(ln(1,069 / 1,050) × 0.5) - 1) + 650,000.00 = 10,740,070.56

State: NAV = 10,740,070.56

2025-05-15

True-Up

Assume a new PCAP is received at EOD on this date. The quarter-end NAV for 2025-03-31 is now externally observed. The current NAV first moves from 2025-05-09 to 2025-05-15 through market adjustment, and the true-up difference is then added as a separate propagated adjustment.

NAV05/15/25 = NAV05/09/25 + Market Adjustment + True-Up Adjustment

= NAV05/09/25 + NAV05/09/25 × (exp(ln(Benchmark 105/15/25 / Benchmark 105/09/25) × Market Sensitivity) - 1) + (New NAV03/31/25 - Previous NAV03/31/25) × exp(ln(Benchmark 105/15/25 / Benchmark 103/31/25) × Market Sensitivity)

= 10,740,070.56 + 10,740,070.56 × (exp(ln(1,100 / 1,069) × 0.5) - 1) + (10,300,000.00 - 10,000,000.00) × exp(ln(1,100 / 1,050) × 0.5)

State: NAV = 11,201,743.45

2025-06-30

Quarter-End NAV Without External Information

Starting from the true-upped state on 2025-05-15, the NAV is rolled forward to the next quarter-end before the new report is received.

NAV06/30/25 = NAV05/15/25 + Market Adjustment

= NAV05/15/25 + NAV05/15/25 × (exp(ln(Benchmark 106/30/25 / Benchmark 105/15/25) × Market Sensitivity) - 1)

= 11,201,743.45 + 11,201,743.45 × (exp(ln(1,140 / 1,100) × 0.5) - 1)

State: NAV = 11,403,592.90

2025-07-18

Contribution Received by EOD

A second contribution is received by EOD. As before, the existing NAV is first rolled forward through market adjustment, and the EOD contribution is then added as a separate cash flow adjustment without any same-day market adjustment on the contributed amount itself.

NAV07/18/25 = NAV06/30/25 + Market Adjustment + Cash Flow Adjustment

= NAV06/30/25 + NAV06/30/25 × (exp(ln(Benchmark 107/18/25 / Benchmark 106/30/25) × Market Sensitivity) - 1) + Contribution07/18/25 EOD

= 11,403,592.90 + 11,403,592.90 × (exp(ln(1,160 / 1,140) × 0.5) - 1) + 400,000.00 = 11,903,189.49

State: NAV = 11,903,189.49

2025-08-14

True-Up

The 2025-06-30 NAV is externally observed on this date. The current NAV first moves from 2025-07-18 to 2025-08-14 through market adjustment, and the true-up difference is then added as a separate propagated adjustment.

NAV08/14/25 = NAV07/18/25 + Market Adjustment + True-Up Adjustment

= NAV07/18/25 + NAV07/18/25 × (exp(ln(Benchmark 108/14/25 / Benchmark 107/18/25) × Market Sensitivity) - 1) + (New NAV06/30/25 - Previous NAV06/30/25) × exp(ln(Benchmark 108/14/25 / Benchmark 106/30/25) × Market Sensitivity)

= 11,903,189.49 + 11,903,189.49 × (exp(ln(1,185 / 1,160) × 0.5) - 1) + (10,620,000.00 - 11,403,592.90) × exp(ln(1,185 / 1,140) × 0.5)

State: NAV = 11,231,864.00

2025-08-20

Distribution Received by BOD

Assume the distribution is known at BOD on this date. The NAV is first market-adjusted from 2025-08-14 to 2025-08-20, and the distribution is then removed using only the last-day adjustment factor rather than the full path.

NAV08/20/25 = NAV08/14/25 + Market Adjustment + Cash Flow Adjustment

= NAV08/14/25 + NAV08/14/25 × (exp(ln(Benchmark 108/20/25 / Benchmark 108/14/25) × Market Sensitivity) - 1) - Distribution08/20/25 × exp(ln(Benchmark 108/20/25 / Benchmark 108/19/25) × Market Sensitivity)

= 11,231,864.00 + 11,231,864.00 × (exp(ln(1,170 / 1,185) × 0.5) - 1) - 900,000.00 × exp(ln(1,170 / 1,172) × 0.5) = 10,261,318.11

State: NAV = 10,261,318.11

2025-09-20

Monthly Roll-Forward

After the distribution event, the path is rolled forward on a monthly step to demonstrate time-consistent behavior across the next cycle.

NAV09/20/25 = NAV08/20/25 + Market Adjustment

= NAV08/20/25 + NAV08/20/25 × (exp(ln(Benchmark 109/20/25 / Benchmark 108/20/25) × Market Sensitivity) - 1)

= 10,261,318.11 + 10,261,318.11 × (exp(ln(1,215 / 1,170) × 0.5) - 1)

State: NAV = 10,456,789.35

2025-09-27

Weekly Roll-Forward

The same framework is then applied on a weekly interval, showing that the propagation rule stays consistent across a shorter step.

NAV09/27/25 = NAV09/20/25 + Market Adjustment

= NAV09/20/25 + NAV09/20/25 × (exp(ln(Benchmark 109/27/25 / Benchmark 109/20/25) × Market Sensitivity) - 1)

= 10,456,789.35 + 10,456,789.35 × (exp(ln(1,208 / 1,215) × 0.5) - 1)

State: NAV = 10,426,623.40

2025-09-28

Daily Roll-Forward

Finally, the path is advanced over a single day, showing the same time-consistent rule at daily frequency.

NAV09/28/25 = NAV09/27/25 + Market Adjustment

= NAV09/27/25 + NAV09/27/25 × (exp(ln(Benchmark 109/28/25 / Benchmark 109/27/25) × Market Sensitivity) - 1)

= 10,426,623.40 + 10,426,623.40 × (exp(ln(1,212 / 1,208) × 0.5) - 1)

State: NAV = 10,443,871.75

Beta Calibration

Self-Calibrating Market Sensitivity

TCBV treats market sensitivity as an operating output rather than a fixed assumption. Each new external observation can trigger a new calibration decision, with a fallback hierarchy for new investments and a governed re-estimation path for existing ones.

Trigger

New Observation Arrives

A new PCAP or NAV observation enters the system.

Decision

New Investment or Existing Investment?

New Investment

Build the initial market sensitivity through a governed fallback hierarchy.

Layer 1

Economic Meaning Proxy

Select the proxy based on industry, strategy, geography, currency, and risk profile.

Layer 2

Asset-Level Historicals

Use exposure-consistent historical observations at the asset level if there are enough datapoints.

Layer 3

Portfolio-Level Historicals

If asset-level history is insufficient, move to portfolio-level historical observations.

Layer 4

Private Market-Level Historicals

If portfolio-level data is still not enough, use a governed private-market-level historical dataset.

Output

Set initial market sensitivity through the fallback hierarchy.

Existing Investment

Re-estimate using the updated information set and keep the result under explicit statistical and governance control.

Full-Size Re-Estimation

Re-estimate market sensitivity using the updated information set and the governed rolling window.

Do Statistical Tests Still Hold?

Check statistical validity, stability, and economic consistency.

↙ ↘

If Yes

Document

Record the dataset, window, diagnostics, and approved parameter. Apply prospectively.

If No

Re-Test And Approve

Refine the dataset or window, re-run the test, and escalate through governance approval.

Governance

Prospective Only

Any recalibrated market sensitivity affects only future periods. Prior NAV is not retroactively rewritten.

Governance

Full-Coverage Governance

Because TCBV is continuous, its governance cannot be episodic. The framework requires event capture, parameter maintenance, policy-governed overrides, and materiality escalation to operate as one connected control system rather than as isolated review checkpoints.

Governance Scope

Control Area

Event Data Capture

Every event row should be recorded, timestamped, and reviewed for completeness. That includes Effective Date, Timing, Known Date, value, source, and asset mapping.

Control Area

Documentation Review

Any update to market sensitivity, proxy selection, fallback use, or calibration evidence should be documented and checked before it becomes part of the governed record.

Control Area

Policy-Governed Idiosyncratic Adjustments

Standard idiosyncratic cases can be handled under standing policy. Non-standard cases, exceptions, or judgment-heavy overrides must move into explicit approval.

Control Area

Trigger-Based Escalation

True-up size and other adjustments should be tested against a defined trigger so that governance effort scales with the investor-facing NAV impact.

Continuous Governance Flow

Input

New Event or Parameter Update

A cash flow, NAV observation, idiosyncratic adjustment, proxy change, or market sensitivity update enters the framework.

Check

Record and Review

Confirm event fields, source evidence, calculation support, and documentation completeness before the item becomes part of the governed state.

Decision

Covered by Standing Policy?

Standard idiosyncratic treatments and routine operating cases can continue under policy. Anything outside the approved policy set moves to formal approval.

Materiality

Breaches NAV per Share Trigger?

Escalate if the fair value impact is large enough to move the reported per-share NAV beyond the governance threshold.

↙ ↘

If No

Document and Apply

Keep the evidence, reviewer record, and final calculation in the controlled log, then apply prospectively.

If Yes

Escalate for Approval

Route the item for approval, record the rationale, and preserve the approval chain together with the calculation support.

Example Trigger Design

One practical trigger is based on the reported impact to NAV per share rather than on gross dollar change alone.

Total Fund NAV = 10,000,000

Total Shares = 1,000,000

NAV per Share = 10.00

Governance Trigger = 0.005 per share

Under this design, governance escalation is tied to whether a true-up or other fair value adjustment moves reported NAV per share by more than 0.005. The purpose is to link the trigger directly to investor-facing reporting materiality.

Calculation Convention

The framework can be implemented on a discrete event basis or on a continuous daily, weekly, monthly, or quarterly basis. Official NAV states are rounded to two decimal places at each governed calculation date.

Small numerical drift may arise between external observations because market roll-forward, timing segmentation, and rounding are all applied on a discrete basis. That drift is expected to remain small under the stated convention.

Each new true-up re-anchors the state to the latest external observation and therefore naturally resets most accumulated numerical drift.

Late-Known Events

Late-Known Idiosyncratic Adjustment

Some asset-specific events matter economically before they are measurable. TCBV separates the effective date from the known date so that a governed estimate can be approved later without losing the economic timing of the underlying shock.

Operating Logic

Scenario

Screened News Event

A material news event is screened on the asset on T0. The event is economically relevant immediately, but there is no measurable amount on the same day.

Known Date

Committee Estimate at T+5

Five days later, the valuation committee approves an estimated idiosyncratic adjustment. That committee date becomes the Known Date.

Effective Date

Back to the News Date

The Effective Date remains the original news date because that is when the economics changed, even though the amount was not yet known.

Adjustment Logic

Correct the Whole Gap

Once known, the idiosyncratic adjustment should correct not only the base NAV level but also the market-linked evolution over the gap between Effective Date and Known Date.

Illustrative Flow

Day T0

Material News Becomes Public

The event is screened and tagged as potentially material for the asset, but there is not yet a measurable valuation amount.

Day T0 to T+5

Continue Market Roll-Forward

The asset continues to roll forward under the standard market rule while the event remains identified but unmeasured.

Day T+5

Committee Approves Estimate

The valuation committee approves a governed estimate. This date becomes the Known Date for the idiosyncratic adjustment.

Application

Apply Propagated Idiosyncratic Adjustment

Apply the approved adjustment as an idiosyncratic term with Effective Date = T0 and Known Date = T+5, so the correction captures the full impact through the five-day market path.

Formula Template

The same time-consistent structure applies here. The late-known idiosyncratic adjustment is recognized on the committee date but carried from the original effective date through the intervening market path.

NAVT+5 = NAVT0 + Market Adjustment + Idiosyncratic Adjustment

= NAVT0 + NAVT0 × (exp(ln(BenchmarkT+5 / BenchmarkT0) × Market Sensitivity) - 1) + Idiosyncratic AdjustmentT0,T+5

In practice, Idiosyncratic AdjustmentT0,T+5 should be designed so that the final state on T+5 reflects both the economic event itself and the portion of market-linked evolution that needs to be corrected over the gap period.

Backtesting

Single-Asset Beta Backtesting

Backtesting gives the framework an evidence layer. The example below shows how one asset's quarterly observations can be converted into calibration points and tested against a selected benchmark in order to support a prospective beta decision.

Step 1: Sample Historical Data

The example starts with one asset and a fixed sequence of historical event rows. NAV observations occur at quarter-end, Known Date follows the standard reporting delay, and cash flows retain explicit Timing.

Data Type Effective Date Timing Known Date Value
NAV2024-03-31EOD2024-05-1510,000,000.00
Distribution2024-05-15BOD2024-05-15250,000.00
NAV2024-06-30EOD2024-08-1410,581,758.87
NAV2024-09-30EOD2024-11-1410,692,695.34
NAV2024-12-31EOD2025-03-3111,271,779.42
NAV2025-03-31EOD2025-05-1510,825,022.03
Contribution2025-05-15EOD2025-05-15400,000.00
NAV2025-06-30EOD2025-08-1412,022,200.16
NAV2025-09-30EOD2025-11-1412,893,514.36
Distribution2025-12-15BOD2025-12-15300,000.00
NAV2025-12-31EOD2026-03-3113,477,135.50

Step 2: Selected Benchmark

The benchmark selected for this example is S&P Composite 1500 (TR). Quarter-end observation dates are aligned to the nearest available benchmark level on or before each stated date.

Step 3: Change Table

Period NAV Adj. Change Benchmark Adj. Change
2024-06-308.09%3.60%
2024-09-301.04%5.87%
2024-12-315.27%2.20%
2025-03-31-4.04%-4.59%
2025-06-306.98%10.05%
2025-09-307.00%7.71%
2025-12-316.66%2.55%

Step 4

Backtesting Results

Benchmark: S&P Composite 1500 (TR)

Intervals: 7

Market Sensitivity: 0.8595

R-Squared: 0.7022

P-Value: 0.0094

Interpretation

Conclusion

In this example, a market sensitivity of 0.8595 implies that each 1% logarithmic benchmark move is associated with about 0.86% asset fair value movement, and the conclusion can be used across frequencies.

P-Value = 0.0094 indicates significance at the 99% confidence level.

Broader Market Betas

Private Market Beta Beyond a Single Asset

TCBV does not require every market sensitivity input to come from a single asset's own backtesting history. When asset-level evidence is thin, broader market evidence can still anchor a defensible sensitivity choice. The broader-market evidence below applies the same frequency-consistent logic to private equity and private credit and shows how wider observed evidence can feed the market sensitivity input used in valuation.

Observed Quarterly Evidence

The examples below keep the same TCBV discipline used elsewhere on this site: contemporaneous quarterly observations, economically aligned benchmarks, and no lag or unsmoothing adjustments. The objective is to show the observed evidence directly.

The benchmark choices follow the economic structure of the asset classes themselves. The Cambridge Associates U.S. Private Equity Index is paired with the S&P Composite 1500 because the question is broad public equity sensitivity, not a sector-specific fit. The Cliffwater Direct Lending Index is paired with the S&P UBS Global Leveraged Loan Index as a public credit comparator. The point is not that the two series are identical instruments, but that they sit in the same credit risk family and provide a consistent public-market reference for observed direct lending performance.

Private Equity
Period S&P Composite 1500 Cambridge Associates U.S. Private Equity Index
2023 Q3-3.42%0.58%
2023 Q411.14%2.93%
2024 Q19.81%1.73%
2024 Q23.60%1.59%
2024 Q35.87%2.50%
2024 Q42.20%1.99%
2025 Q1-4.59%1.13%
2025 Q210.05%2.74%
2025 Q37.71%2.43%
Private Credit
Period S&P UBS Global Leveraged Loan Index Cliffwater Direct Lending Index
2022 Q30.09%1.82%
2022 Q43.83%2.04%
2023 Q13.49%2.69%
2023 Q23.16%2.81%
2023 Q32.90%3.17%
2023 Q43.37%2.95%
2024 Q12.07%3.02%
2024 Q21.81%2.63%
2024 Q32.84%2.65%
2024 Q40.84%2.57%
2025 Q11.44%2.14%
2025 Q23.69%2.34%
2025 Q31.52%2.41%
2025 Q41.10%2.08%

Regression Results

Asset Class Reference Market Beta Std. Error T-Stat P-Value
Private EquityS&P Composite 15000.2440.0564.350.002
Private CreditS&P UBS Global Leveraged Loan Index0.8970.1118.08< 0.001

Interpretation

Conclusion

In this broader-market evidence set, the private equity portfolio exhibits an observed market sensitivity of 0.244. This implies that each 1% logarithmic move in the S&P Composite 1500 benchmark is associated with about 0.24% observed private equity investment movement at a 99% statistical confidence level.

In the same evidence set, the private credit portfolio exhibits an observed market sensitivity of 0.897. This implies that each 1% logarithmic move in the S&P UBS Global Leveraged Loan Index is associated with about 0.90% observed private credit investment movement at a 99% statistical confidence level. In TCBV, these broader-market outputs can be used as market sensitivity inputs when asset-level and portfolio-level backtests have not yet produced enough valid observations.

Workbench

Single-Asset Example

This browser example shows one compact way to operate the framework on a single asset. It is included as an illustrative interface, while the full multi-asset workflow continues in the demo workspace.

1. Event Table Input

Enter one single-asset event stream below. Use the controls to add or remove rows. The calculator will sort the rows by Known Date.

Data Type Effective Date Timing Known Date Value Row

2. Benchmark Inputs

Fill the listed dates with benchmark levels. The calculator uses a log-return market link with one market sensitivity input.

Date Index Value
Generate benchmark dates from the event table first.

Calculated NAVs

Date Previous NAV True-Up Adjustment Cash Flow Adjustment Market Adjustment Idiosyncratic Adjustment Calculated NAV
Enter the benchmark levels and calculate the path.

Resources

References and Profile

The materials below provide supporting context for the framework, including the working paper version, background profile, and the current demo workspace.