The Takahashi-Alexander Model: A Practical Guide

The Takahashi-Alexander (TA) model (a.k.a. “Yale” model) is a powerful tool for modeling pacing and liquidity in private markets. Its simplicity and adaptability make it a favorite among Limited Partners (LPs) investing in private markets. However, like any model, its outputs are only as good as its inputs. Put simply: garbage in, garbage out.

To make the TA model practically useful, it needs to be properly calibrated. In this blog, we’ll walk you through a practical example of calibrating the TA model and provide some example values for key asset classes: private equity (PE), venture capital (VC), real estate (RE), infrastructure (Infra), and private debt (PD).

If you’re new to the TA model or need a refresher, check out our introductory blog here.

Imagine you are a Limited Partner (LP) with investments spanning all major private markets asset classes:

• Private Equity (PE)
• Venture Capital (VC)
• Private Debt (PD)
• Real Estate (RE)
• Infrastructure (INFRA)

You want to understand what the “average profile” for cash flows (calls, distributions, and J-curves) and NAVs might look like under a “baseline” set of conditions. This baseline should reflect the most likely outcome based on historical data combined with reasonable forward-looking adjustments.

How can you approach this? Let’s break it down in 3 steps:

1. Gather the Data
2. Identify Key Parameters
3. Calibrate

Calibrating the TA model starts with understanding the broader context. You’ll need both historical and forward-looking data to make informed assumptions. Here’s how:

• Collect historical data: Look at fund behavior over past vintages to identify patterns in calls, distributions, and NAV growth. This information can be sourced from commercial databases, proprietary datasets, published research, or publicly available reports from government entities involved in private markets.
• Incorporate forward-looking data: Use market forecasts and GP guidance to anticipate future trends. A commonly used resource are “Capital Market Assumptions” issued by asset managers - here is an example with estimates released in 2025.
• Know when to use what: Historical data is an invaluable benchmark for established asset classes like PE, RE and VC, while forward-looking data might play a larger role in nascent or evolving sectors like PD and Infra:

The TA model relies on a few critical parameters. Let’s recap what they are:

• Fund life: Typical duration of a fund, from inception to liquidation
• Call rate: Pace at which capital is called in each period, expressed as a percentage of the outstanding (unfunded) commitments
• Internal rate of return (IRR): Expected annualized return
• Yield: Minimum distribution rate in each period, only relevant for income-generating strategies such as Real Estate, Private Debt, and Infrastructure
• Bow: shape of the distribution rate over the fund’s life

In formulae:

| Calls[t] = Unfunded[t-1] × Call Rate |

| Unfunded[t-1] = Commitment − (All Calls Made To Date t-1) |

| Distributions[t] = Open NAV[t] × Distribution Rate[t] |

| Distribution Rate[t] = max⁡(Yield, Fraction of Fund Life[t]) ^ Bow ) |

| NAV [t] = NAV [t - 1] × (1 + Growth Rate) + Calls[t] − Distributions[t] |

Understanding how these parameters interact is crucial for effective modelling - here is a visual recap:

Keep in mind that TVPI is a derived metric in the model. Faster drawdowns and slower distributions extend the "duration" of NAV, allowing the IRR to work its compounding magic. In other words, for a given call rate, fund horizon, and IRR, a higher bow and lower yield will lead to a higher TVPI—a relationship that proves useful for calibrations in the next section.

With data in hand, it’s time to calibrate the model. Given the relationship between variables, it is important to do this in a predefined sequence:

Fund life, call rate, yield, IRR are independent parameters, making them a natural starting point for calibration:

• Fund Life: Assign realistic durations based on the standards of the asset class, accounting for potential fund extensions.
• Call Rate: Calibrate using historical data while considering regime shifts. For example, be cautious of historical data that doesn't account for drawdown facilities. Two approaches can be used here:
  1. Period-by-Period Calibration: Estimate the call rate from historical data using the formula:
     
                                                                    Call_rate = average [call[t]/unfunded[t−1]]
  2. Curve-Level Calibration: Derive the call rate from the expected cumulative commitment over time using the formula:
     
                                    Call_rate = 1 - (1 - Cumulative call level) ^ (1/years to cumulative call level)
     
     For example, if 90% of commitments are expected to be called by year 5, the implied annual call rate can be calculated as
     
                                                                                  36.9% = 1 - (1- 0.9)^(1/5)

• Yield: Set this parameter to align with historical data or the target returns stated by General Partners (GPs).

The final parameter to calibrate is the elusive bow factor. This can be adjusted to align with either distributions or TVPIs. Using TVPI is particularly effective because, given a fund’s lifetime, IRR, call rate, and yield, a higher bow results in a higher TVPI. This relationship allows you to reverse-engineer the bow factor from TVPI data. Since TVPI is a key metric for many investors, we find this approach especially appealing.

When calibrating parameters, it’s crucial to adjust them to match the frequency used in your projections. While models are often implemented at a quarterly frequency, data is frequently available only at an annual frequency, making these conversions more common than you might expect. Here’s a handy cheat sheet for converting annual data to quarterly frequency:

Let’s apply the framework to create a baseline calibration for Private Equity (PE), Venture Capital (VC), Real Estate (RE), Private Debt (PD), and Infrastructure (INFRA).

Let’s assume the model is calibrated using the following expectation data:

The parameters needed to generate profiles aligned with these expectations are:

Download the Takahashi & Alexander parameters at the end of the blog! 

The example above is purely illustrative. In practice, you would need to:

• Combine historical data with forward-looking insights to determine appropriate parameters.
• Develop alternative parameter sets to evaluate sensitivity across different scenarios.
• Apply bottom-up overrides for funds with unique strategies or those that deviate from market norms.
• Continuously review and update the model to ensure accuracy and relevance.

That said, this should serve as a solid starting point!

The TA model is only as effective as its calibration. By understanding the context, gathering the right data, and fine-tuning key parameters, you can transform the model into a powerful tool for pacing and liquidity planning.

If you’re ready to take this framework to the next level, reach out to our team for expert guidance.

If you would want to familiarize with the Takahashi & Alexander standard parameters, download them from here!