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6 questions · 1 formulas

Coefficient of variation

CV = σ / E[R]

Panel DataD–A levelNormal priority

You want to estimate a panel data regression model. Your key variable of interest is time-invariant. Therefore, you should estimate a_______

→ B) Random effects model

Old Exam — Oct 2023, Q17

Given: Time-invariant key regressor: fixed effects wipes it out; random effects can estimate its coefficient.

A) Fixed effects model
B) Random effects model
C) A fixed effects (FE) model because time-invariant variables are not eliminated with FE model.

A time-invariant regressor has no within-person variation and is eliminated by FE. To estimate its coefficient, use RE (subject to RE assumptions) -> B.

Rule: Time-invariant variable -> FE cannot estimate its coefficient. Small Hausman p-value -> reject RE, prefer FE.

Scenario RiskD–A levelVery high priority

Investment I: scenarios Optimistic 15%(20%), Most likely 10%(60%), Pessimistic 5%(20%). Investment II: Optimistic 20%(20%), Most likely 15%(60%), Pessimistic 5%(20%). Using the Coefficient of Variation (CV = σ/E[IRR]), which investment has less risk per unit of expected return?

→ A) Investment I (CV=0.316) is lower risk per unit of return than Investment II (CV=0.350)

Computer Lab 1 — Exercise 3 Problem 2

A) Investment I (CV=0.316) is lower risk per unit of return than Investment II (CV=0.350)
B) Investment II is lower risk per unit of return because it has a lower standard deviation
C) Both investments have identical CV
D) Investment II is better because its expected IRR (14%) is higher

E[IRR]_I=10%, σ_I=3.16%, CV_I=0.316. E[IRR]_II=14%, σ_II=4.90%, CV_II=0.350. Lower CV means less risk per unit of expected return, so Investment I has the better risk-adjusted profile by this measure, even though II has a higher expected IRR.

Rule: Coefficient of Variation (σ/E[R]) measures risk per unit of expected return; lower CV means better reward-to-risk (though this does not mean universally 'better').

Regression BasicsE-levelVery high priority

In a market-model regression of a stock's return on the market return, what does R² represent, as distinct from beta?

→ A) R² measures the proportion of the stock's return variation explained by the market, while beta is the slope coefficient (market sensitivity)

Computer Lab 3 — Exercise 2, important distinction

A) R² measures the proportion of the stock's return variation explained by the market, while beta is the slope coefficient (market sensitivity)
B) R² and beta measure exactly the same thing and can be used interchangeably
C) R² is the stock's total risk, while beta is its unsystematic (idiosyncratic) risk
D) R² is always equal to beta squared

Beta is the regression slope, quantifying how much the stock return moves per unit of market return. R² is the goodness-of-fit measure, indicating what fraction of the stock's return variance is explained by the market factor — two conceptually distinct statistics.

Rule: Beta = sensitivity to the market (slope); R² = how much of the variance is explained by that market relationship (fit quality). A high beta does not imply a high R², and vice versa.

Scenario RiskD–A levelVery high priority

When comparing two risky investments using scenario analysis, which tool is the STRONGEST way to rank them if one investment's payoff is at least as high in every single scenario?

→ A) Direct scenario-by-scenario (state-by-state) comparison / first-order stochastic dominance — it requires no assumption about risk preference

Computer Lab 3 — Problem 2 recap

A) Direct scenario-by-scenario (state-by-state) comparison / first-order stochastic dominance — it requires no assumption about risk preference
B) The coefficient of variation (σ/E[R]), since it always gives the definitive ranking
C) Standard deviation alone, since lower risk always wins
D) Expected return alone, since higher return always wins

If an investment's payoff is ≥ in every scenario (state-by-state), it dominates regardless of any risk-preference assumption — this is a stronger and more general conclusion than CV, σ, or E[R] comparisons alone, each of which implicitly assumes something about risk tolerance or ignores risk entirely.

Rule: State-by-state (first-order stochastic) dominance, when it exists, is the strongest possible ranking tool because it holds for all risk preferences.

Regression BasicsE-levelVery high priority

Model 1 estimates TestScore = 698.933 − 2.280 × STR. How should the STR coefficient be interpreted?

→ A) A one-unit increase in STR is associated with about a 2.28-point decrease in expected test score

Computer Lab 4 — Exercise 2, Task 6 (Model 1)

A) A one-unit increase in STR is associated with about a 2.28-point decrease in expected test score
B) A one-unit increase in STR causes exactly a 2.28-point decrease in every school's test score
C) A 2.28% increase in STR decreases test scores by one point
D) STR explains 2.28% of the variation in test scores

The coefficient -2.280 means expected test score falls by about 2.28 points per one-unit increase in STR, as an average association, not a guaranteed effect for every unit, and not a causal claim without further assumptions.

Rule: Interpret OLS slopes as changes in expected/average outcome, not as a guarantee for each individual observation.

Logs & DummiesE-levelNormal priority

In ln(PRICE) = 4.8918 + 0.9284·ln(SQFT) + ..., how should the coefficient on ln(SQFT) be interpreted?

→ A) A 1% increase in SQFT is associated with about a 0.93% increase in PRICE, holding other variables constant

Computer Lab 5 — Exercise 4, Log-log

A) A 1% increase in SQFT is associated with about a 0.93% increase in PRICE, holding other variables constant
B) A 1-unit increase in SQFT increases PRICE by 0.9284 dollars
C) A 1% increase in SQFT increases PRICE by 92.84 dollars
D) SQFT explains 92.84% of variation in PRICE

In a log-log model, the coefficient on ln(X) is an elasticity: a 1% change in X is associated with approximately a b% change in Y, here about 0.93%.

Rule: ln(Y) = ... + b·ln(X) ⇒ coefficient b is an elasticity (percent change in Y per 1% change in X).