Emilian Belev presented on constructing private asset benchmarks. He discussed challenges benchmarking private equity funds and explored alternatives including benchmarking private funds against each other or public assets. He proposed using statistical distributions of fund performance over time to derive multi-period covariances between funds and construct efficient portfolios. Valuation models can also price public and private assets using the same risk aversion to determine appropriate public benchmark margins. Forecasting metrics like public market equivalent addresses issues with private fund return smoothing and reporting periodicity. Liability-driven benchmarking assesses the probability of meeting future liquidity needs.

1. Constructing Private Asset Benchmarks
Emilian Belev, CFA
Northfield Information Services
QWAFAFEW
Dec 15,2020
Boston, MA

2. ANNOUNCEMENTS
Hugh Crowther

3. Announcements
■ CFA Boston WEBINARS & VIRTUAL EVENTS
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■ January 14 Tech Talk: A Conversation about Advisors’ Critical Systems and Current
Tech Trends
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4. QU Fall
school
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ML Enablement
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Financial Professionals
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■ https://qufallschool.spla
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5. Slides and Code
■ QuAcademy: www.qu.academy

6. Emilian Belev has led the research and development of
Northfield's Enterprise Risk Analytics at Northfield for about two
decades. He is responsible for an integrated framework of multi-
asset class analysis. The range of modelled assets under his
responsibility includes equity, fixed income, currency, interest
rate, and credit derivatives, structured products, directly owned
real estate, private equity, and infrastructure. He has introduced
innovative methodologies in the areas of convertible bond
analytics, pricing path dependency, credit risk analysis, and
optimal investing in infrastructure, commercial real estate, and
private equity. Emilian has presented on some of these topics at
industry events internationally and published research in peer
reviewed journals and book chapters.

7. www.northinfo.com
Constructing Private Asset
Benchmarks
Emilian Belev, CFA, ARPM
Head of Enterprise Risk Analytics
QWAFAFEW, Boston
November, 2020

8. www.northinfo.com
Overview
We will explore the challenges of benchmarking private equity by looking into
several alternatives, and discuss best practices:
• Private vs. private: A Private Fund returns are benchmarked against the returns
of another Private Fund or a portfolio thereof
• Private vs. public: A Private Fund returns are benchmarked against the returns
of a Public Asset or a portfolio thereof
• PME-style benchmarking: An implicit benchmarking calculation that looks at the
incremental payoff multiple of the Private Fund in comparison to a Public Asset
or a portfolio thereof
• Liability-driven benchmarking: An analysis of the shortfall probability of a
portfolio consisting of liquid and illiquid private assets to meet liabilities in future
periods of time
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Private Asset vs. Private Benchmark
• There are a number of varieties:
• Compare the returns of an asset against an average of other assets with
similar characteristics – vintage, vintage, strategy, etc.
• Compare the returns of an asset against that of a single other asset with
similar characteristics – vintage, vintage, strategy, etc.
• Other varieties – medians, combination between different characteristics
• What is the textbook definition of a benchmark:
• an efficient (minimal variance) portfolio that meets certain constraints
that also apply to the asset we benchmark
• none of the above varieties necessarily meet this criteria by construction
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Private vs. Private (cont’d)
• How can one construct a benchmark:
• Consider a universe of investments
• Limit the universe to only those investments that satisfy the constraints
which also apply to the asset we benchmark – vintage, strategy, etc.
• Construct a covariance matrix of all the funds in the filtered universe
• Perform Mean Variance Optimization on the covariance matrix to derive the
optimal set of weights for each fund in the benchmark
• “…Construct a covariance matrix of all the funds in the filtered universe…”
How?
• Can we use fund manager reported historical returns to calculate
covariances? No – they are smoothed, subjective, and historical
• Can we use unsmoothed manager returns? No – unsmoothing introduces
estimation error that magnifies with the larger universe of funds
• Then what can we do?
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Private vs. Private (cont’d)
• Derive covariances based on a risk model
• Should we consider buy-and-hold or liquidation at any particular period
• Liquidation is disadvantageous due to high transaction cost, so rarely assumed
ex-ante
• Therefore, it is most appropriate to assume that a fund and, in parallel, the
benchmark constituents are held until their stated fund maturity
• The covariances should account for the J-curve of asset fund performance over
time
• We Illustrate this by building statistical distributions for each fund’s performance
over its lifetime using a robust simulation algorithm (1021 realization paths),
developed by Northfield partner Aspequity:
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Statistical Distribution of Cumulative Fund Value
0
0.005
0.01
-500 500 1500 2500
Year 1
0
0.001
0.002
0.003
0.004
-500 500 1500 2500
Year 3
0
0.001
0.002
0.003
-500 0 500 1000 1500 2000 2500
Year 5
0
0.0005
0.001
0.0015
0.002
-500 0 500 1000 1500 2000 2500
Year 7
0
0.0005
0.001
0.0015
0.002
-1000 0 1000 2000 3000
Year 11
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Multi-period Covariance
• Build the cumulative value statistical distribution of a standalone fund B over
T periods, as just shown. Calculate the realized standard deviation of
outcomes of this distribution: 𝝈 𝑩,𝑻
• Utilizing again the simulation algorithm build a statistical distribution of the
cumulative value of one fund B as “driven” solely by another fund A, period
by period, based on a single period beta of B to A, which is derived using a
single-period risk factor model. Calculate the realized standard deviation of
outcomes of this distribution: 𝝈 𝑩~𝒇 𝑨 ,𝑻
• The correlation of funds A and B is equal to the ratio of 𝝈 𝑩,𝑻 and 𝝈 𝑩~𝒇 𝑨 ,𝑻
Proof shown next.
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Correlations from Cumulative Value Distributions
• Can be estimated from the projected cumulative cash flow distribution
processes for 𝑩 and 𝑩~𝒇 𝑨
• A computational short-cut:
𝑪𝒐𝒓𝒓 𝑯𝒐𝒓𝒊𝒛𝒐𝒏 𝑻 𝑩, 𝑨 =
𝝈 𝑩~𝒇 𝑨 ,𝑻
𝝈 𝑩,𝑻
=
𝜷 𝑩−𝒕𝒐−𝑨,𝑻 ∗ 𝝈 𝑨,𝑻
𝝈 𝑩,𝑻
=
𝑪𝑶𝑽(𝑩, 𝑨) 𝑻 ∗ 𝝈 𝑨,𝑻
𝝈 𝑨,𝑻
𝟐 ∗ 𝝈 𝑩,𝑻
=
𝑪𝑶𝑽(𝑩, 𝑨) 𝑻
𝝈 𝑨,𝑻 ∗ 𝝈 𝑩,𝑻
where 𝝈 𝑩~𝒇 𝑨 ,𝑻 and 𝝈 𝑩,𝑻 come directly from the projected cumulative
cash flow distribution processes for 𝑩 and 𝑩~𝒇 𝑨
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Efficient Portfolios by Combining Private Funds
9
0
5
10
15
20
25
30
35
0 100 200 300 400 500 600 700
Expected Total
Cumulative Value of
Portfolio
Variance of Total Cumulative Value of Portfolio
Efficient Frontier for Cumulative Portfolio Value over 10 Years
(Million $)
Minimum Variance Portfolio –
choose as benchmark

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Private Asset vs. Public Benchmark
• A number of varieties, but most often the benchmark chosen is a public index
plus a margin on top. Clearly, there are two parameters to this formulation:
• What public index to choose; traditionally those would have some small-cap
stock content, or at least very broad representation – e.g. Russell 3000
• The thornier question: What should be margin on top be?
• Three general issues with this category of benchmarking:
• Illiquidity premium of private equity
• Smoothing of private asset returns
• Periodicity of reporting
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Private vs. Public (cont’d)
What is the appropriate Margin on top of the public index ?
• Many (subjective) varieties: a vendor supplied capital market assumptions, use
CAPM, expert consensus, etc.
A rigorous approach would be:
• Use a valuation model on the public market index and infer embedded risk aversion
from the traded price P
• Use a valuation model on the private asset and infer embedded risk aversion; can be
done using either through a recent secondary transaction or a recent commitment as
an input for value
• Price the public market index with the private asset risk aversion and derive price P1
• Margin over a public index for PE benchmarking = 100 * (P – P1)/P
• This margin can be thought of to reflect the illiquidity premium
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Valuation Models
Two possibilities to price the statistical distributions of cumulative fund value we
demonstrated earlier:
• A valuation model developed by Northfield partner Aspequity. It finds the
certainty equivalent of a utility function of this form, which captures higher
distributional moments:
Utility = Expected Profit – Risk Aversion * Expected Loss
• A valuation model based on the certainty equivalent of a mean variance utility
function
DCF models based on single-period discount rates (e.g. CAPM) make non-
observable assumptions (how is the multi-period beta of PE derived?), and not to
be used to long term illiquid assets.
Market Comps methods are inherently “somebody else’s black box”, and leave us in
the dark about their biases and changing market conditions
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Valuation Models (cont’d)
13
Use the two valuation
models to price the
Russell 3000 index for
the last two decades
Compare to actual
prices
Use the average share
dividend, forecast
cumulative value and
price using an implicit
risk aversion
according to each
model

20. www.northinfo.com
Private vs. Public: Remaining Issues
• Smoothing of private asset returns
• Due to smoothing, public returns will be much more volatile compared to the
subjective and appraisal based returns reported by funds
• The term “dislocation” was coined to “explain” this
• As noted, econometric unsmoothing introduces estimation error that does not
diversify, so we don’t want to use it in benchmarking
• Substitute appraisal values with the economic valuations derived with the models
described previously, utilizing changing economic and market conditions - this
issue disappears
• Periodicity of reporting
• A data point discrepancy: public indices are priced daily, funds are priced quarterly
• Perform economic valuations at the same periodicity as the public index - this issue
disappears
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Public Market Equivalent (PME) Approach
• Cumulative PME (Kaplan-Schoar)
• Compound historical contributions and distributions of a fund by the
historical return of chosen public market index; we get respectively the
quantities FV(Distr.) and FV(Contr.) as of time Now
• PME = [FV(Distr.) + NAV] / FV(Contr.)
• Direct Alpha (Gredil, Griffiths, Stucke)
• Finds the Alpha equivalent of IRR
• PME Considerations:
• Both of these methods are point estimates based on the past performance
• If inferences about the future are to be made, we need to be able to forecast
these metrics
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Forecast PME and Direct Alpha
Using the simulation and covariance methodology described previously one can:
• Calculate Forward looking PME:
• Run a simulation over the remaining fund life 𝑻 of a ratio where in the
numerator distributions are reinvested by the market index simulated return and
a denominator where contributions are reinvested by the market index
simulated return. We can show that the average of the simulated ratio
statistical distributions is the expected forward looking PME.
• Calculate Forward looking Direct Alpha:
• Take the ratio of the average cumulative value from the standalone fund
distribution and the average from a “public-driven-only” fund distribution; from
our prior covariance discussion these are respectively averages of the
processes 𝑩 and 𝑩~𝒇 𝑨 , where 𝑨 is not a another fund but the market index.
We can show that the ratio of the these averages is also equal to:
(1 + 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝐷𝑖𝑟𝑒𝑐𝑡 𝐴𝑙𝑝ℎ𝑎) 𝑇
16

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Liability-Driven Benchmarking
• This Benchmarking Approach only makes sense about the future:
• Satisfying liabilities in the past is a binary variable
• Satisfying liabilities in the future is a probabilistic variable
• It is relevant to investors with identifiable periodic liabilities in the future –
pensions, insurance companies, endowments, and not rarely - SWF
• Duration-matching is a pointless exercise in the presence of private (not-
marketable) assets.
• What matters is explicitly meeting future liquidity targets that reflect liability
outflows
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Liquidity Planning
• Create Pacing Models for Private Asset Investment Cash Flows
Enhanced version of Takahashi and Alexander model
• Incorporate Uncertainty of Cash Flows
Best of breed risk factor models for equity, debt, and real assets form Northfield
• Convert cash flow projections to cumulative, multi-period statistical probability
distributions of liquid resources available in each future period
Super efficient simulation engine from Aspequity instantaneously captures 1021 cash flows
paths over ten year investment horizon
• Build covariance matrix of asset class cumulative value and probability distribution
thereof of liquid resources available in period N. Calculate the p-value where
liabilities plot on this probability distribution. We can also build an efficient frontier of
the tradeoff between preset confidence liquidity capacity level and expected long term
portfolio value. Pick optimal portfolio based on a desired confidence level (e.g. 85%).
Northfield’s optimization application automatically builds the efficient frontier based on cash
flow covariance model inputs
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Liquidity Planning Illustrated
19
Liability Due

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…more paths…
20
Liability Due

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…our Solution
21
Liability Due
Probability
Distribution of
Cumulative
Liquid
Portfolio Value
Using 1021 cumulative value paths provides a continuous probability distribution
which immensely reduces sampling error of Monte Carlo simulations

28. www.northinfo.com
Conclusions
• Benchmarking private equity is much less developed and standardized than
benchmarking public equity
• Several general approaches have evolved in the industry and academia, and
have been adopted in practice with varieties around these common themes
• Lack of rigor and standard of methodology pervade many of the practical
implementations, producing subjective and unreliable outcomes in the
investment area where this is most undesirable - benchmarking
• Using a set of robust approaches and technology, the investment practitioner
can remedy or mitigate some of these deficiencies and produce much more
accurate outcomes
• The same discussion applies to most other private asset classes
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Thank you
Emilian Belev, CFA, ARPM
Head of Enterprise Risk Analytics
emilian@northinfo.com
23

30. Thanks for joining!
Questions