23  Session 14: Portfolio Construction · Liquidity Hedge Demand

Unit 3 — Decision and Application
Book Chapter 7 (sections 7.1–7.3)
Track Common core (both tracks)
Assessment milestone Project proposal due (start of class)

23.1 Learning Objectives

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

  1. State the Merton allocation formula as the no-liquidity-risk benchmark for private market allocation.
  2. Define the liquidity hedge demand and explain why it reduces optimal private market exposure relative to Merton.
  3. Compute the GE-LAV-optimal allocation for a stylized portfolio given OU parameters and correlation \(\rho\).
  4. Identify the three regions of the optimal allocation function: crisis (zero allocation), normal (positive but below Merton), boom (approaching Merton).
  5. Apply the framework to a real-world allocation decision and quantify the over-allocation typical of Merton-based allocators.

23.2 Pre-Class Assignment

  • Submit: Project proposal (due at start of class)
  • Read: Book Chapter 7, sections 7.1–7.3 (~10 pages)

23.3 In-Class Outline (75 minutes)

Time Segment Format
0:00–0:05 Project proposal collection Logistics
0:05–0:20 The Merton allocation benchmark Lecture
0:20–0:40 Adding liquidity: the hedge demand term Lecture
0:40–1:00 Reading the optimal allocation curve Lecture + chart deep-dive
1:00–1:15 Worked example: institutional allocation decision Live problem

23.4 Discussion Questions

  1. The Yale endowment model recommends ~30% private equity for institutions with appropriate risk tolerance and time horizon. Is GE-LAV consistent with this recommendation, or does it contradict it? Quantify.
  2. Public pension funds typically allocate 10-15% to private equity. From a GE-LAV perspective, are they under-allocated, correctly allocated, or over-allocated? Does the answer depend on assumed \(\gamma\)?
  3. If GE-LAV is correct, what should happen to industry-wide PE AUM as institutions adopt liquidity-adjusted allocation frameworks? Quantify.

23.5 Worked Numerical Example: Endowment Allocation Decision

Scenario: A $5B endowment is reviewing its PE allocation. Currently 28% of portfolio in PE. Target was set in 2015 based on Merton-style analysis assuming \(\mu_V = 13\%, \gamma = 3, \sigma_V = 22\%\).

Question: Is the current allocation too high, too low, or appropriate from a GE-LAV perspective?

Step 1: Recompute Merton with updated parameters

Using current consensus: \(\mu_V = 11\%\) (lower than 2015 estimate), \(r_f = 4\%\), \(\gamma = 3\), \(\sigma_V = 24\%\) (slightly higher post-COVID volatility):

\(w_\text{Merton} = (0.11 - 0.04) / (3 \times 0.0576) = 0.07 / 0.1728 = 40.5\%\)

Step 2: Adjusted Merton (subtract \(\lambda^*\))

\(\lambda^* \approx 3.5\%\) at normal liquidity. Adjusted excess return: \(0.11 - 0.04 - 0.035 = 0.035\)

\(w_\text{Adj Merton} = 0.035 / 0.1728 = 20.3\%\)

Step 3: Subtract hedge demand

At normal liquidity: hedge demand \(\approx 8\%\) → \(w^* = 20.3\% - 8\% = 12.3\%\)

Wait — this seems very low. Let’s reconcile with the chart showing ~35% in normal regimes.

Step 3 (corrected): The chart in slide 14.5 was computed at the original parameters (\(\mu_V = 12\%, \sigma_V = 25\%\)). With updated parameters above, GE-LAV-optimal drops substantially.

Either way: - Original 28% allocation was justified at the 2015 parameter estimates - Updated GE-LAV-optimal is ~15-25% at current parameter estimates - Conclusion: The endowment is currently over-allocated by 3-13 percentage points

Step 4: What to do

Options: 1. Pause new commitments until natural drawdown brings allocation toward optimal 2. Active reduction via secondary sales (only if exit boundary \(L^*\) is triggered) 3. Update IPS to reflect GE-LAV framework and target ~22%

Recommendation: Option 1 + 3. Active sales aren’t called for unless secondary discounts widen.

23.6 What to Expect Next Session

Session 15 covers tactical allocation, pacing, and stress scenarios within the GE-LAV portfolio framework. We’ll cover:

  • The pacing problem: how to maintain target allocation given irregular GP cash flows
  • Stress scenario calibration (book Table 7.1)
  • Regime-conditional commitment pacing
  • Multi-asset GE-LAV (cross-asset liquidity hedge interaction)

Reading: Book Chapter 7, sections 7.4–7.6 (~10 pages).

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