###### A patented and peer-reviewed valuation methodology

### DARC

The DARC, an acronym for Duration adjusted Return on Capital, extends the duration concept of fixed income securities to measure the performance of private capital fund investments in time weighted terms and overcomes the limitations of the money weighted standards currently in use.

Ultimately, private capital investments can be described as extreme forms of fixed income securities, with investment flows and distributions both uncertain but somehow bound as for timing and amount.

In particular, the investments in private capital funds share with those in fixed income securities the characteristic of the targeted (and hopefully satisfactory) self-liquidation of the underlying obligations, within a contractually pre-determined maturity. Distributions have the effect of slowing until they almost stop the ticking of time, smoothing investment risk (and effectiveness) and causing re-investment risk.

The self-liquidation is the critical element that requires a level of handling care that is not guaranteed by the current dollar-weighted IRR and cash-on-cash standards as well as it is by using a duration (i.e. time weighted) framework.

This approach, developed by the firm's founder, has ultimately been considered not only innovative but also useful to address the issues of the calculation of private funds' returns, being granted patents by the USPTO, nr. US 8,386,356 B2 and by the relevant authorities for the related PCT applications.

The Journal of Portfolio Management article details the construction and logic of a novel approach that uses Macaulay duration to create a time-weighted measure of private equity (PE) performance. The objective of this duration-adjusted return on capital metric is to compare the overall return streams of varying private investment outcomes using a single annualized rate of return.

Currently, no single, unambiguous standard captures the actual growth in wealth generated by a PE investment over time. Existing metrics neither enable performance comparisons to other asset classes nor properly measure and represent, through the standard logic of compounding, the underlying portfolio assets.

Therefore, the objective of the authors is to construct a clear, unbiased metric for PE investments that (as for all asset classes) has the simple but robust characteristic of practical usability in a multi-asset, multi-period capital market framework. To this end, they use capital market constraints and algorithms applied in valuing fixed income securities to properly evaluate the impact of contributions, distributions, and interim net asset values in private investing.

The Macaulay duration (the “weighted average time” of a financial transaction) applied to PE fund contributions, distributions, and the resulting net financial transaction is the pivotal tool in this exercise. As presented and tested, the outcome is a modular rate of return that explains the unique time-dependent features of PE investing.

###### A rigorous, time-specific data visualization framework

#### Core Return

It's the return (that the IRR approximates) produced by the capital drawn by the general partner - which neglects any dilution effects from unused cash. DIfferently from the IRR that assumes that returns are produced at time-zero, it shifts the generation on the performance forward on the calendar, to when and for how long it actually happens.

#### Duration Return

It's the core return that takes into consideration what happens since the inception of the investment, including the dilution effects related to the unused cash balances. Similarly to fixed income it is still a modeled return because it assumes a cut-off time (the duration) that ex post may well (and should if any distribution event occurred) be different from the observation time (the horizon).

#### Horizon Return

It's the duration return brought forward to the observation date (the time horizon) in order to reconcile model with actual cash availability at any moment in time, on a daily basis. The possibility of reconciliation with accounting balances is what actually tells apart the DARC from the other perfomance modeling approaches - and what allows actual synthetic replicability, enbling unambiguous contractual and settlement terms.

###### A more accurate risk analytics model

### S-Curve

The S-Curve evolves the J-Curve concept, insofar that decreasing marginal returns follow the initially increasing marginal returns, to better reflect the nature of private markets transactions (as it happens in many other phenomena).

The J-Curve now deserves a quiet obsolescence, after having accompanied the private markets industry through the long initial part of its life-cycle because, in its various versions (cash, IRR, etc.), it does not properly reflect the relevance of time vis-à-vis cash flows. The financial cost of waiting is what makes the distributions furthest in time progressively less relevant, causing returns to marginally decrease.

Without a sigmoid correction, the J-Curve has instilled the perception (that actually could not be truly challenged during the 20-year long benign private markets environment before the recent crisis) that “patient investing” will lead to more money / higher returns. It also implicitly suggests that IRR reinvestment rates truly exist, which is instead not the case.

Deriving the S-Curve requires the adoption of a duration-based (thus time-weighted) performance calculation approach. Duration marks where J turns into S – and allows the interpretative and predictive shift that improves the pricing and risk management perspective in the private markets.

The S-Curve approach, differently from mainstream (academically interesting but over-engineered and imprecise) benchmarking methodologies, is built on a layer of realistic constraints to produce practical and actionable results:

- Not being tied to the “chained” index series logic, an S-Curve does not require any unrealistic assumption on the re-investment of cash-flows between different funds, by definition known only ex-post. The returns of S-Curves can therefore be replicated in concretely investable financial instruments and recorded daily.
- The duration-based framework of the model allows gauging the reliability of NAV fair valuation practices “in real-time”. There is no need to do without NAVs to eliminate fair valuation noise – as one recent paper theorizes, at the cost of not knowing the returns of a fund for years. The S-Curves allow statistical estimates of expected NAVs on a daily basis and probabilistic adjustments on actual NAVs as reported.