37  Session 28: Split Track — Private Credit Case / GE Equilibrium Existence

Unit 5 — Split Track
Track 1 source Class 23 (Private Credit Spread Decomposition)
Track 2 source Class 17 (GE Market Clearing)

37.1 Track 1: Private Credit Case Workshop

37.1.1 Track 1 Learning Objectives

By the end of this session, Track 1 students will be able to:

  1. Apply GE-LAV to a private credit / direct lending position.
  2. Decompose private credit spreads into credit risk, illiquidity premium, and complexity premium components.
  3. Distinguish GE-LAV for credit vs. equity strategies (cash flow profile, default risk interaction).
  4. Compute liquidity-adjusted spread expectations for a direct lending strategy.
  5. Evaluate a real BDC (business development company) or middle-market direct lending fund.

37.1.2 Track 1 Pre-Class Assignment

  • Read: Recent BDC quarterly report or direct lending fund presentation
  • Watch: 10-min video on private credit market structure (link on course site)

37.1.3 Track 1 In-Class Outline (75 minutes)

Time Segment Format
0:00–0:10 Private credit vs. PE: structural differences Lecture
0:10–0:30 Decomposing private credit spreads Lecture + worked example
0:30–0:55 Lab: value a BDC or middle-market direct lending position Group work
0:55–1:15 Group recommendations + risk implications Presentations

37.2 Track 2: GE Equilibrium Existence Proof

37.2.1 Track 2 Learning Objectives

By the end of this session, Track 2 students will be able to:

  1. State and prove the existence of GE-LAV competitive equilibrium (Theorem 17.4).
  2. Apply Schauder’s fixed-point theorem to the market-clearing map.
  3. Identify the market clearing condition mathematically: aggregate supply = aggregate demand for liquidity.
  4. Distinguish partial equilibrium (LAV) from general equilibrium (GE-LAV) at the level of the underlying math.
  5. Connect the existence proof to the calibrated parameter regime where uniqueness holds.

37.2.2 Track 2 Pre-Class Assignment

  • Read: Book Chapter 17 in full (with all proofs)
  • Pre-read: Mas-Colell, The Theory of General Economic Equilibrium, Chapters 4-5

37.2.3 Track 2 In-Class Outline (75 minutes)

Time Segment Format
0:00–0:10 Recap: from MFG to GE Lecture
0:10–0:30 The GE-LAV equilibrium definition Lecture
0:30–0:50 Existence proof via Schauder Lecture + board
0:50–1:05 Uniqueness under stability Lecture
1:05–1:15 Numerical verification Discussion

37.2.4 Track 2 Discussion Questions

  1. The existence proof requires that \(\Psi\) is continuous on \(\mathcal{M}\). What kind of discontinuity could break this? When would discontinuity be economically realistic (e.g., regulatory thresholds, IPS triggers)?
  2. Under the stability condition \(\kappa > \gamma \cdot \text{Lip}(\phi)\), uniqueness holds. If the condition fails temporarily during a stress event but is restored as conditions normalize, what does the system look like during the failure period?
  3. The market clearing condition treats sellers and buyers symmetrically. In real markets, intermediaries (brokers) take spread. How would the proof change if we added market makers?

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