11 Session 2: The Three Structural Failures · LA-CAPM
| Unit | 1 — Why DCF Fails |
| Book Chapter | 1 (sections 1.5–1.7) |
| Track | Common core (both tracks) |
11.1 Learning Objectives
By the end of this session, students will be able to:
- State and explain the three structural failures of DCF for private market valuation.
- Articulate Jensen’s inequality at an intuition level — why \(E[f(X)] \neq f(E[X])\) when \(f\) is nonlinear — and apply it to the discount factor \(e^{-rT}\).
- Explain the McKean-Vlasov externality as a collective-action problem in liquidity provision.
- Position GE-LAV within the existing illiquidity premium literature (Amihud-Mendelson, Pastor-Stambaugh, Acharya-Pedersen).
- State the Liquidity-Adjusted CAPM (LA-CAPM) and how it generalizes standard CAPM.
11.2 Pre-Class Assignment
- Read: Book Chapter 1, sections 1.5–1.7 (~15 pages)
- Optional: Acharya & Pedersen (2005), “Asset Pricing with Liquidity Risk,” Journal of Financial Economics — abstract and conclusion only
11.3 In-Class Outline (75 minutes)
| Time | Segment | Format |
|---|---|---|
| 0:00–0:05 | Recap Session 1: scale, DCF, illiquidity premium | Lecture |
| 0:05–0:25 | Failure 1: The premium is stochastic — secondary market evidence | Lecture |
| 0:25–0:45 | Failure 2: Jensen convexity bias from stochastic premia | Lecture + worked numerical example |
| 0:45–1:05 | Failure 3: Liquidity is collectively determined — McKean-Vlasov | Lecture + thought experiment |
| 1:05–1:15 | LA-CAPM — connection to portfolio theory you already know | Lecture + Q&A |
11.4 Discussion Questions
For the last 10 minutes if time permits:
- Which of the three failures do you think most practitioners are aware of? Which are they unaware of? Why?
- The Pastor-Stambaugh (2003) liquidity factor is widely used in factor models. Is it a satisfactory response to the three failures we covered today? What does it miss?
- Suppose you were the regulator overseeing private market fund NAVs. Which of the three failures would you prioritize fixing first? Why?
11.5 Worked Example: Quantifying Each Failure
Setup: A 10-year private equity fund, current NAV $100M.
Failure 1 (stochastic premium): If the OU stationary std is 0.34 and current state is at the long-run mean, the expected premium next year has standard deviation ~3.4%. A constant premium of 3.5% has 0 std. Failure: ignoring 3.4 percentage points of uncertainty.
Failure 2 (Jensen bias): For T = 10 and the calibrated parameters, \(B(10) \approx 1.7\%\). So LAV value ≈ \(101.7M\) vs. DCF \(100M\). Failure: \(1.7M\) systematic undervaluation in DCF.
Failure 3 (McKean-Vlasov): In normal markets, GE-LAV equilibrium rate exceeds DCF assumed rate by ~1%, so GE-LAV value ≈ \(98M\). In GFC depth, equilibrium rate is 32.3% vs. DCF 7.5% → GE-LAV value ≈ \(30M\).
Walk through: “Are the corrections all in the same direction? Sometimes (Failure 2 always positive). Sometimes they offset (Failure 2 positive, Failure 3 can be negative in crisis). GE-LAV handles them simultaneously and correctly.”
11.6 What to Expect Next Session
Session 3 dives deep into Failure 1: the secondary market evidence. We’ll examine the data carefully — what the secondary market quotes mean, who participates, the four regimes (2003–2007 boom, 2008–2010 GFC, 2011–2019 normalization, 2020–present multi-shock era), and what the discount-to-NAV ratio actually measures. This is the empirical session of Unit 1.
Reading: Book Chapter 2, all sections (~30 pages). Pay particular attention to sections 2.3–2.6.