8 Midterm Exam Blueprint
The midterm exam is held in Session 10, is identical for both tracks, and is worth 20% of the course grade.
8.1 Format
- Duration: 75 minutes
- Location: [TBD]
- Open/closed: Closed-book, closed-laptop
- Permitted aids: One 8.5×11” double-sided handwritten formula sheet (no typed sheets; no photocopies)
- Calculators: Non-programmable scientific calculators permitted; no phones, no graphing calculators with internet
- Honor code: University standard
8.2 Coverage
The midterm covers Sessions 1–9 (book Chapters 1–5):
| Unit | Sessions | Book Chapters | Weight on Exam |
|---|---|---|---|
| Why DCF Fails | 1–5 | Ch. 1–3 | 50% |
| Measurement & Theory | 6–9 | Ch. 4–5 | 50% |
Specifically out of scope (not on midterm):
- Exit timing and the trapped investor (Ch. 6)
- Portfolio construction (Ch. 7)
- Regulatory implications (Ch. 8)
- GE-LAV platform implementation (Ch. 9)
- All Part 2 math content (Ch. 10–20)
8.3 Topic Weighting
| Topic | Approximate % of exam |
|---|---|
| The three structural failures of DCF | 12% |
| Valuation hierarchy (DCF ⊊ LAV ⊊ GE-LAV) | 8% |
| Secondary market evidence and the liquidity illusion | 10% |
| OU process — intuition, parameters, what it captures | 10% |
| Term structure of private capital returns | 10% |
| IRR — definition, two biases, when it fails | 12% |
| PME — Kaplan-Schoar vs. Long-Nickels vs. Direct Alpha | 8% |
| LA-IRR and LA-PME — what they fix | 8% |
| Jensen convexity bias — intuition and magnitude | 12% |
| Five requirements of a correct valuation theory (Ch. 5) | 10% |
8.4 Question Types
The exam contains four question types:
| Type | Count | Points each | Total |
|---|---|---|---|
| Multiple choice / short answer | 8 | 3 | 24 |
| Quantitative problems | 4 | 9 | 36 |
| Conceptual short essays (200 words) | 2 | 10 | 20 |
| Integrative case analysis | 1 | 20 | 20 |
| Total | 15 | 100 |
8.5 Sample Questions
8.5.1 Sample Multiple Choice (3 points)
Q. The Jensen convexity bias arises because:
- IRR is mathematically equivalent to a constant discount rate
- The expected value of a nonlinear function of liquidity differs from the function evaluated at the expected liquidity
- Secondary market discounts are mean-reverting
- The OU process has fat tails
Correct answer: (b)
8.5.2 Sample Short Answer (3 points)
Q. State the GE-LAV stationary distribution of the liquidity state L under the OU calibration κ = 0.45, σ = 0.32, L̄ = 1.0. Show units.
Expected answer: L_∞ ~ N(L̄, σ²/(2κ)) = N(1.0, 0.1138). Variance is dimensionless; mean is in units of the liquidity index.
8.5.3 Sample Quantitative Problem (9 points)
Q. An infrastructure asset has a 10-year hold horizon. The OU process for its liquidity state is calibrated to κ = 0.30, σ = 0.28, L̄ = 1.00, with current state L_0 = 0.85 (slightly stressed). The DCF risk-free rate is 4.5%, the equity risk premium is 6%, the beta is 0.7, and the constant illiquidity premium assumed by the fund is 3%.
Compute the DCF discount rate. (2 pts)
Estimate the LAV-adjusted discount rate using the linear approximation r_LAV(L) ≈ r_DCF + α·(1 − L). Assume α = 0.04. (3 pts)
Approximately what is the Jensen bias contribution to the LAV vs. DCF valuation gap over a 10-year horizon, using the affine bias formula B(T) = A·T + C, with A = 1.4% per year and C = 0.5%? (2 pts)
Comment briefly on which channel (level vs. convexity) dominates the gap in this case. (2 pts)
Solution sketch: (a) r_DCF = 4.5% + 0.7·6% + 3% = 11.7% (b) r_LAV(0.85) ≈ 11.7% + 0.04·(1 − 0.85) = 11.7% + 0.6% = 12.3% (c) B(10) = 1.4%·10 + 0.5% = 14.5% (d) The Jensen bias (convexity channel, 14.5%) dominates the level adjustment (0.6%). This is typical for long-horizon assets where the OU process has time to generate path-dependent valuation.
8.5.4 Sample Conceptual Essay (10 points)
Q. Explain in 200 words why the standard PME (Public Market Equivalent) methodology systematically misvalues private market performance when liquidity premia vary over time. In your answer, distinguish between Kaplan-Schoar PME and Long-Nickels PME, identify which is more vulnerable to the liquidity illusion, and propose what LA-PME does differently.
Marking guide: - 2 pts: Correctly characterize PME as comparing private-market cash flows against discounted public benchmark cash flows - 2 pts: Identify that PME embeds a constant discount assumption that mirrors the constant-rate DCF problem - 2 pts: Distinguish Kaplan-Schoar (ratio of FVs) from Long-Nickels (ICM with reinvestment) - 2 pts: Argue that Long-Nickels is somewhat more vulnerable because it amplifies timing distortions - 2 pts: Explain that LA-PME uses a stochastic discount path L_t-conditional rather than a constant public-benchmark return
8.5.5 Sample Integrative Case (20 points)
Case: Trapped LP in a 2007-vintage Buyout Fund
An LP in a 2007-vintage US buyout fund holds an interest with NAV of $50M. The fund is approaching year 10 of a 10+2 structure. The GP has indicated they will request an extension; the LP is unsure whether to consent or to exit via the secondary market.
Current observed conditions (Q4 2025):
- Secondary market quote: −15% to NAV (so $42.5M cash today)
- Estimated time to natural liquidation if extension is granted: 2 more years
- Liquidity state L_t (from secondary market spreads): 0.82 (stressed but not crisis)
- OU parameters: κ = 0.40, σ = 0.30, L̄ = 1.0
- Expected residual NAV growth (gross, under GP plan): 6% per year over 2 years
Answer the following:
(6 pts) Using DCF reasoning with a 12% discount rate, what is the LP’s expected present value if they hold to liquidation? Should they accept the −15% secondary offer or hold?
(6 pts) Using the LAV adjustment with α = 0.04 (so r_LAV(0.82) ≈ 12% + 0.04·0.18 = 12.7%), how does your conclusion in (a) change? Show your work.
(4 pts) Identify which channel (level vs. convexity) is doing the most work in shifting your conclusion. Quantify roughly.
(4 pts) Discuss in 1–2 paragraphs what additional GE-LAV considerations (exit boundary, externality, regime dependence) the LP should think about that DCF alone does not capture. You do not need to compute these — just explain why they matter.
8.6 Studying for the Midterm
Best preparation strategy:
Re-read book Chapters 1–5 carefully. The exam tracks the book; if you understand the book, you can pass the exam.
Work all PS1 problems — even ones not yet graded. PS1 is designed to be a study aid for the midterm.
Practice with the sample questions above under exam conditions (75 minutes, closed book, formula sheet only).
Make your formula sheet now, not the night before. The act of compressing the course onto one page is itself a study technique. Recommended formulas to include: OU process equation and stationary distribution; standard DCF and LAV discount rate forms; the affine Jensen bias formula B(T) = A·T + C; PME definitions (Kaplan-Schoar, Long-Nickels); the five requirements from Ch. 5.
Attend Session 9 (Midterm Review). Bring questions.
What NOT to spend time on:
- Memorizing proofs (no proofs on the midterm)
- Memorizing platform UI (platform comes after the midterm)
- Part 2 math content (out of scope)
- Specific calibration numbers from the book (you’ll be given parameters)
8.7 Logistics
- Bring: pencil, pen, eraser, calculator, formula sheet, ID
- Arrive 10 minutes early
- No phones at the desk — power off and stowed
- Bathroom breaks permitted; one at a time
- Submit formula sheet with exam (it does not affect your grade — this is honor-code documentation)