Core State
NAVt
The governed fair value state at time t.
TCBV Framework
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.
Core Model
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
Core State
NAVtThe governed fair value state at time t.
Market Base
EtThe exposure base after economically effective cash flows are incorporated and before market adjustment is applied.
Benchmark
BtThe selected market proxy level used to carry the state across time in a frequency-consistent way.
Sensitivity
βThe calibrated market sensitivity that links the asset to the chosen benchmark path.
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 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 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 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
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.
| Data Type | Effective Date | Timing | Known Date | Investment Type | Asset Name | Market Proxy | Value (USD) |
|---|---|---|---|---|---|---|---|
| Contribution | 2025-03-15 | EOD | 2025-03-15 | Fund Interest | Fund 1 | Benchmark 1 | +10,000,000 |
| Idiosyncratic | 2025-03-31 | EOD | 2025-03-31 | Fund Interest | Fund 1 | Benchmark 1 | -246,951 |
| Contribution | 2025-05-09 | EOD | 2025-05-09 | Fund Interest | Fund 1 | Benchmark 1 | +650,000 |
| NAV | 2025-03-31 | EOD | 2025-05-15 | Fund Interest | Fund 1 | Benchmark 1 | 10,300,000 |
| Contribution | 2025-07-18 | EOD | 2025-07-18 | Fund Interest | Fund 1 | Benchmark 1 | +400,000 |
| NAV | 2025-06-30 | EOD | 2025-08-14 | Fund Interest | Fund 1 | Benchmark 1 | 10,620,000 |
| Distribution | 2025-08-20 | BOD | 2025-08-20 | Fund Interest | Fund 1 | Benchmark 1 | -900,000 |
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.
| Market Proxy | Date | Level | Market Sensitivity |
|---|---|---|---|
| Benchmark 1 | 2025-03-15 | 1,000 | 0.5 |
| Benchmark 1 | 2025-03-31 | 1,050 | 0.5 |
| Benchmark 1 | 2025-05-09 | 1,069 | 0.5 |
| Benchmark 1 | 2025-05-15 | 1,100 | 0.5 |
| Benchmark 1 | 2025-06-30 | 1,140 | 0.5 |
| Benchmark 1 | 2025-07-18 | 1,160 | 0.5 |
| Benchmark 1 | 2025-08-14 | 1,185 | 0.5 |
| Benchmark 1 | 2025-08-19 | 1,172 | 0.5 |
| Benchmark 1 | 2025-08-20 | 1,170 | 0.5 |
| Benchmark 1 | 2025-09-20 | 1,215 | 0.5 |
| Benchmark 1 | 2025-09-27 | 1,208 | 0.5 |
| Benchmark 1 | 2025-09-28 | 1,212 | 0.5 |
2025-03-15
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
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
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
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
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
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
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
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
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
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
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
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
A new PCAP or NAV observation enters the system.
Decision
New Investment
Build the initial market sensitivity through a governed fallback hierarchy.
Layer 1
Select the proxy based on industry, strategy, geography, currency, and risk profile.
Layer 2
Use exposure-consistent historical observations at the asset level if there are enough datapoints.
Layer 3
If asset-level history is insufficient, move to portfolio-level historical observations.
Layer 4
If portfolio-level data is still not enough, use a governed private-market-level historical dataset.
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.
Re-estimate market sensitivity using the updated information set and the governed rolling window.
Check statistical validity, stability, and economic consistency.
If Yes
Record the dataset, window, diagnostics, and approved parameter. Apply prospectively.
If No
Refine the dataset or window, re-run the test, and escalate through governance approval.
Governance
Any recalibrated market sensitivity affects only future periods. Prior NAV is not retroactively rewritten.
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.
Control Area
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
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
Standard idiosyncratic cases can be handled under standing policy. Non-standard cases, exceptions, or judgment-heavy overrides must move into explicit approval.
Control Area
True-up size and other adjustments should be tested against a defined trigger so that governance effort scales with the investor-facing NAV impact.
Input
A cash flow, NAV observation, idiosyncratic adjustment, proxy change, or market sensitivity update enters the framework.
Check
Confirm event fields, source evidence, calculation support, and documentation completeness before the item becomes part of the governed state.
Decision
Standard idiosyncratic treatments and routine operating cases can continue under policy. Anything outside the approved policy set moves to formal approval.
Materiality
Escalate if the fair value impact is large enough to move the reported per-share NAV beyond the governance threshold.
If No
Keep the evidence, reviewer record, and final calculation in the controlled log, then apply prospectively.
If Yes
Route the item for approval, record the rationale, and preserve the approval chain together with the calculation support.
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.
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
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.
Scenario
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
Five days later, the valuation committee approves an
estimated idiosyncratic adjustment. That committee date
becomes the Known Date.
Effective 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
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.
Day T0
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
The asset continues to roll forward under the standard market rule while the event remains identified but unmeasured.
Day T+5
The valuation committee approves a governed estimate. This
date becomes the Known Date for the
idiosyncratic adjustment.
Application
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.
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
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.
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 |
|---|---|---|---|---|
| NAV | 2024-03-31 | EOD | 2024-05-15 | 10,000,000.00 |
| Distribution | 2024-05-15 | BOD | 2024-05-15 | 250,000.00 |
| NAV | 2024-06-30 | EOD | 2024-08-14 | 10,581,758.87 |
| NAV | 2024-09-30 | EOD | 2024-11-14 | 10,692,695.34 |
| NAV | 2024-12-31 | EOD | 2025-03-31 | 11,271,779.42 |
| NAV | 2025-03-31 | EOD | 2025-05-15 | 10,825,022.03 |
| Contribution | 2025-05-15 | EOD | 2025-05-15 | 400,000.00 |
| NAV | 2025-06-30 | EOD | 2025-08-14 | 12,022,200.16 |
| NAV | 2025-09-30 | EOD | 2025-11-14 | 12,893,514.36 |
| Distribution | 2025-12-15 | BOD | 2025-12-15 | 300,000.00 |
| NAV | 2025-12-31 | EOD | 2026-03-31 | 13,477,135.50 |
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.
| Period | NAV Adj. Change | Benchmark Adj. Change |
|---|---|---|
| 2024-06-30 | 8.09% | 3.60% |
| 2024-09-30 | 1.04% | 5.87% |
| 2024-12-31 | 5.27% | 2.20% |
| 2025-03-31 | -4.04% | -4.59% |
| 2025-06-30 | 6.98% | 10.05% |
| 2025-09-30 | 7.00% | 7.71% |
| 2025-12-31 | 6.66% | 2.55% |
Step 4
Benchmark: S&P Composite 1500 (TR)
Intervals: 7
Market Sensitivity: 0.8595
R-Squared: 0.7022
P-Value: 0.0094
Interpretation
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
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.
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 Q4 | 11.14% | 2.93% |
| 2024 Q1 | 9.81% | 1.73% |
| 2024 Q2 | 3.60% | 1.59% |
| 2024 Q3 | 5.87% | 2.50% |
| 2024 Q4 | 2.20% | 1.99% |
| 2025 Q1 | -4.59% | 1.13% |
| 2025 Q2 | 10.05% | 2.74% |
| 2025 Q3 | 7.71% | 2.43% |
| Private Credit | ||
|---|---|---|
| Period | S&P UBS Global Leveraged Loan Index | Cliffwater Direct Lending Index |
| 2022 Q3 | 0.09% | 1.82% |
| 2022 Q4 | 3.83% | 2.04% |
| 2023 Q1 | 3.49% | 2.69% |
| 2023 Q2 | 3.16% | 2.81% |
| 2023 Q3 | 2.90% | 3.17% |
| 2023 Q4 | 3.37% | 2.95% |
| 2024 Q1 | 2.07% | 3.02% |
| 2024 Q2 | 1.81% | 2.63% |
| 2024 Q3 | 2.84% | 2.65% |
| 2024 Q4 | 0.84% | 2.57% |
| 2025 Q1 | 1.44% | 2.14% |
| 2025 Q2 | 3.69% | 2.34% |
| 2025 Q3 | 1.52% | 2.41% |
| 2025 Q4 | 1.10% | 2.08% |
| Asset Class | Reference Market | Beta | Std. Error | T-Stat | P-Value |
|---|---|---|---|---|---|
| Private Equity | S&P Composite 1500 | 0.244 | 0.056 | 4.35 | 0.002 |
| Private Credit | S&P UBS Global Leveraged Loan Index | 0.897 | 0.111 | 8.08 | < 0.001 |
Interpretation
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
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.
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 |
|---|
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. | |
| Date | Previous NAV | True-Up Adjustment | Cash Flow Adjustment | Market Adjustment | Idiosyncratic Adjustment | Calculated NAV |
|---|---|---|---|---|---|---|
| Enter the benchmark levels and calculate the path. | ||||||
Resources
The materials below provide supporting context for the framework, including the working paper version, background profile, and the current demo workspace.
Books
Papers
Guidelines
Profile