private equity at center stage optimizing total portfolio ... · who need to understand the...

Private Equity at Center Stage

Optimizing Total Portfolio Performance and Liquidity

Emilian Belev, CFA, ARPM Keith Black, PhD, CFA, CAIA Head, ERM, Northfield Head of Curriculum, CAIA Association

December 2019 Webinar

Private Equity: An OverviewKeith Black, PhD, CFA, CAIA

Showcase your Knowledge @CAIA_Keith Black@CAIAAssociation

Private Equity: An Overview– 3

About CAIA Association

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designations as well as IIROC Understand the core concepts in alternative investments Gain confidence in discussing and positioning alternatives


Private Equity

Private equity investments come in many forms Venture Capital Buyouts Mezzanine and private debt investments

Fund managers can add value through financial engineering or hands-on management involvement

Committed vs. invested capital Institution commits to invest $10 million in a fund Private equity manager calls capital up to three years after

commitment Lockup periods

Capital is only returned to investors after each investment is exited, which can take ten years or longer

Large spread of returns between average and top managers


Venture Capital

Invest in private companies Risk depends on the stage of investment

Seed stage More of an idea than a company, requires investment to build a

team and prove the technology Number of losers far greater than the number of winners, but

profits of winners can be large relative to losses

Growth stage More mature company with products and revenue

Later stage/Pre-IPO Company has proven itself and is nearly ready to exit


Private Debt

Consolidation of large banks is making room for smaller financings that can be closed quickly

Secured/Second Lien Debt Up to 10% annual yield Often highly secure and collateralized

Mezzanine Financing Unsecured debt Up to 16% yield, plus equity warrants or “kickers”

Business Development Companies Publicly traded funds that invest in private debt


Asset Class Performance


Market Size of Investments

Source: 2016 Estimates from Aon Hewitt, HFR, Barclays, Preqin

Traditional Investments

Alternative Investments

U.S. Equity $21,100 Private Equity $4,200 Other Developed Market Equity $15,100 Hedge Funds $3,000 Emerging and Frontier Market Equity $4,100 Real Estate Equity $6,700

Emerging Market Debt $3,000 Infrastructure, Farmland, Timberland, and Private Energy

$620

High Yield Bonds and Bank Loans $3,200 Commodity swaps, ETPs and MTNs $230 Dollar Bonds $19,300 Real Estate Debt $6,000 Other Bonds $21,100 Cash $5,100 Total (in $billions) $98,000 Total $14,750


Participation In Alternatives

Source: Preqin Investor Outlook: Alternative Assets, H1 2019


Institutional Investor Allocation

Source: Preqin Investor Outlook: Alternative Assets, H1 2019


Private Equity Assets Under Management

Source: Preqin Pro

647 666 683 759 8331,044

1,379

1,7571,7411,937

2,1182,2232,410

2,6742,7332,8633,097

3,635

4,203

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

Ass

ets u

nder

Man

agem

ent (

$bn)

Dry Powder ($bn) Unrealized Value ($bn)


Private Equity Dry Powder by Fund Type

Source: Preqin Pro

$294$355$386$376$365$480

$651$779$840$849

$779$757$727$838$841$896

$1,013

$1,238$1,392

$1,617

0

500

1000

1500

2000

Dry

Pow

der

($b

n)

Venture Buyout Growth Early Stage Other Fund of Funds Secondaries


Aggregate Value of Venture Capital Deals* by Region

Source: Preqin Private Equity Online. *Figures exclude add-ons, grants, mergers, secondary stock purchases and venture debt.

0

10

20

30

40

50

60

70

80

Va

lue

of D

eals

$bn

North America Europe Asia ROW


Private Equity Fund Structure

• Organized as a limited partnership• Limited lifetime: 7 – 10 years• Managed by the general partners (GPs)

• Who are GPs and what are their roles?

• Investors are limited partners (LPs)• Who are LPs and what are their roles?

• Pass-through taxation improves efficiency• Typically, not registered with the U.S. SEC


Timing of Private Equity Cash Flows

1 2 3 4 5

Years

6 7 8 9 10 11 12 13 14 15

Exit or Harvest

Management of Portfolio

Allocate Capital

Finding Opportunities

Organization and Fundraising


Annual Capital Called up and Distributed by Private Equity Funds

Source: Preqin Pro

-400

-200

0

200

400

600

800

1000

1200

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

Capital Called up ($bn) Capital Distributed ($bn) Net Cash Flow ($bn)


Cash Flows, Fees and Waterfall

$100 million investment by LP; 2% management fee; 8% hurdle rate; 20% incentive rate; $200 million proceeds from sale

The $100 million gross income is eventually split between GP and LPs

Original contributions Limited Partners-$100

General Partner Total-$100

Management fee (2%) $2 $2Sale of investment for$200 millionReturn of capital $100 $100Preferred return for limited partners

$8 $8

Catch up for general partner

$2 $2

80/20 split or residual amount

$70.4 $17.6 $88

Closing balance $78.4 21.6 $100


Private Equity Performance

• Unique methods to measure performance when compared to traditional assets

• Illiquidity and lack of reliable market prices• Relatively fixed maturity• Timing of cash flows controlled by GP

• Common Measures• Internal rate of return (IRR): also called money-weighted• Total value to paid-in ratio (TVPI): also called total return• Distributed to paid-in ratio (DPI): also called realized return• Residual value to paid-in ratio (RVPI): also called unrealized return


Private Equity PerformanceU.S. Private Equity: Since Inception IRR and Multiples by Fund Vintage Year

Source: Cambridge Associates Q1 2019 Report

Vintage Year

Median (%) Upper Quartile

Lower Quartile

DPI RVPI TVPI

1994 9.68 23.40 1.02 2.41 0.00 2.411995 10.93 30.90 0.64 1.96 0.00 1.961996 8.27 12.30 1.77 1.60 0.00 1.601997 7.15 13.08 -0.49 1.40 0.00 1.401998 9.92 16.30 4.92 1.48 0.02 1.501999 12.13 18.07 5.12 1.91 0.01 1.922000 12.41 21.15 7.48 1.81 0.02 1.832001 17.02 32.62 11.43 2.18 0.03 2.212002 18.23 30.20 6.40 1.89 0.04 1.932003 12.49 16.90 3.68 1.87 0.04 1.912004 10.08 13.32 7.38 1.63 0.06 1.692005 8.13 14.04 3.56 1.52 0.10 1.622006 11.28 15.21 6.40 1.41 0.19 1.602007 11.23 17.92 6.31 1.31 0.38 1.692008 12.50 21.84 7.21 1.20 0.36 1.562009 16.43 23.53 9.39 1.36 0.83 2.192010 17.39 23.10 11.94 1.14 0.59 1.732011 14.32 19.24 8.68 0.79 0.85 1.642012 14.38 19.07 9.28 0.50 1.02 1.522013 15.58 20.02 8.39 0.31 1.07 1.382014 15.46 24.26 10.57 0.31 1.12 1.432015 12.88 22.81 4.58 0.12 1.13 1.242016 9.75 14.15 2.45 0.08 1.08 1.162017 4.36 14.65 -9.06 0.03 0.99 1.03


Dispersion of Private Equity Returns

Source: Kojima, J.C. and D.J. Murphy. “Hitting the Curve Ball: Risk Management in Private Equity.” The Journal of Private Equity, Vol. 14, No. 2, pp. 18-42.

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Illiquid Assets at Center Stage: Optimizing Total Portfolio Performance and Liquidity

Emilian Belev, CFA, ARPMHead of Enterprise Risk Analytics

December, 2019

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Overview • Identify the main investment objectives of an asset owner

• Make an overview of the usual investment vehicles used by asset owners to invest in private market illiquid investments

• Discuss liquidity forecasting and provide some modeling background and industry practices, as well as explore some important ALM and valuation implications

• Describe the impact of liquidity forecasting to the ultimate investment objective of the asset owner

• Illustrate a comprehensive approach to the optimal asset class mix that maximizes the multiperiod total portfolio performance while ensuring that the liquidity targets and liability constraints are not breached in any single period over the investment horizon

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Investment Objective of an Investor with Liabilities • Practically all asset owner have some type of liabilities:

• Legal liabilities – borrowing to be returned, commitments for payout to stakeholders (pensioners, insureds)

• Future Expenditure Liabilities – target amounts that have to be delivered back to the investor so that he can cover expenditure for planned items (house, tuition, scholarships, a new research facility, etc.)

• The ultimate objective of the asset owner is to be able to maximize the upside of their expected performance, while reducing the risk that future periodic liabilities would not be met with some level of confidence (e.g. 97.5%, 95%, or 90%)

• The cornerstone principle in pursuing this objective: the cash flows coming from the illiquid assets have an equivalent role to public assets for the purpose of satisfying liabilities in a future period. A reasonable assumption in this respect is that Illiquid asset cash flows that have occurred in a certain period and have not been used to meet liabilities will be reinvested in the public asset market.

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Illiquid Private Asset Vehicles • The principle ways in which asset owners invest in private illiquid assets are two:

• Through limited partnerships – i.e. private funds• Through direct investing / co-investing with private asset fund managers

• Due to its composite nature, private fund investing is more complex and that is why we will focus on it

• The typical underlying assets in which limited partnerships invest are:• Equity in private companies – common, preferred, hybrid. These investments can be early stage

“venture capital”, growth, or late stage, i.e. “buyouts”.• Debt in private companies – convertible, or not. These investments can be in companies with

stable financial status, or distressed companies.• Real Assets – commercial real estate, real assets.

• Natural resources – farmland, timberland, etc.

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Forecasting Contributions and Distributions of Funds

• Contributions

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$-

$2,000,000.00

$4,000,000.00

$6,000,000.00

$8,000,000.00

$10,000,000.00

$12,000,000.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Sample Periodic Contributions Over The Remaining Fund Life

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Forecasting Contributions and Distributions (cont’d)• Distributions

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$-

$1,000,000.00

$2,000,000.00

$3,000,000.00

$4,000,000.00

$5,000,000.00

$6,000,000.00

$7,000,000.00

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Sample Periodic Distributions Over A Fund Lifecycle

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Forecasting Fund Cashflows (cont’d)• Constant Rate Model – assume some constant rate of contributions and distributions throughout the

life of the fund• Takahashi-Alexander Model (a.k.a. “Yale” model), assumes that distribution rates generally

accelerate due to liquidations as the fund advances in maturity• On the Distributions side assumes a model of the following form where Y is the operational yield from the fund,

B is a “bow” factor, and G is the growth rate:

• On the Contributions side assumes first year 25% called out of outstanding commitments, second year 30% of outstanding commitments, and then 50% for the rest of the fund life

• The Logistic Function Rate Model𝑓𝑓 𝑡𝑡 =

1

[1 + (1𝑎𝑎 − 1)𝑒𝑒−𝑏𝑏𝑏𝑏]

• The BOSTON Model by Aspequity - “Bow-speed Time Option Normalized”: Structurally similar to the “Yale” model, but accounts for the fact that the manager have less of an option to wait to liquidate in the late stage of the fund lifecycle, as they had in the beginning

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Distr. Rate t = max [Yt,(t/T)B] => Distribution t = Distr. Rate t * NAV t-1 * (1+G)

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Forecasting Fund Cashflows (cont’d)

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0

1000000

2000000

3000000

4000000

5000000

6000000

7000000

Periodic Non-cumulative Cash Flow Contributions over Remaining Quarters*

* Powered by Aspequity Cash Flow Model and Northfield Risk Model

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Forecasting Fund Cashflows (cont’d)

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-2000000

-1000000

0

1000000

2000000

3000000

4000000

5000000

Periodic Non-cumulative Cash Flow Distributions over Remaining Quarters*

* Powered by Aspequity Cash Flow Model and Northfield Risk Model

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Cumulative Statistical Distribution of a Private Fund CFs

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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 11Powered by Aspequity Cash Flow Model and Simulation Technology (effectively captures 1021 cash flow paths), in combination with the Northfield Risk Model

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Cumulative Distribution is Key to Risk-Aware Valuation

• One of the most sophisticated methods for Fair Value estimation of private interests stipulated by the authoritative industry bodies (AICPA, IPEV, CFA Institute) is the “certainty equivalent” income method. It employs essentially the same mathematical logic as pricing a financial derivative instrument – finds the price that makes an investor indifferent between investing in a risky vs. a riskless asset.

• Private fund interests with all their embedded dynamics and contingencies (capital calls, waterfalls, distributions) are in all aspects a complex derivative contract between the GP and the LP

• Aspequity’s valuation methodology implements the “certainty equivalent” approach, making use of its cash flow forecasting capabilities, and the robustness of the Northfield’s risk models

• The results is a valuation method that is risk aware, forward-looking, and independent of GPs and accounting ambiguities

• Measures diversification impact at the various stage (e.g. does a FOF add value, does a tail-end fund represent higher risk, etc.)

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Fair Risk-Aware Valuation*

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$-

$200,000,000.00

$400,000,000.00

$600,000,000.00

$800,000,000.00

$1,000,000,000.00

$1,200,000,000.00

$1,400,000,000.00

$1,600,000,000.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Estimated Residual Fund Value over Remaining Life of the Fund

0.0000.2000.4000.6000.8001.0001.2001.4001.6001.800

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

DPI RVPI TVPI

* Powered by Aspequity Cash Flow and Valuation Model, and Northfield Risk Model

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The Objective of a Liability Driven Investor• Let’s take a pension plan as an example. Their objective is normally defined as having a “fully funded

status”, i.e. PV (assets) > PV (liabilities)

• This raises the question what PV discount rate should be used for liabilities; regulators in different jurisdictions have not provided a consistent answer

• A traditional approach to having optimal outcomes is to perform mean-variance optimization of the fund assets. But this faces two ostensible challenges:

• MVO is a single period approach, while investors face periodic liabilities• It is not clear how to translate the periodic liabilities into a MBO risk aversion parameter.

• We should formulate the objective of the investor in a new way:• what is the portfolio that max imizes long term performanc e, while ensuring that the

liquid component of the portfolio performance never falls below a certain level of confidence at any given time horizon when periodic liabilities are due

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The Objective (cont’d)• This newly formulated objective puts illiquid assets at center stage. Rather than calling them

illiquid we can think of them as “ non-tradable, but periodically liquid.”

• We can then formulate the optimization problem at each period over the investment horizon, taking into account the interplay between periodic and cumulative performance of liquid and “non-tradeable” assets.

• What we care about is the performance of the liquid public assets over each horizon, as well as the cash flows produced by the illiquid asset over the same period, as well as the reinvestment value of those cashflows to a later period.

• Given the monetary value of the periodic liabilities, we should operate in monetary space and not in return space. We have to also account for higher moments, particularly from illiquid assets.

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Approach to finding an Optimal Solution• Build Covariance Matrices among the Asset Classes over Different Horizons

• Project the cumulative performance of public assets under multi-period assumptions

• Project expected periodic fund cashflows of “non-traded” assets using the Aspequity cash flow model. Introduce the volatility dimension to the expected CF using the Northfield risk model. Northfield provides risk models with asset-by-asset granularity for equity, debt, and real assets inclusive of CRE, infrastructure, and natural resources. This step produces periodic statistical distributions of the private fund portfolio cash flows.

• Utilizing the Aspequity simulation algorithm build a statistical distribution of the cumulative performance of the private asset class over each time horizon.

• Capture the one period “beta” of each asset class against each other one using the Northfield risk model. Cont’d…

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Approach to finding an Optimal Solution (cont’d)• Build Covariance Matrices over Different Horizons (cont’d)

• Utilizing the Aspequity simulation algorithm build a distribution of one asset class as “driven” solely by the other asset class, period by period.

• Both in the standalone simulation, and the “another asset class driven” simulation, particular attention should be given to the fact that when periodic “non-traded” asset class cashflow occur, they compound at a reinvestment rate that is equal e.g. to the realized public assets in which they get reinvested. The assigned reinvestment asset class for “non-traded” asset cash flow should be specified in advance.

• Based on the realized variance of the asset class over the particular horizon derived in this way, and comparing it to the variance of the standalone driver asset class, calculate n-period beta of that asset class against the “driver” asset class. Using the beta and the variances of both asset classes calculate a covariance between the two assets.

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Approach to finding an Optimal Solution (cont’d)• Set up the Inputs and perform a set of Mean-Variance Optimizations at Each Liability

Horizon • In conjunction with the covariance matrices among all the asset classes, we also have the

expected values for each asset class from the standalone asset class distributions. In essence, we have defined a “one period” Asset Class Risk Model for each liability horizon.

• This allows us to perform a range of “one period“ mean variance optimizations at each horizon by varying the risk aversion parameter with sufficiently broad range and granularity. The resulting alternative allocations form “efficient frontiers” at each horizon.

• For each of the points on the efficient frontier we can calculate e.g. 95% confidence quantile. Using the skew and kurtosis calculated form the distributions we can also calculate an adjusted 95% quantile from a Cornish-Fisher approximation.

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Approach to finding an Optimal Solution (cont’d)• Find the optimal multi-period solution

• We can perform the same procedure for each liability horizon

• At the longest horizon, identify all allocations that have the contemporaneous liability to be positioned at less than or equal to the 95% quantile identified for that period and that particular allocation

• Within the feasible set, find the portfolio with the highest expected value over the long run. This is the one that best fits the objective.

• Confirm that the allocation chosen is also adequately liquid to cover liabilities in prior years. If not, pick a less aggressive efficient asset allocation, or linearly add a liquid asset to the more aggressive efficient asset allocation.

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Optimization Example: Maximizing Long Term Wealth

while Assuring Liquidity Capacity

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Feasible Set of Efficient Portfolios

0

5

10

15

20

25

30

35

0 100 200 300 400 500 600 700

Expexted Total Cumulative Cash Flow

Varinace of Total Cumulative Cash Flow

Efficient Frontier for Cumulative Cash Flow available to cover Liabilities after 10 Years

(Axes in Million $)

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Efficient Portfolios with different Liquidity Levels

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12 14

Expected Total Cumulative Cash Flow

90% Confidence Level Cutoff for Cumulative Cashflow Available to cover Liabilities

Cash Flow Efficient Portfolios over 10 Years(Axes in Million $)

Portfolio A – e.g. a Pension Plan

Portfolio B – e.g. a Sovereign Wealth Fund

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Efficient Portfolios with different Liquidity Levels

Asset Class Portfolio WeightBonds 52%PE 34%Stocks 14%

Asset Class Portfolio WeightBonds 35%PE 46%Stocks 19%

Portfolio A:Provides $ 6.3 Mill.

with 90% confidence

Portfolio B:Provides $ 2.4 Mill.

with 90% confidence

NOTE: The examples herein are for illustration purposes only and do not represent investment advice or recommendations. Investor and investment circumstances vary widely including but not limited to number of asset class definitions, asset classunderlying investment cash flow capacity and dispersion, investment horizons, etc. and each set of circumstances should be evaluated on a case by case basis.

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Is “10 Year Efficient” liquid enough in prior years

-10 0 10 20 30 40 50 60Total Optimal Portfolio Cumulative Cash Flow avaiable to cover Liabilities at the end of the specific period (in Millions of Dollars

10 Year Efficient Portfolio: Cummulative Cash Flow Statistical Distributoins in Prior Years

Year 3

Year 1

Year 5

Year 7

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Is “10 Year Efficient” liquid enough in prior years

-6 -4 -2 0 2 4 6 8 10 12Total Optimal Portfolio Cumulative Cash Flow avaiable to cover Liabilities at the end of the specific period (in Millions of Dollars)

10 Year Efficient Portfolio: Confirming it is Sufficiently Liquid in Prior Periods, as well, with the chosen

level of confidence (90% Cum. CF quantile > Liability for Period)

Year 3

Year 1

Year 5

Year 7

90% Probability Confidence Cutoff

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Key Points About the Optimization Approach

48

• The approach uses cash flows rather than returns. Periodic cash flows of private funds are arm-length measurement of their performance, and periodic returns are not, because there is no consensus pricing in the historical time series on which a private asset return model would be calibrated.

• MVO is only used a baseline tool, not the end objective, as there are multi period constraints and dependencies that should be factored into the analysis.

• Optimization is applied on the cumulative cash flow distribution of the portfolio. The derivation of those as well as the correlations among them for the different asset classes is based on unique and robust simulation that takes all investment details into account.

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Key Points About the Optimization Approach

49

• If the Private Assets to which the investor has access are strong performers, they can get high weights in the optimal mix. Otherwise public equities compete well on the growth dimension. There is no one-size fits-all prescribed allocation, the investor and investment details are important.

• Not only applicable to Private Equity. Real Assets and Resource Assets also weave into well using granular cash flow and risk model as the ones made available by Northfield and Aspequity.

• It may make sense in the early periods to offset redemption liabilities with borrowing in order to have a more aggressive profile that will bring higher expected results with high liquidity confidence in later periods… Or not. Cannot be determined without first performing the type of rigorous analysis outlined here

• Asset Allocation is more about growth and liquidity rather than about diversification. The latter is limited by the number of asset classes and the fact that they all moved by the same broad economics.

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Summary

50

• We have explored methods to capture the liquidity parameters of “illiquid” assets in a multi-period setting, and have made certain preference choices based on robustness and empirical support

• We have observed the transferal of the periodic liquidity properties of illiquid assets into a number of other uses like the cumulative cash flow distribution, GP-independent fair valuation, and liquidity driven Total Portfolio Optimization

• Simulations that derive the specific horizon asset class risk models are accounting for the very complex dynamics of the cash flow accumulation and incorporating higher distributional moments

• The approach also puts emphasis on the fact that multi-period asset class correlations are distinct and different form a single-period correlations, and handles that transformation starting with a baseline risk model with broad asset class coverage and ends with a multi-period representation

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Question and Answer Session

Emilian Belev, CFA, ARPMHead of Enterprise Risk Analytics

[email protected]

Keith Black, PhD, CAIA, CFA, Head of Exams and Curriculum CAIA Association

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mailto:[email protected]

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Appendix: Mechanics of a LP Fund • A would-be General Partner , i.e. sponsor, assigns an advisory entity, i.e. a fund manager, sets a fund

size target, and starts raising capital to meet this target. The investors in the fund, the would-be Limited Partners, commit, but do not pay in committed capital until the capital raising period is over. Usually this last 12 to 18 months.

• The manager starts calling committed capital as they identify attractive deals. This period usually last 2 to 5 years, with the ability of investor to put in follow-on capital in existing deals, up to later years in the fund (e.g. 8).

• As the manager liquidates underlying fund assets through IPOs, sale to another fund or a strategic buyer, or redemption (for debt), the limited partners receive proceeds from those liquidations, alongside the income received of companies and assets that are still not liquidated. When distribution start outweighing contributions over time, by design, the fund starts to wind down in size until it reaches zero residual value which is mandated to occur somewhere between years 10 and 12 from the origination.

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Appendix: LP Funds Additional Characteristics• The way distributions are carried out to investors is guided by the partnership agreement and follows

what is known as waterfall provisions. This is generally done in a precedence of: “return of capital to LPs”, “preferred return of capital to LPs”, “carried interest to GPs”, “additional return to LPs”.

• In general (but not necessarily) the distribution to LPs is proportional to their investment size, as measured by called capital, at the time of the liquidation. The distribution to the GP, above asset management fees, is associated with a proportion of profits, known as “carried interest”.

• Carried interest can be calculated on individual deals (American waterfall) and on the fund as a whole (European waterfall), or according to another arrangement.

• In addition to first-hand investment, funds can also invest in other first-hand investment funds, which is the private version of “fund of funds”, as well as funds that invest in secondary LP stakes that range from mid-cycle to tail-end funds.

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