38 Session 29: Split Track — Digital Assets & Climate / Jensen + Pigouvian Proofs
| Unit | 5 — Split Track |
| Track 1 source | Classes 30 (Digital Assets) + 31 (Climate Risk) |
| Track 2 source | Classes 11 (Jensen Bias) + 18 (Welfare) + 20 (Pigouvian Tax) |
38.1 Track 1: Frontier Cases — Digital Assets + Climate
38.1.1 Track 1 Learning Objectives
By the end of this session, Track 1 students will be able to:
- Apply GE-LAV to crypto-adjacent investments (token venture funds, defi protocols, NFT funds).
- Adapt the calibration when secondary market data is thin (or doesn’t exist yet).
- Apply GE-LAV to ultra-long-duration climate-exposed infrastructure (50-100 year assets).
- Decompose climate risk into transition + physical risk channels.
- Identify how GE-LAV’s stochastic-premium framework handles novel risks (climate transition, regulatory uncertainty).
38.1.2 Track 1 Pre-Class Assignment
- Skim: Recent report on crypto fund returns or NFT secondaries (link on course site)
- Skim: Climate-aware infrastructure investing report (Bloomberg NEF or similar)
38.1.3 Track 1 In-Class Outline (75 minutes)
| Time | Segment | Format |
|---|---|---|
| 0:00–0:15 | Digital assets in private markets | Lecture |
| 0:15–0:30 | Applying GE-LAV when secondary data is thin | Lecture |
| 0:30–0:50 | Climate risk and ultra-long-duration assets | Lecture |
| 0:50–1:05 | Lab: value a climate-exposed infrastructure asset | Group work |
| 1:05–1:15 | Synthesis + research frontier discussion | Discussion |
38.2 Track 2: Jensen Bias + Pigouvian Tax + Welfare Derivations
38.2.1 Track 2 Learning Objectives
By the end of this session, Track 2 students will be able to:
- Prove Theorem 18.1 (Jensen convexity bias) — the closed-form formula derivation.
- Prove Theorem 19.1 (constrained Pareto inefficiency) — that decentralized exit decisions are not socially optimal.
- Derive the Pigouvian exit tax as the welfare-maximizing corrective instrument.
- Quantify the welfare gap in the calibrated framework (~2.3%/yr).
- Discuss the regulatory implementation considerations.
38.2.2 Track 2 Pre-Class Assignment
- Read: Book Chapters 18, 19 in full (with proofs)
- Pre-read: Mas-Colell, Whinston, Green, Microeconomic Theory, Chapters 11-13 (externalities and public goods)
38.2.3 Track 2 In-Class Outline (75 minutes)
| Time | Segment | Format |
|---|---|---|
| 0:00–0:10 | Recap: the externality concept | Lecture |
| 0:10–0:30 | Jensen bias theorem and proof | Lecture + board |
| 0:30–0:50 | Welfare gap: quantifying the externality | Lecture |
| 0:50–1:05 | Pigouvian tax derivation | Lecture |
| 1:05–1:15 | Implementation considerations | Discussion |
38.2.4 Track 2 Discussion Questions
- The Pigouvian tax is welfare-maximizing in theory. But it requires the regulator to know the population state \(\mu\) in real time. In practice, this is hard. What’s the welfare cost of using a constant tax rate (e.g., 3%) instead?
- The 2.3%/yr welfare gap aggregates to ~$300B/year. Of this, what fraction would be recovered by an imperfect Pigouvian tax (say, only on transactions during designated stress windows)?
- The Pareto inefficiency theorem assumes LPs are rational. Behavioral biases (loss aversion, herding) would likely amplify the externality. How would the welfare gap change with behavioral agents?