12  Session 3: The Liquidity Illusion · Secondary Market Evidence

Unit 1 — Why DCF Fails
Book Chapter 2 (sections 2.1–2.7)
Track Common core (both tracks)

12.1 Learning Objectives

By the end of this session, students will be able to:

  1. Describe the structure of the private market secondary market — who trades, why, through which brokers, at what volume.
  2. Interpret the discount-to-NAV ratio as a market-implied measurement of the aggregate liquidity premium.
  3. Identify the four regimes of secondary market discounts 2003–2024 and describe what economic conditions characterize each.
  4. Define the liquidity illusion rigorously: the gap between GP-reported NAV and economic clearing value.
  5. Distinguish level illusion (level of NAV is wrong) from convexity illusion (NAV’s sensitivity to liquidity state is wrong).

12.2 Pre-Class Assignment

  • Read: Book Chapter 2, all sections (~30 pages)
  • View: Pre-class video (5 min) — “What is the PE secondary market?” (link on course site)
  • Skim: Most recent Preqin or Setter Capital secondary market report (link on course site)

12.3 In-Class Outline (75 minutes)

Time Segment Format
0:00–0:05 Recap Session 2: three failures, focus today on Failure 1 evidence Lecture
0:05–0:25 Secondary market structure — who, what, how, why Lecture + diagram
0:25–0:50 The four regimes 2003–2024: empirical walkthrough Lecture + chart deep-dive
0:50–1:05 Level illusion vs. convexity illusion Lecture
1:05–1:15 Implications for portfolio mark-to-market Discussion + Q&A

12.4 Discussion Questions

  1. The 2008 crisis revealed the constant-premium assumption was wrong. Why did it take 17+ years (and counting) for the industry to seriously revisit DCF methodology?
  2. If GP-reported NAVs smooth and lag, is private market “diversification” partly an illusion? How big is the illusion?
  3. The denominator effect (LPs selling secondaries because public market declines push private allocations over limits) is mechanical, not a true liquidity signal. How would you adjust the discount-to-NAV interpretation to account for this?

12.5 Worked Numerical Example

Computing the implied liquidity state from a secondary discount

Setup:

  • Secondary discount: 18%
  • Remaining fund life: 6 years
  • Risk-free rate: 4%, ERP × β = 4%, size = 1%
  • GP-assumed illiquidity premium: 3.5%
  • DCF total rate: 12.5%

Step 1: Implied total discount rate from secondary:

For a perpetuity approximation: \(\text{Discount} \approx 1 - e^{-r \cdot T_\text{eff}}\) where \(T_\text{eff}\) is the duration-weighted hold.

With 6 years, the implied rate \(r_\text{implied}\) satisfies \(0.18 = 1 - e^{-r_\text{implied} \cdot 6}\), giving \(r_\text{implied} \approx 3.3\%\) premium above the DCF rate.

Step 2: Implied excess premium:

Excess above GP-assumed: ~3.3 percentage points. So implied total illiquidity premium = 3.5% + 3.3% = 6.8%, roughly double the GP assumption.

Step 3: Liquidity state inversion:

Using \(\pi(L) = \pi_0 - \pi_1 L + \pi_2 L^2\) with calibrated \(\pi_0 = 0.045\), \(\pi_1 = 0.025\), \(\pi_2 = 0.021\), and current premium 6.8%, solve for \(L\):

\(0.068 = 0.045 - 0.025 L + 0.021 L^2\)

Quadratic in \(L\): \(0.021 L^2 - 0.025 L - 0.023 = 0\)

Solutions: \(L = (0.025 ± \sqrt{0.000625 + 0.001932}) / 0.042 = (0.025 ± 0.0506) / 0.042\)

Taking the negative root (since \(L\) should drop below \(\bar{L}\) when premium rises): \(L \approx -0.61\), or 0.61σ below the long-run mean.

Interpretation: Current secondary market is pricing in a moderate-stress liquidity state. Not crisis (which would be −1.5σ or worse), but not normalization either.

12.6 What to Expect Next Session

Session 4 introduces the Ornstein-Uhlenbeck process that governs the liquidity state \(L_t\) — but at the intuition level only. We’ll cover:

  • What an OU process is (the simplest mean-reverting random process)
  • Why it’s the right model for liquidity dynamics
  • The parameters κ, \(\bar{L}\), σ and what they mean economically
  • How to simulate paths
  • Connection to Vasicek interest rate models (for students who know them)

Session 4 is a deliberate self-diagnostic for track selection. If the OU process feels intuitive and you want more depth, you may be a Track 2 candidate. If you find it manageable but don’t want the proofs, Track 1 is right for you.

Reading: Book Chapter 2, sections 2.8–2.9 (OU calibration and properties).


← Session 2 | Schedule | Next: Session 4 →