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:
- Describe the structure of the private market secondary market — who trades, why, through which brokers, at what volume.
- Interpret the discount-to-NAV ratio as a market-implied measurement of the aggregate liquidity premium.
- Identify the four regimes of secondary market discounts 2003–2024 and describe what economic conditions characterize each.
- Define the liquidity illusion rigorously: the gap between GP-reported NAV and economic clearing value.
- 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
- 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?
- If GP-reported NAVs smooth and lag, is private market “diversification” partly an illusion? How big is the illusion?
- 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).